# Two-stage estimation for regression 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. ```r 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 ## Returns - **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 ## 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. ## Examples ```r 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) ```

R2SPrInDT function