Skip to contents

Prediction of ODT for an input matrix or data frame.

Usage

# S3 method for class 'ODT'
predict(
  object,
  Xnew,
  Xsplit = NULL,
  type = c("pred", "leafnode", "prob")[1],
  ...
)

Arguments

object

An object of class ODT, the same as that created by the function ODT.

Xnew

An n by d numeric matrix (preferable) or data frame. The rows correspond to observations and columns correspond to features. Note that if there are NA values in the data 'Xnew', which will be replaced with the average value.

Xsplit

Splitting variables used to construct linear model trees. The default value is NULL and is only valid when split="linear".

type

Type of prediction required. Choosing "pred" (default) gives the prediction result, and choosing "leafnode" gives the leaf node sequence number that Xnew is partitioned into. For classification tasks, including classification trees (split= "gini" or "entropy") and linear classification models (split= "linear" and glmnetParList= list(family="binomial" or "multinomial")). Setting type="prob" gives the prediction probabilities.

...

Arguments to be passed to methods.

Value

A vector of the following:

  • pred: the prediced response of the new data.

  • leafnode: the leaf node sequence number that the new data is partitioned.

  • prob: the prediction probabilities for classification tasks.

References

Zhan, H., Liu, Y., & Xia, Y. (2022). Consistency of The Oblique Decision Tree and Its Random Forest. arXiv preprint arXiv:2211.12653.

See also

Examples

# Classification with Oblique Decision Tree.
data(seeds)
set.seed(221212)
train <- sample(1:209, 100)
train_data <- data.frame(seeds[train, ])
test_data <- data.frame(seeds[-train, ])
tree <- ODT(varieties_of_wheat ~ ., train_data, split = "entropy")
pred <- predict(tree, test_data[, -8])
# classification error
(mean(pred != test_data[, 8]))
#> [1] 0.09174312
(prob=predict(tree, test_data[, -8],type = "prob"))
#>                 1          2         3
#>   [1,] 0.95121951 0.04878049 0.0000000
#>   [2,] 0.95121951 0.04878049 0.0000000
#>   [3,] 0.00000000 1.00000000 0.0000000
#>   [4,] 0.95121951 0.04878049 0.0000000
#>   [5,] 0.95121951 0.04878049 0.0000000
#>   [6,] 0.00000000 1.00000000 0.0000000
#>   [7,] 0.05882353 0.00000000 0.9411765
#>   [8,] 0.95121951 0.04878049 0.0000000
#>   [9,] 0.95121951 0.04878049 0.0000000
#>  [10,] 0.95121951 0.04878049 0.0000000
#>  [11,] 0.95121951 0.04878049 0.0000000
#>  [12,] 0.95121951 0.04878049 0.0000000
#>  [13,] 0.95121951 0.04878049 0.0000000
#>  [14,] 0.95121951 0.04878049 0.0000000
#>  [15,] 0.95121951 0.04878049 0.0000000
#>  [16,] 0.00000000 1.00000000 0.0000000
#>  [17,] 0.00000000 1.00000000 0.0000000
#>  [18,] 0.00000000 1.00000000 0.0000000
#>  [19,] 0.00000000 1.00000000 0.0000000
#>  [20,] 0.00000000 1.00000000 0.0000000
#>  [21,] 0.00000000 1.00000000 0.0000000
#>  [22,] 0.00000000 1.00000000 0.0000000
#>  [23,] 0.95121951 0.04878049 0.0000000
#>  [24,] 0.00000000 1.00000000 0.0000000
#>  [25,] 0.00000000 1.00000000 0.0000000
#>  [26,] 0.00000000 1.00000000 0.0000000
#>  [27,] 0.00000000 1.00000000 0.0000000
#>  [28,] 0.00000000 1.00000000 0.0000000
#>  [29,] 0.00000000 1.00000000 0.0000000
#>  [30,] 0.00000000 1.00000000 0.0000000
#>  [31,] 0.00000000 1.00000000 0.0000000
#>  [32,] 0.00000000 1.00000000 0.0000000
#>  [33,] 0.00000000 1.00000000 0.0000000
#>  [34,] 0.00000000 1.00000000 0.0000000
#>  [35,] 0.95121951 0.04878049 0.0000000
#>  [36,] 0.00000000 1.00000000 0.0000000
#>  [37,] 0.95121951 0.04878049 0.0000000
#>  [38,] 0.00000000 1.00000000 0.0000000
#>  [39,] 0.95121951 0.04878049 0.0000000
#>  [40,] 0.00000000 1.00000000 0.0000000
#>  [41,] 0.00000000 1.00000000 0.0000000
#>  [42,] 0.00000000 1.00000000 0.0000000
#>  [43,] 0.00000000 1.00000000 0.0000000
#>  [44,] 0.00000000 1.00000000 0.0000000
#>  [45,] 0.00000000 1.00000000 0.0000000
#>  [46,] 0.00000000 1.00000000 0.0000000
#>  [47,] 0.00000000 1.00000000 0.0000000
#>  [48,] 0.00000000 1.00000000 0.0000000
#>  [49,] 0.00000000 1.00000000 0.0000000
#>  [50,] 0.05882353 0.00000000 0.9411765
#>  [51,] 0.05882353 0.00000000 0.9411765
#>  [52,] 0.05882353 0.00000000 0.9411765
#>  [53,] 0.05882353 0.00000000 0.9411765
#>  [54,] 0.05882353 0.00000000 0.9411765
#>  [55,] 0.05882353 0.00000000 0.9411765
#>  [56,] 0.05882353 0.00000000 0.9411765
#>  [57,] 0.05882353 0.00000000 0.9411765
#>  [58,] 0.05882353 0.00000000 0.9411765
#>  [59,] 0.05882353 0.00000000 0.9411765
#>  [60,] 0.05882353 0.00000000 0.9411765
#>  [61,] 0.05882353 0.00000000 0.9411765
#>  [62,] 0.05882353 0.00000000 0.9411765
#>  [63,] 0.05882353 0.00000000 0.9411765
#>  [64,] 0.05882353 0.00000000 0.9411765
#>  [65,] 0.05882353 0.00000000 0.9411765
#>  [66,] 0.05882353 0.00000000 0.9411765
#>  [67,] 0.05882353 0.00000000 0.9411765
#>  [68,] 0.05882353 0.00000000 0.9411765
#>  [69,] 0.05882353 0.00000000 0.9411765
#>  [70,] 0.05882353 0.00000000 0.9411765
#>  [71,] 0.05882353 0.00000000 0.9411765
#>  [72,] 0.05882353 0.00000000 0.9411765
#>  [73,] 0.05882353 0.00000000 0.9411765
#>  [74,] 0.05882353 0.00000000 0.9411765
#>  [75,] 0.05882353 0.00000000 0.9411765
#>  [76,] 0.05882353 0.00000000 0.9411765
#>  [77,] 0.05882353 0.00000000 0.9411765
#>  [78,] 0.05882353 0.00000000 0.9411765
#>  [79,] 0.05882353 0.00000000 0.9411765
#>  [80,] 0.05882353 0.00000000 0.9411765
#>  [81,] 0.95121951 0.04878049 0.0000000
#>  [82,] 0.95121951 0.04878049 0.0000000
#>  [83,] 0.95121951 0.04878049 0.0000000
#>  [84,] 0.95121951 0.04878049 0.0000000
#>  [85,] 0.05882353 0.00000000 0.9411765
#>  [86,] 0.95121951 0.04878049 0.0000000
#>  [87,] 0.95121951 0.04878049 0.0000000
#>  [88,] 0.95121951 0.04878049 0.0000000
#>  [89,] 0.95121951 0.04878049 0.0000000
#>  [90,] 0.95121951 0.04878049 0.0000000
#>  [91,] 0.95121951 0.04878049 0.0000000
#>  [92,] 0.95121951 0.04878049 0.0000000
#>  [93,] 0.95121951 0.04878049 0.0000000
#>  [94,] 0.00000000 1.00000000 0.0000000
#>  [95,] 0.00000000 1.00000000 0.0000000
#>  [96,] 0.00000000 1.00000000 0.0000000
#>  [97,] 0.00000000 1.00000000 0.0000000
#>  [98,] 0.00000000 1.00000000 0.0000000
#>  [99,] 0.95121951 0.04878049 0.0000000
#> [100,] 0.00000000 1.00000000 0.0000000
#> [101,] 0.00000000 1.00000000 0.0000000
#> [102,] 0.05882353 0.00000000 0.9411765
#> [103,] 0.05882353 0.00000000 0.9411765
#> [104,] 0.05882353 0.00000000 0.9411765
#> [105,] 0.05882353 0.00000000 0.9411765
#> [106,] 0.05882353 0.00000000 0.9411765
#> [107,] 0.05882353 0.00000000 0.9411765
#> [108,] 0.05882353 0.00000000 0.9411765
#> [109,] 0.05882353 0.00000000 0.9411765

# Regression with Oblique Decision Tree.
data(body_fat)
set.seed(221212)
train <- sample(1:252, 100)
train_data <- data.frame(body_fat[train, ])
test_data <- data.frame(body_fat[-train, ])
tree <- ODT(Density ~ ., train_data, split = "mse")
pred <- predict(tree, test_data[, -1])
# estimation error
mean((pred - test_data[, 1])^2)
#> [1] 3.513866e-05

# Use "Z" as the splitting variable to build a linear model tree for "X" and "y".
set.seed(1)
n = 200
p = 10
q = 5
X = matrix(rnorm(n*p), n, p)
Z = matrix(rnorm(n*q), n, q)
y = (Z[,1] > 1)*(X[,1] - X[,2] + 2)  +
(Z[,1] < 1)*(Z[,2] > 0)*(X[,1] + X[,2] + 0) +
(Z[,1] < 1)*(Z[,2] < 0)*(X[,3] - 2)
my.tree <- ODT(X=X, y=y, Xsplit=Z, split = "linear",
               NodeRotateFun = "RotMatRF",MinLeaf = 10, MaxDepth = 5,
               glmnetParList=list(lambda = 0.1,family = "gaussian"))
(leafnode <- predict(my.tree, X, Xsplit=Z, type="leafnode"))
#>   [1] 5 5 3 4 4 5 4 4 4 4 4 4 5 4 5 3 4 4 4 3 5 4 4 5 3 4 4 5 4 5 5 4 4 4 3 3 3
#>  [38] 4 4 3 4 5 5 4 5 3 5 3 4 4 3 4 4 4 4 4 4 5 5 5 3 4 5 5 5 5 5 4 4 5 3 4 4 4
#>  [75] 5 3 4 4 5 3 5 5 5 5 4 4 5 5 5 4 4 4 4 5 4 5 3 4 5 5 4 5 3 3 5 5 3 4 4 5 5
#> [112] 3 3 5 5 5 3 5 4 5 4 4 3 4 3 4 5 5 5 3 5 5 5 5 3 4 5 5 4 4 5 5 3 4 4 5 3 5
#> [149] 5 5 5 3 4 3 5 5 4 5 4 5 4 4 5 3 4 5 3 5 3 5 3 4 5 3 4 5 4 3 5 5 4 4 4 5 4
#> [186] 5 5 5 4 5 3 3 5 4 4 3 3 5 4 3

y1 = (y>0)*1
my.tree <- ODT(X=X, y=y1, Xsplit=Z, split = "linear",
               NodeRotateFun = "RotMatRF",MinLeaf = 10, MaxDepth = 5,
               glmnetParList=list(family = "binomial"))
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
(class <- predict(my.tree, X, Xsplit=Z, type="pred"))
#>   [1] "0" "1" "0" "0" "0" "1" "0" "0" "0" "0" "0" "0" "0" "0" "1" "1" "0" "0"
#>  [19] "0" "1" "0" "0" "0" "0" "1" "0" "0" "0" "0" "1" "1" "0" "0" "0" "1" "1"
#>  [37] "1" "0" "0" "1" "0" "1" "1" "0" "1" "1" "0" "1" "0" "0" "1" "0" "0" "0"
#>  [55] "0" "0" "0" "0" "1" "0" "1" "0" "1" "1" "1" "1" "0" "0" "0" "1" "1" "0"
#>  [73] "0" "0" "0" "1" "0" "0" "0" "1" "0" "0" "1" "0" "1" "1" "1" "1" "1" "0"
#>  [91] "0" "1" "0" "0" "1" "1" "1" "0" "0" "0" "0" "0" "0" "1" "1" "1" "1" "0"
#> [109] "0" "1" "1" "1" "1" "0" "0" "1" "1" "0" "0" "1" "0" "0" "1" "0" "1" "0"
#> [127] "0" "1" "0" "1" "0" "0" "1" "0" "1" "0" "1" "0" "0" "0" "0" "1" "1" "0"
#> [145] "0" "0" "1" "0" "0" "1" "1" "1" "0" "1" "1" "0" "0" "0" "0" "1" "0" "0"
#> [163] "1" "1" "0" "1" "1" "0" "1" "0" "1" "0" "0" "1" "0" "0" "0" "1" "1" "1"
#> [181] "0" "0" "0" "0" "0" "0" "0" "0" "0" "0" "1" "1" "1" "0" "0" "1" "1" "0"
#> [199] "0" "1"
(prob <- predict(my.tree, X, Xsplit=Z, type="prob"))
#>                   0            1
#>   [1,] 7.361984e-01 2.638016e-01
#>   [2,] 5.614501e-03 9.943855e-01
#>   [3,] 5.809401e-01 4.190599e-01
#>   [4,] 9.952352e-01 4.764753e-03
#>   [5,] 9.954732e-01 4.526754e-03
#>   [6,] 6.607188e-03 9.933928e-01
#>   [7,] 9.949961e-01 5.003895e-03
#>   [8,] 9.942252e-01 5.774821e-03
#>   [9,] 8.348773e-01 1.651227e-01
#>  [10,] 9.974380e-01 2.561992e-03
#>  [11,] 9.952092e-01 4.790824e-03
#>  [12,] 9.616973e-01 3.830274e-02
#>  [13,] 9.461532e-01 5.384682e-02
#>  [14,] 9.977972e-01 2.202804e-03
#>  [15,] 2.587238e-03 9.974128e-01
#>  [16,] 4.667517e-02 9.533248e-01
#>  [17,] 9.228440e-01 7.715601e-02
#>  [18,] 9.936824e-01 6.317612e-03
#>  [19,] 9.994198e-01 5.801747e-04
#>  [20,] 3.313809e-02 9.668619e-01
#>  [21,] 9.306931e-01 6.930693e-02
#>  [22,] 9.975037e-01 2.496263e-03
#>  [23,] 9.908083e-01 9.191700e-03
#>  [24,] 9.991579e-01 8.420794e-04
#>  [25,] 2.685172e-03 9.973148e-01
#>  [26,] 7.814873e-01 2.185127e-01
#>  [27,] 9.996191e-01 3.809421e-04
#>  [28,] 9.998866e-01 1.134419e-04
#>  [29,] 9.971283e-01 2.871722e-03
#>  [30,] 1.470187e-01 8.529813e-01
#>  [31,] 2.621479e-01 7.378521e-01
#>  [32,] 9.715553e-01 2.844471e-02
#>  [33,] 9.995281e-01 4.718828e-04
#>  [34,] 9.900370e-01 9.963029e-03
#>  [35,] 2.618100e-01 7.381900e-01
#>  [36,] 1.567081e-02 9.843292e-01
#>  [37,] 4.162082e-02 9.583792e-01
#>  [38,] 9.900513e-01 9.948671e-03
#>  [39,] 9.971657e-01 2.834272e-03
#>  [40,] 8.229623e-02 9.177038e-01
#>  [41,] 9.956316e-01 4.368444e-03
#>  [42,] 7.923239e-02 9.207676e-01
#>  [43,] 6.536988e-02 9.346301e-01
#>  [44,] 9.435624e-01 5.643756e-02
#>  [45,] 2.378245e-01 7.621755e-01
#>  [46,] 9.825755e-03 9.901742e-01
#>  [47,] 7.023141e-01 2.976859e-01
#>  [48,] 1.374405e-02 9.862559e-01
#>  [49,] 9.831646e-01 1.683540e-02
#>  [50,] 9.999090e-01 9.097536e-05
#>  [51,] 2.367199e-02 9.763280e-01
#>  [52,] 9.969065e-01 3.093521e-03
#>  [53,] 9.977097e-01 2.290329e-03
#>  [54,] 9.995504e-01 4.496194e-04
#>  [55,] 9.994473e-01 5.527075e-04
#>  [56,] 9.882691e-01 1.173091e-02
#>  [57,] 9.710798e-01 2.892020e-02
#>  [58,] 8.149363e-01 1.850637e-01
#>  [59,] 8.053859e-02 9.194614e-01
#>  [60,] 8.684725e-01 1.315275e-01
#>  [61,] 7.261438e-03 9.927386e-01
#>  [62,] 5.377990e-01 4.622010e-01
#>  [63,] 2.920704e-01 7.079296e-01
#>  [64,] 6.921289e-02 9.307871e-01
#>  [65,] 4.492427e-02 9.550757e-01
#>  [66,] 2.168222e-01 7.831778e-01
#>  [67,] 9.982178e-01 1.782170e-03
#>  [68,] 9.634895e-01 3.651046e-02
#>  [69,] 8.238482e-01 1.761518e-01
#>  [70,] 3.127447e-02 9.687255e-01
#>  [71,] 8.345488e-03 9.916545e-01
#>  [72,] 9.996046e-01 3.954405e-04
#>  [73,] 9.915972e-01 8.402791e-03
#>  [74,] 9.747391e-01 2.526090e-02
#>  [75,] 9.708486e-01 2.915137e-02
#>  [76,] 1.557076e-02 9.844292e-01
#>  [77,] 9.782946e-01 2.170541e-02
#>  [78,] 9.832753e-01 1.672472e-02
#>  [79,] 9.772084e-01 2.279165e-02
#>  [80,] 9.944429e-02 9.005557e-01
#>  [81,] 6.477719e-01 3.522281e-01
#>  [82,] 8.444649e-01 1.555351e-01
#>  [83,] 8.834760e-04 9.991165e-01
#>  [84,] 9.986516e-01 1.348395e-03
#>  [85,] 4.441043e-01 5.558957e-01
#>  [86,] 3.966614e-01 6.033386e-01
#>  [87,] 2.932546e-01 7.067454e-01
#>  [88,] 1.402287e-01 8.597713e-01
#>  [89,] 1.033928e-01 8.966072e-01
#>  [90,] 9.707759e-01 2.922408e-02
#>  [91,] 9.988449e-01 1.155075e-03
#>  [92,] 4.773340e-01 5.226660e-01
#>  [93,] 9.982498e-01 1.750178e-03
#>  [94,] 9.230684e-01 7.693160e-02
#>  [95,] 3.960538e-02 9.603946e-01
#>  [96,] 1.075109e-01 8.924891e-01
#>  [97,] 4.292088e-01 5.707912e-01
#>  [98,] 9.988825e-01 1.117467e-03
#>  [99,] 9.741490e-01 2.585100e-02
#> [100,] 9.060536e-01 9.394636e-02
#> [101,] 9.877650e-01 1.223497e-02
#> [102,] 9.431436e-01 5.685640e-02
#> [103,] 7.016110e-01 2.983890e-01
#> [104,] 4.629971e-02 9.537003e-01
#> [105,] 5.768612e-02 9.423139e-01
#> [106,] 8.766523e-05 9.999123e-01
#> [107,] 3.217938e-02 9.678206e-01
#> [108,] 9.936626e-01 6.337446e-03
#> [109,] 8.997076e-01 1.002924e-01
#> [110,] 3.710176e-03 9.962898e-01
#> [111,] 2.318858e-01 7.681142e-01
#> [112,] 1.620768e-02 9.837923e-01
#> [113,] 5.783552e-03 9.942164e-01
#> [114,] 9.830564e-01 1.694358e-02
#> [115,] 6.516742e-01 3.483258e-01
#> [116,] 1.357144e-01 8.642856e-01
#> [117,] 1.862108e-02 9.813789e-01
#> [118,] 8.055981e-01 1.944019e-01
#> [119,] 9.949898e-01 5.010219e-03
#> [120,] 3.077004e-01 6.922996e-01
#> [121,] 9.976364e-01 2.363621e-03
#> [122,] 9.812554e-01 1.874458e-02
#> [123,] 5.815020e-02 9.418498e-01
#> [124,] 9.841056e-01 1.589444e-02
#> [125,] 6.198875e-02 9.380113e-01
#> [126,] 9.996539e-01 3.461128e-04
#> [127,] 8.058943e-01 1.941057e-01
#> [128,] 3.728543e-01 6.271457e-01
#> [129,] 9.885991e-01 1.140090e-02
#> [130,] 1.421219e-01 8.578781e-01
#> [131,] 7.585505e-01 2.414495e-01
#> [132,] 9.982655e-01 1.734520e-03
#> [133,] 3.094094e-01 6.905906e-01
#> [134,] 6.282343e-01 3.717657e-01
#> [135,] 3.204202e-02 9.679580e-01
#> [136,] 9.977859e-01 2.214072e-03
#> [137,] 1.475878e-01 8.524122e-01
#> [138,] 8.341364e-01 1.658636e-01
#> [139,] 9.652878e-01 3.471215e-02
#> [140,] 9.943559e-01 5.644062e-03
#> [141,] 9.751336e-01 2.486637e-02
#> [142,] 4.791231e-01 5.208769e-01
#> [143,] 1.154605e-01 8.845395e-01
#> [144,] 9.891247e-01 1.087532e-02
#> [145,] 8.665846e-01 1.334154e-01
#> [146,] 9.981867e-01 1.813264e-03
#> [147,] 3.786805e-02 9.621319e-01
#> [148,] 6.448327e-01 3.551673e-01
#> [149,] 8.328005e-01 1.671995e-01
#> [150,] 3.337966e-01 6.662034e-01
#> [151,] 3.414607e-03 9.965854e-01
#> [152,] 2.562229e-02 9.743777e-01
#> [153,] 9.989055e-01 1.094479e-03
#> [154,] 1.443614e-02 9.855639e-01
#> [155,] 4.717371e-01 5.282629e-01
#> [156,] 8.105132e-01 1.894868e-01
#> [157,] 9.999070e-01 9.303201e-05
#> [158,] 9.101187e-01 8.988126e-02
#> [159,] 9.961887e-01 3.811251e-03
#> [160,] 8.743745e-03 9.912563e-01
#> [161,] 9.991032e-01 8.967719e-04
#> [162,] 9.899880e-01 1.001200e-02
#> [163,] 2.494082e-01 7.505918e-01
#> [164,] 1.756523e-02 9.824348e-01
#> [165,] 9.969209e-01 3.079139e-03
#> [166,] 2.411388e-04 9.997589e-01
#> [167,] 2.826215e-01 7.173785e-01
#> [168,] 9.300752e-01 6.992476e-02
#> [169,] 1.151274e-02 9.884873e-01
#> [170,] 9.684758e-01 3.152420e-02
#> [171,] 2.112066e-03 9.978879e-01
#> [172,] 9.439466e-01 5.605337e-02
#> [173,] 7.797773e-01 2.202227e-01
#> [174,] 2.641557e-02 9.735844e-01
#> [175,] 9.440357e-01 5.596426e-02
#> [176,] 5.720634e-01 4.279366e-01
#> [177,] 9.670529e-01 3.294707e-02
#> [178,] 8.908167e-03 9.910918e-01
#> [179,] 7.363893e-02 9.263611e-01
#> [180,] 2.076778e-04 9.997923e-01
#> [181,] 9.993533e-01 6.466713e-04
#> [182,] 9.853368e-01 1.466319e-02
#> [183,] 7.909454e-01 2.090546e-01
#> [184,] 9.753683e-01 2.463170e-02
#> [185,] 9.722575e-01 2.774250e-02
#> [186,] 7.520352e-01 2.479648e-01
#> [187,] 8.744222e-01 1.255778e-01
#> [188,] 7.964764e-01 2.035236e-01
#> [189,] 9.777777e-01 2.222228e-02
#> [190,] 9.934724e-01 6.527559e-03
#> [191,] 4.450502e-01 5.549498e-01
#> [192,] 4.595539e-02 9.540446e-01
#> [193,] 2.344225e-01 7.655775e-01
#> [194,] 9.987123e-01 1.287668e-03
#> [195,] 9.998554e-01 1.446417e-04
#> [196,] 1.672380e-02 9.832762e-01
#> [197,] 1.280865e-01 8.719135e-01
#> [198,] 9.429641e-01 5.703590e-02
#> [199,] 9.376825e-01 6.231752e-02
#> [200,] 3.474767e-02 9.652523e-01

y2 = (y < -2.5)*1+(y>=-2.5&y<2.5)*2+(y>=2.5)*3
my.tree <- ODT(X=X, y=y2, Xsplit=Z, split = "linear",
               NodeRotateFun = "RotMatRF",MinLeaf = 10, MaxDepth = 5,
               glmnetParList=list(family = "multinomial"))
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: from glmnet C++ code (error code -94); Convergence for 94th lambda value not reached after maxit=100000 iterations; solutions for larger lambdas returned
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
#> Warning: one multinomial or binomial class has fewer than 8  observations; dangerous ground
(prob <- predict(my.tree, X, Xsplit=Z, type="prob"))
#>                   1          2           3
#>   [1,] 2.388572e-02 0.93436323 0.041751047
#>   [2,] 1.608888e-02 0.89322784 0.090683276
#>   [3,] 1.968674e-01 0.76363998 0.039492632
#>   [4,] 8.080246e-02 0.65454931 0.264648232
#>   [5,] 3.284806e-01 0.58960657 0.081912821
#>   [6,] 1.775984e-02 0.95413717 0.028102991
#>   [7,] 1.994059e-01 0.70477239 0.095821679
#>   [8,] 1.316470e-01 0.73078318 0.137569818
#>   [9,] 2.722229e-03 0.90530439 0.091973386
#>  [10,] 6.201278e-01 0.35509434 0.024777892
#>  [11,] 8.610333e-02 0.68813425 0.225762424
#>  [12,] 2.659525e-02 0.88234489 0.091059858
#>  [13,] 1.643865e-02 0.95634464 0.027216707
#>  [14,] 5.611557e-01 0.43417561 0.004668700
#>  [15,] 1.488829e-02 0.70784884 0.277262861
#>  [16,] 3.018891e-02 0.89292271 0.076888379
#>  [17,] 1.124815e-02 0.92667329 0.062078567
#>  [18,] 1.417569e-01 0.75087634 0.107366749
#>  [19,] 2.244151e-02 0.70537071 0.272187778
#>  [20,] 1.867106e-02 0.82227434 0.159054600
#>  [21,] 1.727951e-02 0.78332712 0.199393370
#>  [22,] 5.192266e-01 0.38558012 0.095193231
#>  [23,] 1.169493e-01 0.80730597 0.075744760
#>  [24,] 3.630042e-02 0.95385961 0.009839974
#>  [25,] 2.093973e-02 0.80931388 0.169746397
#>  [26,] 1.547101e-03 0.95772574 0.040727164
#>  [27,] 8.769918e-01 0.11137833 0.011629877
#>  [28,] 2.320449e-02 0.96542431 0.011371201
#>  [29,] 6.619416e-01 0.32117100 0.016887406
#>  [30,] 2.028676e-02 0.83963733 0.140075907
#>  [31,] 1.542255e-02 0.64724426 0.337333189
#>  [32,] 3.517372e-02 0.88255681 0.082269470
#>  [33,] 8.370454e-01 0.13737423 0.025580325
#>  [34,] 2.289458e-02 0.89054709 0.086558329
#>  [35,] 2.222956e-02 0.96390830 0.013862146
#>  [36,] 2.082751e-01 0.73374450 0.057980379
#>  [37,] 2.675520e-02 0.90888760 0.064357202
#>  [38,] 1.369577e-01 0.78590663 0.077135623
#>  [39,] 3.079425e-01 0.56673802 0.125319452
#>  [40,] 2.046654e-02 0.76066143 0.218872030
#>  [41,] 2.299307e-01 0.69178344 0.078285887
#>  [42,] 9.103905e-03 0.96353726 0.027358835
#>  [43,] 1.643180e-02 0.81980763 0.163760569
#>  [44,] 6.836813e-03 0.90637229 0.086790895
#>  [45,] 1.555241e-02 0.95795211 0.026495479
#>  [46,] 2.178717e-02 0.94970183 0.028510999
#>  [47,] 2.431178e-02 0.82854727 0.147140956
#>  [48,] 2.236731e-01 0.62499733 0.151329546
#>  [49,] 6.342354e-02 0.88712517 0.049451287
#>  [50,] 9.550946e-01 0.03247400 0.012431358
#>  [51,] 1.500068e-02 0.88507425 0.099925066
#>  [52,] 4.635261e-01 0.50268405 0.033789879
#>  [53,] 6.502518e-01 0.31379907 0.035949115
#>  [54,] 9.540142e-01 0.04400966 0.001976156
#>  [55,] 7.001844e-01 0.20876676 0.091048851
#>  [56,] 4.462391e-02 0.69589972 0.259476369
#>  [57,] 4.912549e-02 0.89826664 0.052607862
#>  [58,] 3.251525e-02 0.93441341 0.033071333
#>  [59,] 2.145845e-02 0.79581130 0.182730258
#>  [60,] 2.413489e-02 0.89987348 0.075991633
#>  [61,] 6.708816e-03 0.31616554 0.677125640
#>  [62,] 2.564186e-04 0.94916680 0.050576785
#>  [63,] 1.690076e-02 0.82254904 0.160550200
#>  [64,] 1.587953e-02 0.91573954 0.068380935
#>  [65,] 1.737177e-02 0.95391474 0.028713493
#>  [66,] 2.508182e-02 0.84704510 0.127873074
#>  [67,] 1.910517e-02 0.97432200 0.006572828
#>  [68,] 1.273496e-02 0.84807809 0.139186951
#>  [69,] 1.469539e-03 0.94019148 0.058338985
#>  [70,] 7.655319e-03 0.49794198 0.494402705
#>  [71,] 5.343370e-01 0.37049555 0.095167459
#>  [72,] 9.188509e-01 0.07503477 0.006114367
#>  [73,] 2.304923e-01 0.66336384 0.106143867
#>  [74,] 2.645819e-02 0.94532714 0.028214670
#>  [75,] 2.140291e-02 0.96261899 0.015978106
#>  [76,] 8.253893e-01 0.15128827 0.023322410
#>  [77,] 4.496383e-02 0.91134460 0.043691572
#>  [78,] 5.640376e-02 0.87603876 0.067557488
#>  [79,] 1.455585e-02 0.92888411 0.056560034
#>  [80,] 1.911446e-02 0.94441825 0.036467291
#>  [81,] 1.870768e-02 0.94601832 0.035274009
#>  [82,] 2.026144e-02 0.91586789 0.063870662
#>  [83,] 1.529307e-02 0.67124244 0.313464488
#>  [84,] 2.177441e-02 0.96757353 0.010652063
#>  [85,] 1.924902e-04 0.92676294 0.073044572
#>  [86,] 1.312152e-04 0.93729653 0.062572255
#>  [87,] 1.790359e-02 0.71104411 0.271052305
#>  [88,] 2.236513e-02 0.91522432 0.062410543
#>  [89,] 1.925616e-02 0.85435221 0.126391627
#>  [90,] 2.820203e-02 0.89278063 0.079017337
#>  [91,] 2.414063e-02 0.93145949 0.044399879
#>  [92,] 2.228522e-04 0.89319804 0.106579106
#>  [93,] 4.497179e-01 0.40330097 0.146981112
#>  [94,] 2.069407e-02 0.79644547 0.182860459
#>  [95,] 1.188865e-05 0.91654426 0.083443854
#>  [96,] 1.999394e-02 0.81528115 0.164724907
#>  [97,] 1.850535e-02 0.96746240 0.014032251
#>  [98,] 6.971666e-01 0.27990976 0.022923680
#>  [99,] 1.572741e-02 0.97225978 0.012012808
#> [100,] 1.853809e-02 0.94385510 0.037606810
#> [101,] 1.111005e-01 0.85795175 0.030947737
#> [102,] 1.692422e-02 0.91877048 0.064305298
#> [103,] 6.575580e-01 0.32415573 0.018286273
#> [104,] 6.947504e-02 0.85515929 0.075365676
#> [105,] 2.004273e-02 0.94287877 0.037078506
#> [106,] 9.613456e-03 0.55383817 0.436548373
#> [107,] 2.208770e-02 0.75433143 0.223580872
#> [108,] 8.406194e-02 0.78375865 0.132179415
#> [109,] 3.787479e-03 0.90783804 0.088374483
#> [110,] 1.331548e-02 0.49296042 0.493724100
#> [111,] 1.872859e-02 0.94734836 0.033923051
#> [112,] 2.093034e-02 0.93460340 0.044466262
#> [113,] 1.258235e-02 0.67155979 0.315857866
#> [114,] 2.087253e-02 0.94652885 0.032598613
#> [115,] 2.040426e-02 0.91948320 0.060112537
#> [116,] 1.857960e-02 0.93488799 0.046532414
#> [117,] 2.501441e-01 0.70033486 0.049521069
#> [118,] 2.254647e-02 0.91744350 0.060010032
#> [119,] 1.369546e-01 0.74586014 0.117185274
#> [120,] 2.408009e-02 0.89907730 0.076842610
#> [121,] 4.139720e-01 0.54142772 0.044600316
#> [122,] 3.237234e-02 0.74495644 0.222671220
#> [123,] 4.785881e-01 0.48384414 0.037567739
#> [124,] 4.596853e-02 0.89441301 0.059618455
#> [125,] 1.347265e-01 0.78946582 0.075807682
#> [126,] 8.542548e-01 0.12052686 0.025218294
#> [127,] 2.006631e-02 0.91101213 0.068921562
#> [128,] 1.653704e-02 0.92148708 0.061975888
#> [129,] 1.735562e-02 0.95703487 0.025609510
#> [130,] 4.507960e-02 0.90657154 0.048348857
#> [131,] 2.199512e-02 0.88762273 0.090382150
#> [132,] 2.188147e-02 0.94349853 0.034620004
#> [133,] 1.082930e-02 0.90629000 0.082880697
#> [134,] 2.660600e-02 0.95807561 0.015318383
#> [135,] 1.046008e-03 0.93292876 0.066025234
#> [136,] 5.321375e-01 0.44799409 0.019868420
#> [137,] 1.837964e-02 0.93010737 0.051512986
#> [138,] 2.380481e-02 0.93022876 0.045966433
#> [139,] 2.893082e-02 0.93043524 0.040633937
#> [140,] 1.999676e-01 0.74695642 0.053075979
#> [141,] 2.414663e-02 0.96800873 0.007844636
#> [142,] 1.463685e-02 0.73536162 0.250001539
#> [143,] 2.557686e-02 0.95670346 0.017719672
#> [144,] 1.581823e-01 0.78453029 0.057287435
#> [145,] 1.048707e-02 0.96376076 0.025752172
#> [146,] 2.037155e-02 0.95330840 0.026320044
#> [147,] 9.200603e-03 0.38040042 0.610398973
#> [148,] 1.676392e-02 0.91747612 0.065759958
#> [149,] 2.889170e-02 0.94941883 0.021689467
#> [150,] 2.165344e-02 0.96731738 0.011029183
#> [151,] 1.620225e-02 0.85585555 0.127942199
#> [152,] 1.985331e-02 0.90085867 0.079288027
#> [153,] 6.782924e-01 0.29377340 0.027934200
#> [154,] 3.005734e-01 0.67173958 0.027687021
#> [155,] 2.037042e-02 0.96721165 0.012417933
#> [156,] 2.411961e-02 0.95229620 0.023584191
#> [157,] 9.508534e-01 0.03384293 0.015303677
#> [158,] 1.891513e-02 0.94918505 0.031899818
#> [159,] 4.172381e-01 0.56348511 0.019276759
#> [160,] 1.050096e-02 0.50964976 0.479849281
#> [161,] 6.501322e-01 0.29904801 0.050819823
#> [162,] 6.892109e-02 0.86917142 0.061907490
#> [163,] 1.463490e-02 0.76460794 0.220757165
#> [164,] 1.804090e-01 0.63512650 0.184464547
#> [165,] 5.369111e-01 0.44489719 0.018191714
#> [166,] 6.529609e-03 0.49778318 0.495687206
#> [167,] 1.033075e-01 0.82846836 0.068224165
#> [168,] 2.270243e-02 0.96335803 0.013939532
#> [169,] 2.502690e-02 0.89800431 0.076968790
#> [170,] 1.653749e-02 0.90706130 0.076401207
#> [171,] 3.979026e-01 0.32312216 0.278975270
#> [172,] 9.947524e-03 0.90839557 0.081656911
#> [173,] 1.803549e-02 0.86114591 0.120818595
#> [174,] 2.207595e-02 0.90082026 0.077103799
#> [175,] 1.552291e-02 0.94898149 0.035495594
#> [176,] 1.601944e-02 0.92452104 0.059459520
#> [177,] 2.695114e-02 0.86092332 0.112125544
#> [178,] 3.053887e-04 0.77145760 0.228237015
#> [179,] 1.787570e-02 0.71398715 0.268137152
#> [180,] 1.622222e-02 0.62618542 0.357592366
#> [181,] 8.235968e-01 0.16616616 0.010237070
#> [182,] 2.973629e-02 0.83357580 0.136687907
#> [183,] 1.448461e-03 0.93451390 0.064037638
#> [184,] 1.436260e-02 0.97755488 0.008082523
#> [185,] 3.053058e-02 0.86831876 0.101150655
#> [186,] 2.199849e-02 0.90898342 0.069018087
#> [187,] 1.129861e-02 0.72784598 0.260855405
#> [188,] 2.154926e-02 0.94730217 0.031148570
#> [189,] 8.685499e-02 0.84924945 0.063895557
#> [190,] 2.191810e-02 0.95460010 0.023481802
#> [191,] 1.796040e-02 0.92100029 0.061039311
#> [192,] 1.601325e-02 0.87280845 0.111178298
#> [193,] 1.801943e-02 0.95313902 0.028841552
#> [194,] 6.242149e-01 0.29440818 0.081376921
#> [195,] 9.710651e-01 0.02733155 0.001603336
#> [196,] 1.557376e-02 0.97035190 0.014074340
#> [197,] 1.611370e-02 0.50614500 0.477741295
#> [198,] 1.710175e-02 0.96554497 0.017353278
#> [199,] 1.163398e-02 0.91467703 0.073688990
#> [200,] 5.374753e-01 0.43456381 0.027960864