PrInDTCstruc: Structured subsampling for classification

In PrInDT: Prediction and Interpretation in Decision Trees for Classification and Regression

Structured subsampling for classification

Description

The function PrInDTCstruc applies structured subsampling for finding an optimal subsample to model 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 subsampling from a substructure and 'Ni' repetitions of subsampling from the predictors. The optimization citerion is the balanced accuracy on the validation sample 'valdat' (default is the full input sample 'datain'). Other criteria are possible (cf. parameter description of 'crit'). 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 substructure of the observations used for subsampling in modelling is specified by the list 'Struc' which consists of the factor variable 'name' representing the substructure, the name 'check' of the factor variable with the information about the categories of the substructure, and the matrix 'labs' which specifies the values of 'check' corresponding to two categories in its rows, i.e. in 'labs[1,]' and 'labs[2,]'. The names of the categories have to be specified by rownames(labs).
See parameter description of 'Struc' for its specification for 'vers="b"' and 'indrep > 0'.
The number of predictors 'Pit' to be included in the model and the number of elements of the substructure 'Eit' have to be specified (lists allowed), and undersampling of the categories of 'classname' can be controlled by 'undersamp=TRUE/FALSE'.
In structured subsampling, 'N' repetitions of subsampling of the variable 'name' with 'Eit' different elements of each category in 'check' are realized. If 'Eit' is a list, each entry is employed individually. If 'Eit' is larger than the maximum available number of elements with a certain value of 'check', the maximum possible number of elements is used.
Four different versions of structured subsampling exist:
a) just of the elements in the substructure (possibly with additional undersampling) with parameters 'N' and 'Eit',
b) just of the predictors with parameters 'Ni' and 'Pit',
c) of the predictors and for each subset of predictors subsampling of the elements of the substructure (possibly with additional undersampling) with parameters 'N', 'Ni', 'Eit', and 'Pit', and
d) of the elements of the substructure (possibly with additional undersampling) and for each of these subsets subsampling of the predictors with the same parameters as version c).
Sampling of the elements of the substructure can be influenced by using weights of the elements ('weights=TRUE') according to the number of appearances of the smaller class of 'classnames'. This way, elements with more realisations in the smaller class are preferred in modelling.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

The parameter 'indrep' indicates repeated measurement situations ('indrep > 0', only implemented for 'crit="ba"'); default = 0.
Repeated measurements are multiple measurements of the same variable taken on the same subjects (or objects) either under different conditions or over two or more time periods.
The variable with the repeatedly observed subjects (or objects) has to be specified by 'name' in 'Struc'. Only one value of 'classname' is allowed for each value of 'Struc$name'. In case of 'indrep > 0' it is automatically assumed that the same number of subjects (or objects) of the two classes under study have to be used for model building. Possible such numbers can be specified by 'Eit'.
For indrep=1, models are optimized for individual observations and the classes of the substructure elements are subsequently determined via the parameter 'thr'.
For indrep=2, models are optimized so that the criterion "ba" is maximal for the substructure elements taking 'thr' into account.
For indrep > 0 and 'valdat' unequal 'datain', the variable 'repvar' defines the substructure for 'valdat', length = dim(valdat)[1] necessary; default = NA'

Usage

PrInDTCstruc(datain,classname,ctestv=NA,Struc=NA,vers="d",weight=FALSE,
                Eit=NA,Pit=NA,N=99,Ni=99,undersamp=TRUE,crit="ba",ktest=0,
                stest=integer(length=0),conf.level=0.95,indrep=0,
                minsplit=NA,minbucket=NA,repvar=NA,valdat=datain,thr=0.5)

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.
Struc	= list(name,check,labs), cf. description for explanations; Struc not needed for vers="b"; for indrep=1, Struc = list(name);
vers	Version of structured subsampling: "a", "b", "c", "d", cf. description; default = "d"
weight	Weights to be used for subsampling of elements of substructure (logical, TRUE or FALSE); default = FALSE
Eit	List of number of elements of substructure (integers); default = c((Cl-4):Cl), Cl = maximum number of elements in both categories
Pit	List of number of predictors (integers) default = c(max(1,(D-3)):D), D = maximum number of predictors
N	Number of repetitions of subsampling from substructure (integer) default = 0 for vers="b", = 99 otherwise; if vers="b", any input is overwritten by the default
Ni	Number of repetitions of subsampling from predictors default = 0 for vers="a", = 99 for vers="b", = N otherwise; if vers="a", any input is overwritten by the default
undersamp	Undersampling of categories of 'classname' to be used ((logical, TRUE or FALSE) default = TRUE; if indrep=1 or vers="b", undersamp = FALSE
crit	Optimisation criterion: "ba" for balanced accuracy, "bat" for balanced accuracy on test sets, "ta" for test accuracy, "tal" for test accuracy of continuing parts of length 'ktest' in substructure elements 'stest'; default = "ba"
ktest	Length of continuing parts to be tested (for crit="tal"); default = 0
stest	Part of substructure to be tested (for crit="tal")(integer vector); default = integer vector of length 0
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
indrep	Indicator for repeated measurements, i.e. more than one observation with the same class for each element; for indrep=1, Struc=list(name) only; default = 0
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7
repvar	Values of variable defining the substructure corresponding to valdat in the case of repeated measurements, length = dim(valdat)[1] necessary; default = NA
valdat	validation data; default = datain
thr	threshold for element classfication: minimum percentage of correct class entries; default = 0.5

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.1, for further information.

Standard output can be produced by means of print(name$besttree) or just name$besttree as well as plot(name$besttree) where 'name' is the output data frame of the function.

Value

modbest

Best tree

interp

Number of interpretable trees, overall number of trees

dmax

Number of predictors in training set for best tree

ntmax

Size of training set for best tree

acc1

Accuracy of best tree on large class

acc2

Accuracy of best tree on small class

bamax

Balanced accuracy of best tree

tamax

Test accuracy of best tree

kumin

Number of elements with misclassified parts longer than 'ktest' for best tree

elems

Elements with long misclassified parts for best tree

mindlong

Indices of long misclassified parts for best tree

ind1max

Elements of 1st category of substructure used by best tree

ind2max

Elements of 2nd category of substructure used by best tree

indmax

Predictors used by best tree

bestTrain

Training set for best tree

bestTest

Test set for best tree

labs

labs from Struc

lablarge

Label of large class

labsmall

Label of small class

vers

Version used for structured subsampling

acc1E

Accuracy of large class on Elements of best tree

acc2E

Accuracy of small class on Elements of best tree

bamaxE

Balanced accuracy of best tree on Elements

nam1

Names of misclassified Elements of large class

nam2

Names of misclassified Elements of small class

thr

Threshold for element classification

Examples

data <- PrInDT::data_zero
data <- na.omit(data) # cleaned full data: no NAs
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
# substructure
name <- PrInDT::participant_zero
check <- "data$ETH"
labs <- matrix(1:6,nrow=2,ncol=3)
labs[1,] <- c("C1a","C1b","C1c")
labs[2,] <- c("C2a","C2b","C2c")
rownames(labs) <- c("Children 1","Children 2")
Struc <- list(name=name,check=check,labs=labs)
out <- PrInDTCstruc(data,"real",ctestv,Struc,vers="c",weight=TRUE,N=5,Pit=5,conf.level=0.99)
out
plot(out)
# indrep = 1
Struc <- list(name=name)
out <- PrInDTCstruc(data,"real",Struc=Struc,vers="c",Pit=5,Eit=5,N=5,crit="ba",indrep=1,
           conf.level=0.99)

PrInDT documentation built on Sept. 11, 2025, 5:11 p.m.