Package 'PrInDT'

Two-stage estimation for classification

Description

The function C2SPrInDT applies two-stage estimation for finding an optimal model for relationships between the two-class factor variables specified as column indices of 'datain' in the vector 'inddep' and all other factor and numerical variables in the data frame 'datain' by means of 'N' repetitions of random subsampling with percentages 'percl' for the large classes and 'percs' for the small classes. One percentage of observations for each dependent variable has to be specified for the larger and the smaller class. For example, for three dependent variables, 'percl' consists of three percentages specified in the order in which the dependent variables appear in 'inddep'.
The dependent variables have to be specified as dummies, i.e. as 0 for 'property absent' or 1 for 'property present' for a certain property the dependent variable is representing.
The indices of the predictors relevant at 1st stage modeling can be specified in the vector 'indind'. If 'indind' is not specied, then all variables in 'datain' which are not specified in 'inddep' are used as predictors at 1st stage. At 2nd stage, all such variables are used as predictors anyway.
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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

C2SPrInDT(datain,ctestv=NA,conf.level=0.95,percl,percs,N=99,indind=NA,inddep,
                                 minsplit=NA,minbucket=NA)

Arguments

datain	Input data frame with class factor variables and the influential variables, which need to be factors or numericals (transform logicals and character variables to factors)
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.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
percl	list of undersampling percentages of larger class (numerical, > 0 and <= 1): one per dependent class variable in the same order as in 'inddep'
percs	list of undersampling percentage of smaller class (numerical, > 0 and <= 1); one per dependent class variable in the same order as in 'inddep'
N	no. of repetitions (integer > 0); default = 99
indind	indices of independent variables at stage 1; default = NA (means all independent variables used)
inddep	indices of dependent variables
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.1, for further information.

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.

Value

models1

Best trees at stage 1

models2

Best trees at stage 2

classnames

names of classification variables

baAll

balanced accuracies of best trees at both stages

Examples

data <- PrInDT::data_land # load data
dataclean <- data[,c(1:7,23:24,11:13,22,8:10)]  # only relevant features
indind <- c(1:9) # original predictors
inddep <- c(14:16) # dependent variables
dataland <- na.omit(dataclean)
ctestv <- NA
perc <- c(0.45,0.05,0.25)   # percentages of observations of larger class, 
# 1 per dependent class variable
perc2 <- c(0.75,0.95,0.75)  # percentages of observations of smaller class, 
# 1 per dependent class variable
outland <- C2SPrInDT(dataland,percl=perc,percs=perc2,N=19,indind=indind,inddep=inddep)
outland
plot(outland)

---

Landscape analysis

Description

The use of language(s) on public signs and categorization criteria.

Usage

data_land

Format

A data frame with 149 observations and 28 columns

coder

who coded the sign: Factor (3 levels "C","E","S") (anonymized)

researcher

who took a photograph of the sign: Factor (2 levels "L","S") (anonymized)

sign

where the sign was found: Factor (11 levels "digi","door","graf",...)

type.of.sign

kind of sign: Factor (5 levels "com","commem","infra","reg","trans")

permanent

was the sign permanent? Factor (2 levels "no","yes")

proper.noun

kind of proper noun on the sign: Factor (9 levels "bn","bn+","cn",...)

no.languages

number of languages on sign: Factor (4 levels "1","2","3","4+")

French

French on sign? Factor (2 levels "0","1")

Dutch

Dutch on sign? Factor (2 levels "0","1")

English

English on sign? Factor (2 levels "0","1")

Italian

Italian on sign? Factor (2 levels "0","1")

Spanish

Spanish on sign? Factor (2 levels "0","1")

German

German on sign? Factor (2 levels "0","1")

Indian,Mandarin,Greek,Indonesian,Portuguese,Libanese,Japanese,Russian,Danish, Norwegian,Hebrew,Catalan

12 infrequent languages: Factor (2 levels "0","1")

bn.unclear

brand name unclear: Factor (2 levels "0","1")

multilingual.type

type of multilingualism on sign: Factor (6 levels "0","1","2","3","4","uc")

location

location of sign: Factor (2 levels "M","P") (anonymized)

Source

Sarah Buschfeld, TU Dortmund

---

Subject pronouns and a predictor with one very frequent level

Description

Usage of subject pronouns and its predictors; speaker level "adult" very frequent.

Usage

data_speaker

Format

A data frame with 3370 observations and 6 columns

class

subject pronoun realized? Factor (2 levels "zero","realized")

AGE

age: Numerical (in months)

ETHN_GROUP

ethnic group: Factor (3 levels "C","I","n_a") (anonymized)

MLU

mean length of utterance: Factor (5 levels "1","2","3","adult","OL")

PRN_TYPE

pronoun type: Factor (5 levels "dem","it_con","it_ex","it_ref","refer")

SPEAKER

speaker: Factor (2 levels "adult","child")

Source

Sarah Buschfeld, TU Dortmund

---

Vowel length

Description

Vowel length and categorization criteria.

Usage

data_vowel

Format

A data frame with 82 observations and 22 columns

Nickname

nickname: Factor (43 levels "Nick1","Nick2",...,"Nick43") (anonymized)

LiBa

linguistic background: Factor (2 levels "mono","multi")

MLU

mean length of utterance: Factor (3 levels "1","2","3")

phone_label

phone label: Factor (2 levels "fleece","kit")

lexeme

lexeme: Factor (14 levels "bee","cheek","cheese","chicken", ...)

phone_left_1_duration

duration of phone to the left of the vowel: Numerical (in msec)

phone_right_1_duration

duration of phone to the right of the vowel: Numerical (in msec)

word_duration

duration of word: Numerical (in msec)

vowel_minimum_pitch

minimum pitch of vowel: Numerical (in Hertz)

vowel_maximum_pitch

maximum pitch of vowel: Numerical (in Hertz)

vowel_intensity_mean

mean intensity of vowel: Numerical (in decibel)

f1_fifty

first formant F1 at midpoint of vowel (50%): Numerical (in Hertz)

f2_fifty

second formant F2 at midpoint of vowel (50%): numercial (in Hertz)

target

vowel length: Numerical (in msec)

cons_class_l

class of consonant to the left of the vowel: Factor (6 levels "l","r","tsh",...)

cons_class_r

class of consonant to the right of the vowel: Factor (7 levels "?"(glottal stop),"empty","nas",...)

ETH

ethnic group: Factor (6 levels "C1a","C1b","C1c","C2a","C2b","C2c") (anonymized)

SEX

gender: Factor (2 levels "female","male)

AGE

age: Numerical (in months)

syllables

number of syllables in lexeme: integer (1,2)

speed

speed of speech: Numerical (word duration / syllables; in msec)

country

country: Factor (2 levels "E","S") (anonymized)

Source

Sarah Buschfeld, TU Dortmund

---

Subject pronouns

Description

Usage of subject pronouns and its predictors.

Usage

data_zero

Format

A data frame with 1024 observations and 7 columns

real

subject pronoun realized? Factor (2 levels "zero","realized")

AGE

age: Numerical (in months)

LiBa

linguistic background: Factor (3 levels "mono","multi", NA)

ETH

ethnic group: Factor (6 levels "C1a","C1b","C1c","C2a","C2b","C2c") (anonymized)

SEX

gender: Factor (2 levels "female","male")

MLU

mean length of utterance: Factor (4 levels "1","2","3","OL")

PRN

pronoun: Factor (7 levels "I","you_s","he","she","it","we","they")

Source

Sarah Buschfeld, TU Dortmund

---

Two-stage estimation for classification-regression mixtures

Description

The function Mix2SPrInDT applies 'N' repetitions of subsampling for finding an optimal subsample to model the relationship between the dependent variables specified in the sublist 'targets' of the list 'datalist' and all other factor and numerical variables in the corresponding data frame specified in the sublist 'datanames' of the list 'datalist' in the same order as 'targets'.
The function is prepared to handle classification tasks with 2 or more classes and regression tasks. At first stage, the targets are estimated only on the basis of the exogenous predictors. At second stage, summaries of the predictions of the endogenous features from the first stage models are added as new predictors.
Subsampling of observations and predictors uses the percentages specified in the matrix 'percent', one row per estimation taks. For classification tasks, percentages 'percl' and 'percs' for the larger and the smaller class have to be specified. For regression tasks, 'pobs' and 'ppre' have to specified for observations and predictors, respectively.
For generating summaries, the variables representing the substructure have to be specified in the sublist 'datastruc' of 'datalist'.
The sublist 'summ' of 'datalist' includes for each discrete target the classes for which you want to calculate the summary percentages and for each continuous target just NA (in the same order as in the sublist 'targets'). For a discrete target in this list, you can provide a sublist of classes to be combined (for an example see the below example).
The optimization citerion is the balanced accuracy for classification and R2 for regression, both evaluated 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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

Mix2SPrInDT(datalist,ctestv=NA,N=99,percent=NA,conf.level=0.95,minsplit=NA,minbucket=NA)

Arguments

datalist	list(datanames,targets,datastruc,summ) Input data: For specification see the above description
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 of repetitions of subsampling for predictors (integer); default = 99
percent	matrix of percent spefications: For specification see the above description; default: 'percent = NA' meaning default values for percentages.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.1, for further information.

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.

Value

models1

Best trees at stage 1

models2

Best trees at stage 2

depnames

names of dependent variables

nmod

number of models of tasks

nlev

levels of tasks

accAll

accuracies of best trees at both stages

Examples

# zero data
datazero <- PrInDT::data_zero
datazero <- na.omit(datazero) # cleaned full data: no NAs
names(datazero)[names(datazero)=="real"] <- "zero"
CHILDzero <- PrInDT::participant_zero
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
##
# multi-level data
datastrat <- PrInDT::data_zero
datamult <- na.omit(datastrat)
# ctestv <- NA
datamult$mult[datamult$ETH %in% c("C1a","C1b","C1c") & datamult$real == "zero"] <- "zero1"
datamult$mult[datamult$ETH %in% c("C2a","C2b","C2c") & datamult$real == "zero"] <- "zero2"
datamult$mult[datamult$real == "realized"] <- "real"
datamult$mult <- as.factor(datamult$mult) # mult is new class variable
datamult$real <- NULL # remove old class variable
CHILDmult <- CHILDzero
##
# vowel data
data <- PrInDT::data_vowel
data <- na.omit(data)
CHILDvowel <- data$Nickname
data$Nickname <- NULL
syllable <- 3 - data$syllables
data$syllabels <- NULL
data$syllables <- syllable
data$speed <- data$word_duration / data$syllables
names(data)[names(data) == "target"] <- "vowel"
datavowel <- data
##
# function preparation and call
datanames <- list("datazero","datamult","datavowel")
targets <- c("zero","mult","vowel")
datastruc <- list(CHILDzero,CHILDmult,CHILDvowel)
summult <- paste("zero1","zero2",sep=",")  
summ <- c("zero",summult,NA)
datalist <- list(datanames=datanames,targets=targets,datastruc=datastruc,summ=summ)
percent <- matrix(NA,nrow=3,ncol=2)
percent[1,] <- c("percl=0.075","percs=0.9") # percentages for datazero
# no percentages needed for datapast
percent[3,] <- c("pobs=0.9","ppre=c(0.9,0.8)") # percentages for datavowel
out2SMix <- Mix2SPrInDT(datalist,ctestv=ctestv,N=19,percent=percent,conf.level=0.99)
out2SMix
plot(out2SMix)

---

Nested PrInDT with additional undersampling of a factor with two unbalanced levels

Description

Function for additional undersampling of the factor 'nesvar' with two unbalanced levels to avoid dominance of the level with higher frequency. The factor 'nesvar' is allowed not be part of the input data frame 'datain'. The data of this factor is given in the vector 'nesunder'. The observations in 'nesunder' have to represent the same cases as in 'datain' in the same ordering.
PrInDT is called 'repin' times with subsamples of the original data so that the level with the larger frequency in the vector 'nesunder' has approximately the same number of values as the level with the smaller frequency.
Only the arguments 'nesvar', 'nesunder', and 'repin' relate to the additional undersampling, all the other arguments relate to the standard PrInDT procedure.
As in PrInDT, the aim is to optimally 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 undersampling. The trees generated by PrInDT can be restricted by excluding unacceptable trees which include split results specified in the character strings of the vector 'ctestv'.
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'.
The results are evaluated on the full sample and on the subsamples of 'nesunder'. The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Reference
Weihs, C., Buschfeld, S. 2021b. NesPrInDT: Nested undersampling in PrInDT. arXiv:2103.14931

Usage

NesPrInDT(datain,classname,ctestv=NA,N,plarge,psmall=1.0,conf.level=0.95,
       thres=0.5,stratvers=0,strat=NA,seedl=TRUE,nesvar,nesunder,repin,
       minsplit=NA,minbucket=NA)

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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
N	Number of repetitions (integer > 0)
plarge	Undersampling percentage of larger class (numerical, > 0 and <= 1)
psmall	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; 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
nesvar	Name of factor to be undersampled (character)
nesunder	Data of factor to be undersampled (integer)
repin	Number of repetitions (integer) for undersampling of 'nesvar'
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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

undba

balanced accuracies on undersamples

imax

indices of best trees on undersamples

undba3en

balanced accuracies of ensembles of 3 best trees on undersamples

accF

balanced accuracies on full sample

accE

balanced accuracy on full sample of best ensemble of 3 trees from undersampling

maxt

indices of best trees on full sample

treesb

3 best trees of all undersamples of 'nesunder'; refer to an individual tree as treesb[[k]], k = 1, ..., 3*repin

Examples

# data input and preparation --> data frame with 
#   class variable, factors, and numericals (no character variables)!!
data <- PrInDT::data_speaker
data <- na.omit(data)
nesvar <- "SPEAKER"
N <- 49  # no. of repetitions in inner loop
plarge <- 0.06 # sampling percentage for larger class in nesunder-subsample
psmall <- 1 # sampling percentage for smaller class in nesunder-subsample
nesunder <- data$SPEAKER
data[,nesvar] <- list(NULL)
outNes <- NesPrInDT(data,"class",ctestv=NA,N,plarge,psmall,conf.level=0.95,nesvar=nesvar,
  nesunder=nesunder,repin=5)
outNes
plot(outNes)
hist(outNes$undba,main=" ",xlab = "balanced accuracies of 3 best trees of all undersamples")

---

Optimisation of undersampling percentages for classification

Description

The function OptPrInDT applies an iterative technique for finding optimal undersampling percentages 'percl' for the larger class and 'percs' for the smaller class by a nested grid search for the use of the function PrInDT for the relationship between the two-class factor variable 'classname' and all other factor and numerical variables in the data frame 'data' by means of 'N' repetitions of undersampling. The optimization citerion is the balanced accuracy on the validation sample 'valdat' (default = full sample 'data'). 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 inputs plmax and psmax determine the maximal values of the percentages and the inputs distl and dists the the distances to the next smaller percentage to be tried.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.
The parameter 'steps' controls, how many of the 3 possible optimization steps should be carried out; default=3.

Usage

OptPrInDT(data,classname,ctestv=NA,N=99,plmax=0.09,psmax=0.9,
               distl=0.01,dists=0.1,conf.level=0.95,minsplit=NA,minbucket=NA,
               valdat=data,steps=3)

Arguments

data	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 (> 7) of repetitions (integer)
plmax	Maximal undersampling percentage of larger class (numerical, > 0 and <= 1); default = 0.09
psmax	Maximal undersampling percentage of smaller class (numerical, > 0 and <= 1); default = 0.9
distl	Distance to the next lower undersampling percentage of larger class (numerical, > 0 and < 1); default = 0.01
dists	Distance to the next lower undersampling percentage of smaller class (numerical, > 0 and < 1); default = 0.1
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7
valdat	validation data; default = data
steps	number of optimization steps = 1, 2, 3; default = 3

Details

See help("RePrInDT") and help("PrInDT") 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

besttree

best tree on full sample

bestba

balanced accuracy of best tree on full sample

percl

undersampling percentage of large class of best tree on full sample

percs

undersampling percentage of small class of best tree on full sample

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
# call of OptPrInDT
out <- OptPrInDT(data,"real",ctestv,N=24,conf.level=0.99,steps=1) # unstratified
out # print best model and ensembles as well as all observations
plot(out)

---

Participants of subject pronoun study

Description

Participants (random excerpt according to data_zero)

Usage

participant_zero

Format

A dataset with 1024 observations and 1 column

participant

participant of study (P1 - P51)

Source

Sarah Buschfeld, TU Dortmund

---

Posterior analysis of conditional inference trees: distribution of a specified variable in the terminal nodes.

Description

The conditional inference tree 'ct' is analyzed according to the distribution of a variable 'var' in its terminal nodes.
In the case of a discrete variable 'var', the appearance of the different levels is considered for each terminal node.
In the case of a continuous variable 'var', means and standard deviations of 'var' or the target variable are considered for each terminal node.
In particular, this function can be used for the posterior analysis of a tree regarding the distribution of a variable not present in the tree.

Usage

PostPrInDT(datain, ct, target, var, vardata, vt)

Arguments

datain	input data frame with the observatios of all variables used in the model
ct	conditional inference tree to be analyzed
target	name of target variable of 'ct' (character)
var	name of variable of interest (character)
vardata	observations of 'var'
vt	type of variables: 'dd' for discrete target (classification) and discrete variable 'var', 'dc' for discrete target (classification) and continuous 'var', 'cd' for continuous target (regression) and discrete 'var', and 'cc' for continuous target (regression) and continuous 'var'.

Value

None: Relevant output is produced by the function.

Examples

data <- PrInDT::data_zero
data <- na.omit(data)
outAll <- PrInDTAll(data,"real") 
PostPrInDT(data,outAll$treeAll,"real","ETH",data$ETH,vt="dd")
PostPrInDT(data,outAll$treeAll,"real","AGE",data$AGE,vt="dc")
datareg <- PrInDT::data_vowel
outregAll <- PrInDTregAll(datareg,"target") 
PostPrInDT(datareg,outregAll$treeAll,"target","Nickname",datareg$Nickname,vt="cd")
PostPrInDT(datareg,outregAll$treeAll,"target","AGE",datareg$AGE,vt="cc")

---

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 validation sample 'valdat' (default = full input sample 'datain'). 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).
A 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 option 'stratvers'.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

In the case of repeated measurements ('indrep=1'), the values of the substructure variable have to be given in 'repvar'. Only one value of 'classname' is allowed for each value of 'repvar'. If for a value of 'repvar' the percentage 'thr' of the observed occurence of a value of 'classname' is not reached by the number of predictions of the value of 'classname', a misclassification is detected.

Usage

PrInDT(datain,classname,ctestv=NA,N,percl,percs=1,conf.level=0.95,thres=0.5,
         stratvers=0,strat=NA,seedl=TRUE,minsplit=NA,minbucket=NA,repvar=NA,indrep=0,
         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.
N	Number (> 2) of repetitions (integer)
percl	Undersampling percentage of larger class (numerical, > 0 and <= 1); if percs = default, default of percl = percentage of large class resulting in the same number of observations as in the small class
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
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 in the case of repeated measurements, length = dim(valdat)[1] necessary; default = NA
indrep	Indicator of repeated measurements ('indrep=1'); default = 0
valdat	Validation data; default = datain
thr	threshold for element classification: minimum percentage of correct class entries; default = 0.5

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 uses 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 validation sample

tree2nd

2nd-best tree on validation sample

tree3rd

3rd-best tree on validation 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 validation and test sample

ba2nd

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

ba3rd

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

baen

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

bafull

vector of balanced accuracies of all trees from undersampling

batest

vector of test accuracies of all trees from undersampling

treeAll

tree based on all observations

baAll

balanced accuracy of 'treeAll'

interpAll

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

confAll

confusion matrix of 'treeAll'

acc1AE

Accuracy of full sample tree on Elements of large class

acc2AE

Accuracy of full sample tree on Elements of small class

bamaxAE

balanced accuracy of full sample tree on Elements

namA1

Names of misclassified Elements by full sample tree of large class

namA2

Names of misclassified Elements by full sample tree of small class

acc1E

Accuracy of best tree on Elements of large class

acc2E

Accuracy of best tree on Elements of small class

bamaxE

balanced accuracy of best tree on Elements

nam1

Names of misclassified Elements by best tree of large class

nam2

Names of misclassified Elements by best tree of small class

lablarge

Label of large class

labsmall

Label of small class

valdat

Validation set after edit

thr

Threshold for repeated measurements

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

---

Conditional inference tree (ctree) based on all observations

Description

ctree based on all observations in 'datain'. Interpretability is checked (see 'ctestv'); probability threshold can be specified. The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Reference
Weihs, C., Buschfeld, S. 2021a. Combining Prediction and Interpretation in Decision Trees (PrInDT) - a Linguistic Example. arXiv:2103.02336

In the case of repeated measurements ('indrep=1'), the values of the substructure variable have to be given in 'repvar'. Only one value of 'classname' is allowed for each value of 'repvar'. If for a value of 'repvar' the percentage 'thr' of the observed occurence of a value of 'classname' is not reached by the number of predictions of the value of 'classname', a misclassification is detected.

Usage

PrInDTAll(datain, classname, ctestv=NA, conf.level=0.95, thres=0.5,
                 minsplit=NA,minbucket=NA,repvar=NA,indrep=0,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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
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
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 in the case of repeated measurements, length = dim(datain)[1] necessary; default=NA
indrep	Indicator of repeated measurements ('indrep=1'); default = 0
thr	threshold for element classification: minimum percentage of correct class entries; default = 0.5

Details

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.

Value

treeall

ctree based on all observations

baAll

balanced accuracy of 'treeall'

interpAll

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

confAll

confusion matrix of 'treeall'

acc1AE

Accuracy of full sample tree on Elements of large class

acc2AE

Accuracy of full sample tree on Elements of small class

bamaxAE

balanced accuracy of full sample tree on Elements

namA1

Names of misclassified Elements by full sample tree of large class

namA2

Names of misclassified Elements by full sample tree of small class

lablarge

Label of large class

labsmall

Label of small class

thr

Threshold for repeated measurements

Examples

datastrat <- PrInDT::data_zero
data <- na.omit(datastrat)
ctestv <- rbind('ETH == {C2a,C1a}','MLU == {1, 3}')
conf.level <- 0.99 # 1 - significance level (mincriterion) in ctree
outAll <- PrInDTAll(data,"real",ctestv,conf.level) 
print(outAll) # print model based on all observations
plot(outAll) # plot model based on all observations

---

Conditional inference trees (ctrees) based on consecutive parts of the full sample

Description

ctrees based on the full sample of the smaller class and consecutive parts of the larger class of the nesting variable 'nesvar'. The variable 'nesvar' has to be part of the data frame 'datain'.
Interpretability is checked (see 'ctestv'); probability threshold can be specified. The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Reference
Weihs, C., Buschfeld, S. 2021b. NesPrInDT: Nested undersampling in PrInDT. arXiv:2103.14931

Usage

PrInDTAllparts(datain, classname, ctestv=NA, conf.level=0.95, thres=0.5,
       nesvar, divt,minsplit=NA,minbucket=NA)

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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
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
nesvar	Name of nesting variable (character)
divt	Number of parts of nesting variable nesvar for which models should be determined individually
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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

Value

baAll

balanced accuracy of tree on full sample

nesvar

name of nesting variable

divt

number of consecutive parts of the sample

badiv

balanced accuracy of trees on 'divt' consecutive parts of the sample

Examples

data <- PrInDT::data_speaker
data <- na.omit(data)
nesvar <- "SPEAKER"
outNesAll <- PrInDTAllparts(data,"class",ctestv=NA,conf.level=0.95,thres=0.5,nesvar,divt=8)
outNesAll

---

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)

---

Multiple label classification based on resampling by PrInDT

Description

Multiple label classification based on resampling by PrInDT. We consider two ways of modeling (Binary relevance modeling, dependent binary modeling) and three ways of model evaluation: single assessment, joint assessment, and true prediction (see the Value section for more information).
Variables should be arranged in 'datain' according to indices specified in 'indind', 'indaddind', and 'inddep'.
Please note that the dependent variables have to be specified as dummies, i.e. as 'absent' (value 0) or 'present' (value 1).
Undersampling is repeated 'N' times.
Undersampling percentages 'percl' for the larger class and 'percs' for the smaller class can be specified, one each per dependent class variable.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

References
- Buschfeld, S., Weihs, C. and Ronan, P.. 2024. Modeling linguistic landscapes: A comparison of St Martin’s two capitals Philipsburg and Marigot Linguistic Landscape 10(3): 302–334. https://doi.org/10.1075/ll.23070.bus
- Probst, P., Au, Q., Casalicchio, G., Stachl, C., and Bischl, B. 2017. Multilabel Classification with R Package mlr. arXiv:1703.08991v2

Usage

PrInDTMulab(datain,classnames=NA,ctestv=NA,conf.level=0.95,percl,percs=1,N,
               indind=NA,indaddind=NA,inddep,minsplit=NA,minbucket=NA)

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)
classnames	names of class variables (character vector); default = NA: from old version: superfluous now
ctestv	Vector of character strings of forbidden split results; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
percl	list of undersampling percentages of larger class (numerical, > 0 and <= 1): one per dependent class variable
percs	list of undersampling percentage of smaller class (numerical, > 0 and <= 1); one per dependent class variable
N	no. of repetitions (integer > 0)
indind	indices of independent variables
indaddind	indices of additional independent variables used in the case of dependent binary relevance modeling
inddep	indices of dependent variables
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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

accbr

model errors for Binary Relevance (single assessment) - only independent predictors are used for modeling one label at a time, the other labels are not used as predictors. As the performance measure for the resulting classification rules, the balanced accuracy of the best model from PrInDT is employed for each individual label.

errbin

combined error for Binary Relevance (joint assessment) - the best prediction models for the different labels are combined to assess the combined prediction. The 01-accuracy counts a label combination as correct only if all labels are correctly predicted. The hamming accuracy corresponds to the proportion of labels whose value is correctly predicted.

accdbr

model errors for Dependent Binary Relevance (Extended Model) (single assessment) - each label is trained by means of an extended model which not only includes the independent predictors but also the other labels. For these labels, the truly observed values are used for estimation and prediction. In the extended model, other labels, which are not treated as dependent variables, can also be used as additional predictors.

errext

combined errors for Dependent Binary Relevance (Extended Model) (joint assessment)

errtrue

combined errors for Dependent Binary Relevance (True Prediction) - in the prediction phase, the values of all modeled labels are first predicted by the independent predictors only and then the predicted labels are used in the estimated extended model in a 2nd step to ultimately predict the labels.

coldata

column names of input data

inddep

indices of dependent variables (labels to be modeled)

treebr

list of trees from Binary Relevance modeling, one tree for each label; refer to an individual tree as treebr[[i]], i = 1, ..., no. of labels

treedbr

list of trees from Dependent Binary Relevance modeling, one for each label; refer to an individual tree as treedbr[[i]], i = 1, ..., no. of labels

Examples

data <- PrInDT::data_land # load data
dataclean <- data[,c(1:7,23:24,11:13,22,8:10)]  # only relevant features
indind <- c(1:9) # original predictors
indaddind <- c(10:13) # additional predictors
inddep <- c(14:16) # dependent variables
dataclean <- na.omit(dataclean)
ctestv <- NA
N <- 21  # no. of repetitions
perc <- c(0.45,0.05,0.25)   # percentages of observations of larger class, 
#                             1 per dependent class variable
perc2 <- c(0.75,0.95,0.75)  # percentages of observations of smaller class, 
#                             1 per dependent class variable
##
# Call PrInDT: language by language
##
outmult <- PrInDTMulab(dataclean,ctestv=NA,conf.level=0.95,percl=perc,percs=perc2,N=N,
                  indind=indind,indaddind=indaddind,inddep=inddep)
print(outmult)
plot(outmult)

---

Multiple label classification based on all observations

Description

Multiple label classification based on all observations. We consider two ways of modeling (Binary relevance modeling, dependent binary modeling) and three ways of model evaluation: single assessment, joint assessment, and true prediction (see the Value section for more information).
Interpretability is checked (see ctestv).
Variables should be arranged in 'datain' according to indices specified in 'indind', 'indaddind', and 'inddep'.
Please note that the dependent variables have to be specified as dummies, i.e. as 'absent' (value 0) or 'present' (value 1).
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Reference
Probst, P., Au, Q., Casalicchio, G., Stachl, C., and Bischl, B. 2017. Multilabel Classification with R Package mlr. arXiv:1703.08991v2

Usage

PrInDTMulabAll(datain,classnames=NA,ctestv=NA,conf.level=0.95,indind=NA,
               indaddind=NA,inddep,minsplit=NA,minbucket=NA)

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)
classnames	names of class variables (character vector)
ctestv	Vector of character strings of forbidden split results; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
indind	indices of independent variables
indaddind	indices of additional predictors used in the case of dependent binary relevance modeling
inddep	indices of dependent variables
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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

accabr

model errors for Binary Relevance (single assessment) - only independent predictors are used for modeling one label at a time, the other labels are not used as predictors. The classification rules are trained on all observations. As the performance measure for the resulting classification rules, the balanced accuracy of the models for each individual label is employed.

errabin

combined error for Binary Relevance (joint assessment) - the best prediction models for the different labels are combined to assess the combined prediction. The 01-accuracy counts a label combination as correct only if all labels are correctly predicted. The hamming accuracy corresponds to the proportion of labels whose value is correctly predicted.

accadbr

model errors in Dependent Binary Relevance (Extended Model) (single assessment) - each label is trained by means of an extended model which not only includes the independent predictors but also the other labels. For these labels the truly observed values are used for estimation and prediction. In the extended model, further labels, which are not treated as dependent variables, can be used as additional predictors.

erraext

combined errors for Dependent Binary Relevance (Extended Model) (joint assessment)

erratrue

combined errors for Dependent Binary Relevance (True Prediction) - in the prediction phase, the values of all modeled labels are first predicted by the independent predictors only (see Binary Relevance) and then the predicted labels are used in the estimated extended model in a 2nd step to ultimately predict the labels.

coldata

column names of input data

inddep

indices of dependent variables (labels to be modeled)

treeabr

list of trees from Binary Relevance modeling, one tree for each label; refer to an individual tree as treeabr[[i]], i = 1, ..., no. of labels

treeadbr

list of trees from Dependent Binary Relevance modeling, one for each label; refer to an individual tree as treeadbr[[i]], i = 1, ..., no. of labels

Examples

data <- PrInDT::data_land # load data
dataclean <- data[,c(1:7,23:24,11:13,22,8:10)]  # only relevant features
indind <- c(1:9) # original predictors
indaddind <- c(10:13) # additional predictors
inddep <- c(14:16) # dependent variables
dataclean <- na.omit(dataclean)
ctestv <- NA
##
# Call PrInDTAll: language by language
##
outmultAll <- PrInDTMulabAll(dataclean,colnames(dataclean)[inddep],ctestv,conf.level=0.95,
                     indind,indaddind,inddep)
outmultAll
plot(outmultAll)

---

PrInDT analysis for a classification problem with multiple classes.

Description

PrInDT analysis for a classification problem with more than 2 classes. For each combination of one class vs. the other classes a 2-class PrInDT analysis is carried out.
The percentages for undersampling of the larger class ('percl' in PrInDT) are chosen so that the resulting sizes are comparable with the size of the smaller classes for which all their observations are used in undersampling ('percs' = 1 in PrInDT).
The class with the highest probability in the K (= number of classes) analyses is chosen for prediction.
Interpretability is checked (see 'ctestv'). The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

PrInDTMulev(datain,classname,ctestv=NA,N,conf.level=0.95,seedl=FALSE,
                                    minsplit=NA,minbucket=NA)

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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
N	Number of repetitions (integer > 0)
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1) (default = 0.95)
seedl	Should the seed for random numbers be set (TRUE / FALSE)? default = FALSE
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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

class

levels of class variable

trees

trees for the levels of the class variable; refer to an individual tree as trees[[k]], k = 1, ..., no. of levels

ba

balanced accuracy of combined predictions

conf

confusion matrix of combined predictions

ninterp

no. of non-interpretable trees

acc

balanced accuracies of best models for individual classes

Examples

datastrat <- PrInDT::data_zero
data <- na.omit(datastrat)
ctestv <- NA
data$rel[data$ETH %in% c("C1a","C1b","C1c") & data$real == "zero"] <- "zero1"
data$rel[data$ETH %in% c("C2a","C2b","C2c") & data$real == "zero"] <- "zero2"
data$rel[data$real == "realized"] <- "real"
data$rel <- as.factor(data$rel) # rel is new class variable
data$real <- NULL # remove old class variable
N <- 51
conf.level <- 0.99 # 1 - significance level (mincriterion) in ctree
out <- PrInDTMulev(data,"rel",ctestv,N,conf.level) 
out # print best models based on subsamples
plot(out) # corresponding plots

---

Conditional inference tree (ctree) for multiple classes on all observations

Description

ctree for more than 2 classes on all observations. Interpretability is checked (see 'ctestv'). The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

PrInDTMulevAll(datain,classname,ctestv=NA,conf.level=0.95,minsplit=NA,minbucket=NA)

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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1) (default = 0.95)
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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.

Value

treeall

ctree 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)
ctestv <- rbind('ETH == {C2a,C1a}', 'MLU == {1, 3}')
data$rel[data$ETH %in% c("C1a","C1b","C1c") & data$real == "zero"] <- "zero1"
data$rel[data$ETH %in% c("C2a","C2b","C2c") & data$real == "zero"] <- "zero2"
data$rel[data$real == "realized"] <- "real"
data$rel <- as.factor(data$rel) # rel is new class variable
data$real <- NULL # remove old class variable
conf.level <- 0.99 # 1 - significance level (mincriterion) in ctree
outAll <- PrInDTMulevAll(data,"rel",ctestv,conf.level) 
outAll # print model based on all observations
plot(outAll)

---

Regression tree resampling by the PrInDT method

Description

The function PrInDTreg realizes regression tree optimization to identify the best interpretable tree; interpretability is checked (see 'ctestv').
The relationship between the target variable 'regname' and all other factor and numerical variables in the data frame 'datain' is optimally modeled by means of 'N' repetitions of subsampling.
The optimization criterion is the R2 of the model on the validation sample 'valdat'.
Default for the validation sample is the full sample 'datain'.
Multiple subsampling percentages of observations and predictors can be specified (in 'pobs' and 'ppre', correspondingly).
The trees generated from subsampling can be restricted by rejecting unacceptable trees which include split results specified in the character strings of the vector 'ctestv'.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.
Besides the maximal R2, the minimal MAE (Mean Absolute Error) is reported.

Usage

PrInDTreg(datain,regname,ctestv=NA,N,pobs=c(0.9,0.7),ppre=c(0.9,0.7),
               conf.level=0.95,seedl=TRUE,minsplit=NA,minbucket=NA,valdat=datain)

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)
regname	name of regressand variable (character)
ctestv	Vector of character strings of forbidden split results; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
N	Number of repetitions (integer > 0)
pobs	Vector of resampling percentages of observations (numerical, > 0 and <= 1)
ppre	Vector of resampling percentages of predictor variables (numerical, > 0 and <= 1)
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
seedl	Should the seed for random numbers be set (TRUE / FALSE)? default = TRUE
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7
valdat	Validation data; default = datain

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). We 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.

Reference
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

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

meanint

Mean number of interpretable trees over the combinations of individual percentages in 'pobs' and 'ppre'

ctmax

best resampled regression tree on the validation data set

percmax

Best model achieved for %observations

perfeamax

Best model achieved for %predictors

maxR2

maximum R2 on the validation data set for resampled regression trees (for 'ctmax')

minMAE

minimum MAE (Mean Absolute Error) on the validation data set for resampled regression trees (for 'ctmax')

interpmax

interpretability of best tree 'ctmax'

ctmax2

second best resampled regression tree on the full data set

percmax2

second best model achieved for %observations

perfeamax2

second best model achieved for %features

max2R2

second best R2 on the validation data set for resampled regression trees (for 'ctmax2')

min2MAE

second best MAE on the validation data set for resampled regression trees (for 'ctmax2')

interp2max

interpretability of second-best tree 'ctmax2'

Examples

data <- PrInDT::data_vowel
data <- na.omit(data)
ctestv <- 'vowel_maximum_pitch <= 320'
N <- 30 # no. of repetitions
pobs <- c(0.70,0.60) # percentages of observations
ppre <- c(0.90,0.70) # percentages of predictors
outreg <- PrInDTreg(data,"target",ctestv,N,pobs,ppre)
outreg
plot(outreg)

---

Regression tree based on all observations

Description

Regression tree based on the full sample; interpretability is checked (see 'ctestv').
The relationship between the target variable 'regname' and all other factor and numerical variables in the data frame 'datain' is modeled based on all observations.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.
Besides the maximal R2, the minimal MAE (Mean Absolute Error) is reported.

Usage

PrInDTregAll(datain,regname,ctestv=NA,conf.level=0.95,minsplit=NA,minbucket=NA)

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)
regname	name of regressand variable (character)
ctestv	Vector of character strings of forbidden split results; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

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.

Value

treeall

tree based on all observations

R2All

goodness of fit of 'treeall' based on all observations

MAEAll

MAE of 'treeall' based on all observations

interpAll

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

Examples

data <- PrInDT::data_vowel
data <- na.omit(data)
ctestv <- 'vowel_maximum_pitch <= 320'
outreg <- PrInDTregAll(data,"target",ctestv)
outreg
plot(outreg)

---

Structured subsampling for regression

Description

The function PrInDTRstruc applies structured subsampling for finding an optimal subsample to model the relationship between the continuous variable 'regname' and all other factor and numerical variables in the data frame 'datain' by means of 'M' repetitions of subsampling from a substructure and 'N' repetitions of subsampling from the predictors. The optimization citerion is the goodness of fit R2 on the validation sample 'valdat' (default = 'datain'). 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 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).
In structured subsampling, 'M' repetitions of subsampling of the variable 'name' with 'Mit' different elements of each category in 'check' are realized. If 'Mit' is a list, each entry is employed individually. If 'Mit' is larger than the maximum available number of elements with a certain value of 'check', the maximum possible number of elements is used.
The number of predictors 'Pit' to be included in the model and the number of elements of the substructure 'Mit' have to be specified (lists allowed).
The percentages of involved observations and predictors can be controlled by the parameters 'pobs' and 'ppre', respectively.
The parameter 'Struc' is needed for all versions of subsampling except "b". Four different versions of structured subsampling exist:
a) just of the elements in the substructure with parameters 'M' and 'Mit',
b) just of the predictors with parameters 'N' and 'Pit',
c) of the predictors and for each subset of predictors subsampling of the elements of the substructure with parameters 'M', 'N', 'Mit', 'Pit', 'pobs', and 'ppre', and
d) of the elements of the substructure and for each of these subsets subsampling of the predictors with the same parameters as version c).
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.
Besides the maximal R2, the minimal MAE (Mean Absolute Error) is reported.

Repeated measurements can also be handled by this function (indrep=1). They 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) is assumed to be 'name' in 'Struc'.
The measure MAE is split according to the values of 'name'.

Usage

PrInDTRstruc(datain,regname,ctestv=NA,Struc=NA,vers="d",M=NA,Mit=NA,N=99,Pit=NA,
               pobs=c(0.9,0.7),ppre=c(0.9,0.7),conf.level=0.95,minsplit=NA,minbucket=NA,
               valdat=datain,indrep=0)

Arguments

datain	Input data frame with continuous target variable 'regname' and the influential variables, which need to be factors or numericals (transform logicals and character variables to factors)
regname	Name of target 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"
vers	Version of structured subsampling: "a", "b", "c", "d", cf. description; default = "d"
M	Number of repetitions of subsampling from substructure (integer) in versions "a" and "d"; default = 99
Mit	List of number of elements of substructure (integers); default = c((Cl-4):Cl), Cl = maximum number elements in both categories
N	Number of repetitions of subsampling from predictors (integer) in versions "b" and "c"; default = 99
Pit	List of number of predictors (integers) default = c(max(1,(D-3)):D), D = maximum number of predictors
pobs	Percentage(s) of observations for subsampling in versions "c" and "d"; default=c(0.9,0.7)
ppre	Percentage(s) of predictors for subsampling in versions "c" and "d"; default=c(0.9,0.7)
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7
valdat	Validation data; default = datain
indrep	Indicator for repeated measurements, i.e. more than one observation with the same class for each element; indrep=1: Struc=list(name) only; default = 0

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.4, 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

outmax

Best tree

interp

Number of interpretable trees, overall number of trees

ntmax

Size of training set for best tree

R2max

R squared of best tree

R2sub

Mean R squared of objects in substructure

MAEmax

MAE (Mean Absolute Error) of best tree

MAEsub

Mean MAE of objects in substructure

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

gmaxTrain

Training set for best tree

labs

labs from Struc

vers

Version used for structured subsampling

lMit

Number of different numbers of substructure elements

lPit

Number of different numbers of predictors

M

Number of repetitions of selection of substructure elements

N

Number of repetitions of selection of predictors

indrep

Indicator of repeated measurements: indrep=1

Examples

data <- PrInDT::data_vowel
data <- na.omit(data)
CHILDvowel <- data$Nickname
data$Nickname <- NULL
data$syllables <- 3 - data$syllables
data$speed <- data$word_duration / data$syllables  ## NEW NEW
names(data)[names(data) == "target"] <- "vowel_length"
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
name <- CHILDvowel
check <- "data$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)
outstruc <- PrInDTRstruc(data,"vowel_length",ctestv=ctestv,Struc=Struc,vers="d",
                  M=3,Mit=21,N=9,pobs=c(0.95,0.7),ppre=c(1,0.7),conf.level=0.99)
outstruc
plot(outstruc)

---

Two-stage estimation for regression

Description

The function R2SPrInDT applies 'N' repetitions of subsampling for finding an optimal subsample to model the relationship between the continuous variables with indices 'inddep' and all other factor and numerical variables in the data frame 'datain'.
Subsampling of observations and predictors uses the percentages in 'pobs1' and 'ppre1', respectively, at stage 1, and the percentages 'pobs2' and 'ppre2' at stage 2, accordingly. The optimization criterion is the goodness of fit R2 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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

R2SPrInDT(data,ctestv=NA,inddep,N=99,pobs1=c(0.90,0.70),ppre1=c(0.90,0.70),
                pobs2=pobs1,ppre2=ppre1,conf.level=0.95,minsplit=NA,minbucket=NA)

Arguments

data	Input data frame with continuous target variable 'regname' and the influential variables, which need to be factors or numericals (transform logicals and character variables to factors)
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.
inddep	Column indices of target variables in datain
N	Number of repetitions of subsampling from predictors (integer) in versions "b" and "c"; default = 99
pobs1	Percentage(s) of observations for subsampling at stage 1; default=c(0.9,0.7)
ppre1	Percentage(s) of predictors for subsampling at stage 1; default=c(0.9,0.7)
pobs2	Percentage(s) of observations for subsampling at stage 2"; default=pobs1
ppre2	Percentage(s) of predictors for subsampling at stage 2; default=ppre1
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.1, for further information.

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.

Value

models1

Best trees at stage 1

models2

Best trees at stage 2

depnames

names of dependent variables

R2both

R2s of best trees at both stages

Examples

data <- PrInDT::data_vowel
data <- na.omit(data)
CHILDvowel <- data$Nickname
data$Nickname <- NULL
syllable <- 3 - data$syllables
data$syllabels <- NULL
data$syllables <- syllable
data$speed <- data$word_duration / data$syllables
names(data)[names(data) == "target"] <- "vowel_length"
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
inddep <- c(13,9) 
out2SR <- R2SPrInDT(data,ctestv=ctestv,inddep=inddep,N=9,conf.level=0.99)
out2SR
plot(out2SR)

---

Repeated PrInDT for specified percentage combinations

Description

By the function RePrInDT, the function PrInDT is called repeatedly according to all combinations of the percentages specified in the vectors 'plarge' and 'psmall'.
The relationship between the two-class factor variable 'classname' and all other factor and numerical variables in the data frame 'datain' is optimally modeled by means of 'N' repetitions of undersampling.
The optimization citerion is the balanced accuracy on the validation sample 'valdat' (default = full input sample 'datain').
The trees generated from undersampling can be restricted by rejecting unacceptable trees which include split results specified in the character strings of the vector 'ctestv'.
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'.
The parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Reference
Weihs, C., Buschfeld, S. 2021c. Repeated undersampling in PrInDT (RePrInDT): Variation in undersampling and prediction, and ranking of predictors in ensembles. arXiv:2108.05129

Usage

RePrInDT(datain, classname, ctestv=NA, N, plarge, psmall, conf.level=0.95,
       thres=0.5, stratvers=0, strat=NA, seedl=TRUE,minsplit=NA,minbucket=NA,
       valdat=datain)

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; (see function PrInDT for details.) If no restrictions exist, the default = NA is used.
N	Number of repetitions (integer > 0)
plarge	Vector of undersampling percentages of larger class (numerical, > 0 and <= 1)
psmall	Vector of undersampling percentages of smaller class (numerical, > 0 and <= 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
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7
valdat	Validation data; default = datain

Details

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

treesb

best trees for the different percentage combinations; refer to an individual tree as treesb[[k]], k = 1, ..., length(plarge)*length(psmall)

acc1st

accuracies of best trees on full sample

acc3en

accuracies of ensemble of 3 best trees on full sample

simp_m

mean of permutation losses for the predictors

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}')
N <- 51  # no. of repetitions
conf.level <- 0.99 # 1 - significance level (mincriterion) in ctree
psmall <- c(0.95,1)     # percentages of the small class
plarge <- c(0.09,0.1)  # percentages of the large class
outRe <- RePrInDT(data,"real",ctestv,N,plarge,psmall,conf.level) 
outRe
plot(outRe)

---

Interdependent estimation for classification

Description

The function SimCPrInDT applies interdependent estimation (endogenous case) for finding an optimal model for relationships between the two-class factor variables specified as column indices of 'data' in the vector 'inddep' and all other factor and numerical variables in the data frame 'data' by means of 'N' repetitions of random subsampling with percentages 'percl' for the large classes and 'percs' for the small classes. One percentage of observations for each dependent variable has to be specified for the larger and the smaller class. For example, for three dependent variables, 'percl' consists of three percentages specified in the order in which the dependent variables appear in 'inddep'.
The dependent variables have to be specified as dummies, i.e. as 'property absent' (value 0) or 'property present' (value 1).
The optimization citerion is the balanced accuracy on the full sample.
In an additional step, the mean balanced accuracy over all class variables is optimized (joint optimization).
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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

SimCPrInDT(data,ctestv=NA,inddep,percl,percs,N=99,M,psize,conf.level=0.95,
                                  minsplit=NA,minbucket=NA)

Arguments

data	Input data frame with class factor variables and the influential variables, which need to be factors or numericals (transform logicals and character variables to factors)
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.
inddep	indices of dependent variables
percl	list of undersampling percentages of larger class (numerical, > 0 and <= 1): one per dependent class variable in the same order as in 'inddep'
percs	list of undersampling percentage of smaller class (numerical, > 0 and <= 1); one per dependent class variable in the same order as in 'inddep'
N	no. of repetitions of subsampling of observations (integer > 0); default = 99
M	no. of repetitions of subsampling of predictors
psize	no. of predictors in the subsamples of the predictors
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.2, for further information.

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.

Value

models1

Best trees at stage 1

models2

Best trees at stage 2

models3

Best trees from mean maximization

classnames

names of classification variables

baAll

balanced accuracies of best trees at both stages

Examples

data <- PrInDT::data_land # load data
dataclean <- data[,c(1:7,23:24,11:13,22,8:10)]  # only relevant features
inddep <- c(14:16) # dependent variables
dataland <- na.omit(dataclean)
ctestv <- NA
perc <- c(0.45,0.05,0.25)   # percentages of observations of larger class, 
# 1 per dependent class variable
perc2 <- c(0.75,0.95,0.75)  # percentages of observations of smaller class, 
# 1 per dependent class variable
outland <- SimCPrInDT(dataland,percl=perc,percs=perc2,N=9,inddep=inddep,M=2,psize=10)
outland
plot(outland)

---

Interdependent estimation for classification-regression mixtures

Description

The function SimMixPrInDT applies structured subsampling for finding an optimal subsample to model the relationship between the dependent variables specified in the sublist 'targets' of the list 'datalist' and all other factor and numerical variables in the corresponding individual data frame specified in the sublist 'datanames' of the list 'datalist' in the same order as 'targets'. The data frames have to be different of each other!
The function is prepared to handle classification tasks with 2 or more classes and regression tasks. At first stage, the targets are estimated based on the full sample of all exogenous variables and on summaries of the observed endogenous variables.
For generating summaries, the variables representing the substructure have to be specified in the sublist 'datastruc' of 'datalist'.
The sublist 'summ' of 'datalist' includes for each discrete target the classes for which you want to calculate the summary percentages and for each continuous target just NA (in the same order as in the sublist 'targets'). For a discrete target in this list, you can provide a sublist of classes to be combined (for an example see the below example).
At second stage, structured subsampling is used for improving the models from first stage. The substructure of the observations used for structured subsampling is specified by the list 'Struc' which here only consists of the name 'check' of the variable with the information about the categories of the substructure (without specification of the dataset names already specified in 'datanames', see example below), 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).
In structured subsampling, first 'M' repetitions of subsampling of the variable 'name' with 'nsub' different elements of each category in 'check' are realized. If 'nsub' is a list, each entry is employed individually. If 'nsub' is larger than the maximum available number of elements with a certain value of 'check', the maximum possible number of elements is used. Then, for each of the subsamples 'N' repetitions of subsampling in classification or regression with the specified percentages of classes, observations, and predictors are carried out.
These percentages are specified in the matrix 'percent', one row per estimation task. For binary classification tasks, percentages 'percl' and 'percs' for the larger and the smaller class have to be specified. For multilevel classification tasks, NA is specified (see the below example) since the percentages are generated automatically. For regression tasks, 'pobs' and 'ppre' have to be specified for observations and predictors, respectively.
The optimization citerion is balanced accuracy for classification and goodness of fit R2 for regression on the full sample, respectively. At stage 2, the models are optimized individually. At stage 3, the models are optimized on the maximum of joint elements in their substructures.
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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

SimMixPrInDT(datalist,ctestv=NA,Struc,M=12,N=99,nsub,percent=NA,conf.level=0.95,
                                      minsplit=NA,minbucket=NA)

Arguments

datalist	list(datanames,targets,datastruc,summ) Input data: For specification see the above description
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) Paprametes for structured subsampling, as explained in the desciption above.
M	Number of repetitions of subsampling of elements of substructure; default = 12
N	Number of repetitions of subsampling for predictors (integer); default = 99
nsub	(List of) numbers of different elements of substructure per subsample
percent	matrix of percent spefications: For specification see the above description; default: 'percent = NA' meaning default values for percentages.
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.2, for further information.

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.

Value

modelsF

Best trees at stage 1 (Full sample)

modelsI

Best trees at stage 2 (Individual optimization)

modelsJ

Best trees at stage 3 (Joint optimization)

depnames

names of dependent variables

nmod

number of models of tasks

nlev

levels of tasks

accAll

accuracies of best trees at both stages

Examples

# zero data
datazero <- PrInDT::data_zero
datazero <- na.omit(datazero) # cleaned full data: no NAs
names(datazero)[names(datazero)=="real"] <- "zero"
CHILDzero <- PrInDT::participant_zero
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
##
# multi-level data
datastrat <- PrInDT::data_zero
datamult <- na.omit(datastrat)
# ctestv <- NA
datamult$mult[datamult$ETH %in% c("C1a","C1b","C1c") & datamult$real == "zero"] <- "zero1"
datamult$mult[datamult$ETH %in% c("C2a","C2b","C2c") & datamult$real == "zero"] <- "zero2"
datamult$mult[datamult$real == "realized"] <- "real"
datamult$mult <- as.factor(datamult$mult) # mult is new class variable
datamult$real <- NULL # remove old class variable
CHILDmult <- CHILDzero
##
# vowel data
data <- PrInDT::data_vowel
data <- na.omit(data)
CHILDvowel <- data$Nickname
CHILDvowel <- as.factor(gsub("Nick","P",CHILDvowel))
data$Nickname <- NULL
syllable <- 3 - data$syllables
data$syllabels <- NULL
data$syllables <- syllable
data$speed <- data$word_duration / data$syllables
names(data)[names(data) == "target"] <- "vowel"
datavowel <- data
##
# function preparation and call
# datalist and percent
datanames <- list("datazero","datamult","datavowel")
targets <- c("zero","mult","vowel")
datastruc <- list(CHILDzero,CHILDmult,CHILDvowel)
summult <- paste("zero1","zero2",sep=",")  
summ <- c("zero",summult,NA)
datalist <- list(datanames=datanames,targets=targets,datastruc=datastruc,summ=summ)
percent <- matrix(NA,nrow=3,ncol=2)
percent[1,] <- c("percl=0.075","percs=0.9") # percentages for datazero
# no percentages needed for datapast
percent[3,] <- c("pobs=0.9","ppre=c(0.9,0.8)") # percentages for datavowel
# substructures
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(check="ETH",labs=labs)
outSimMix <- SimMixPrInDT(datalist,ctestv=ctestv,Struc=Struc,M=2,N=9,nsub=c(19,20),
                       percent=percent,conf.level=0.99)
outSimMix
plot(outSimMix)+

---

Interdependent estimation for regression

Description

The function SimRPrInDT applies structured subsampling for finding an optimal subsample to model the relationship between the continuous variables with indices 'inddep' and all other factor and numerical variables in the data frame 'datain'.
The substructure of the observations used for subsampling 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).
In structured subsampling, first 'M' repetitions of subsampling of the variable 'name' with 'nsub' different elements of each category in 'check' are realized. If 'nsub' is a list, each entry is employed individually. If 'nsub' is larger than the maximum available number of elements with a certain value of 'check', the maximum possible number of elements is used. Then, for each of the subsamples 'N' repetitions of subsampling of 'ppre' percentages of the predictors are carried out.
Subsampling of observations can additionally be restricted to 'pobs' percentages.
The optimization citerion is the goodness of fit R2 on the full sample. At stage 2, the models are optimized individually. At stage 3, the mean of accuracies is optimized over all models.
Struc=NA causes random subsampling of observations instead of structured subsampling.
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 parameters 'conf.level', 'minsplit', and 'minbucket' can be used to control the size of the trees.

Usage

SimRPrInDT(data,ctestv=NA,Struc=NA,inddep,N=99,pobs=0.9,ppre=c(0.9,0.7),
                M=1,nsub=1,conf.level=0.95,minsplit=NA,minbucket=NA)

Arguments

data	Input data frame with continuous target variables with column indices 'inddep' and the influential variables, which need to be factors or numericals (transform logicals and character variables to factors)
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
inddep	Column indices of target variables in datain
N	Number of repetitions of subsampling (integer) of predictors; default = 99
pobs	Percentage(s) of observations for subsampling; default=0.9
ppre	Percentage(s) of predictors for subsampling; default=c(0.9,0.7)
M	Number of repetitions of subsampling of elements of substructure
nsub	(List of) numbers of different elements of substructure per subsample
conf.level	(1 - significance level) in function ctree (numerical, > 0 and <= 1); default = 0.95
minsplit	Minimum number of elements in a node to be splitted; default = 20
minbucket	Minimum number of elements in a node; default = 7

Details

See Buschfeld & Weihs (2025), Optimizing decision trees for the analysis of World Englishes and sociolinguistic data. Cambridge University Press, section 4.5.6.2, for further information.

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.

Value

modelsF

Best trees at stage 1

modelsI

Best trees for the different values of 'nsub' at stage 2

modelsJ

Best trees for the different values of 'nsub' after mean optimization

Struc

Used structure

msub

Best numbers of elements in substructure: 2nd stage, 3rd stage

depnames

names of dependent variables

R2All

R2s of best trees at stages 1, 2, mean max.

Examples

data <- PrInDT::data_vowel
data <- na.omit(data)
CHILDvowel <- data$Nickname
data$Nickname <- NULL
syllable <- 3 - data$syllables
data$syllabels <- NULL
data$syllables <- syllable
data$speed <- data$word_duration / data$syllables
names(data)[names(data) == "target"] <- "vowel_length"
# interpretation restrictions (split exclusions)
ctestv <- rbind('ETH == {C2a, C1a}','MLU == {1, 3}') # split exclusions
# structure definition
name <- CHILDvowel
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)
# column indices of dependent variables
inddep <- c(13,9) 
outSimR <- SimRPrInDT(data,ctestv=ctestv,Struc=Struc,inddep=inddep,N=3,M=2,
                   nsub=c(19,20),conf.level=0.99)
outSimR
plot(outSimR)

---