PrInDT {PrInDT}

The basic undersampling loop for classification

Description

The function PrInDT uses ctrees (conditional inference trees from the package "party") for optimal modeling of the relationship between the two-class factor variable 'classname' and all other factor and numerical variables in the data frame 'datain' by means of 'N' repetitions of undersampling. The optimization citerion is the balanced accuracy on the full sample. The trees generated from undersampling can be restricted by not accepting trees including split results specified in the character strings of the vector 'ctestv'.
The undersampling percentages are 'percl' for the larger class and 'percs' for the smaller class (default = 1).
The probability threshold 'thres' for the prediction of the smaller class may be specified (default = 0.5).
Undersampling may be stratified in two ways by the feature 'strat'.

Usage

PrInDT(datain, classname, ctestv=NA, N, percl, percs=1, conf.level=0.95, thres=0.5,
       stratvers=0, strat=NA, seedl=TRUE)

Arguments

datain

Input data frame with class factor variable 'classname' and the
influential variables, which need to be factors or numericals (transform logicals and character variables to factors)

classname

Name of class variable (character)

ctestv

Vector of character strings of forbidden split results;
Example: ctestv <- rbind('variable1 == {value1, value2}','variable2 <= value3'), where character strings specified in 'value1', 'value2' are not allowed as results of a splitting operation in variable 1 in a tree.
For restrictions of the type 'variable <= xxx', all split results in a tree are excluded with 'variable <= yyy' and yyy <= xxx.
Trees with split results specified in 'ctestv' are not accepted during optimization.
A concrete example is: 'ctestv <- rbind('ETH == {C2a, C1a}','AGE <= 20')' for variables 'ETH' and 'AGE' and values 'C2a','C1a', and '20';
If no restrictions exist, the default = NA is used.

N

Number (> 2) of repetitions (integer)

percl

Undersampling percentage of larger class (numerical, > 0 and <= 1)

percs

Undersampling percentage of smaller class (numerical, > 0 and <= 1);
default = 1

conf.level

(1 - significance level) in function ctree (numerical, > 0 and <= 1);
default = 0.95

thres

Probability threshold for prediction of smaller class (numerical, >= 0 and < 1); default = 0.5

stratvers

Version of stratification;
= 0: none (default),
= 1: stratification according to the percentages of the values of the factor variable 'strat',
> 1: stratification with minimum number "stratvers" of observations per value of "strat"

strat

Name of one (!) stratification variable for undersampling (character);
default = NA (no stratification)

seedl

Should the seed for random numbers be set (TRUE / FALSE)?
default = TRUE

Details

For the optimzation of the trees, we employ a method we call Sumping (Subsampling umbrella of model parameters), a variant of Bumping (Bootstrap umbrella of model parameters) (Tibshirani & Knight, 1999) which use subsampling instead of bootstrapping. The aim of the optimization is to identify conditional inference trees with maximum predictive power on the full sample under interpretability restrictions.

References
– Tibshirani, R., Knight, K. 1999. Model Search and Inference By Bootstrap "bumping". Journal of Computational and Graphical Statistics, Vol. 8, No. 4 (Dec., 1999), pp. 671-686
– Weihs, C., Buschfeld, S. 2021a. Combining Prediction and Interpretation in Decision Trees (PrInDT) - a Linguistic Example. arXiv:2103.02336

Standard output can be produced by means of print(name) or just name as well as plot(name) where 'name' is the output data frame of the function.
The plot function will produce a series of more than one plot. If you use R, you might want to specify windows(record=TRUE) before plot(name) to save the whole series of plots. In R-Studio this functionality is provided automatically.

Value

tree1st

best tree on full sample

tree2nd

2nd-best tree on full sample

tree3rd

3rd-best tree on full sample

treet1st

best tree on test sample

treet2nd

2nd-best tree on test sample

treet3rd

3rd-best tree on test sample

ba1st

accuracies: largeClass, smallClass, balanced of 'tree1st', both for full and test sample

ba2nd

accuracies: largeClass, smallClass, balanced of 'tree2nd', both for full and test sample

ba3rd

accuracies: largeClass, smallClass, balanced of 'tree3rd', both for full and test sample

baen

accuracies: largeClass, smallClass, balanced of ensemble of all interpretable, 3 best acceptable, and all acceptable trees on full sample

bafull

vector of balanced accuracies of all trees from undersampling

batest

vector of test accuracies of all trees from undersampling

dataout

transformed data set 'datain' for further analyses

treeAll

tree based on all observations

baAll

balanced accuracy of 'treeAll'

interpAll

criterion of interpretability of 'treeall' (TRUE / FALSE)

confAll

confusion matrix of 'treeAll'

Examples

datastrat <- PrInDT::data_zero
data <- na.omit(datastrat) # cleaned full data: no NAs
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
N <- 41  # no. of repetitions
conf.level <- 0.99 # 1 - significance level (mincriterion) in ctree
percl <- 0.08  # undersampling percentage of the larger class
percs <- 0.95 # undersampling percentage of the smaller class
# calls of PrInDT
out <- PrInDT(data,"real",ctestv,N,percl,percs,conf.level) # unstratified
out # print best model and ensembles as well as all observations
plot(out)
out <- PrInDT(data,"real",ctestv,N,percl,percs,conf.level,stratvers=1,
              strat="SEX") # percentage stratification
out <- PrInDT(data,"real",ctestv,N,percl,percs,conf.level,stratvers=50,
              strat="SEX") # stratification with minimum no. of tokens
out <- PrInDT(data,"real",ctestv,N,percl,percs,conf.level,thres=0.4) # threshold = 0.4