# Detection of Differential Item Functioning Using the Lasso Approach: Selection of Optimal $\lambda$ via Cross-Validation Performs DIF detection using a lasso-penalized logistic regression model for dichotomous items and selects the optimal penalty parameter $\lambda$ via cross-validation. ```r lassoDIF.CV(Data, group, nfold = 5, lambda = NULL, ...) ``` ## Arguments - `...`: Additional arguments passed to internal methods. - `Data`: A numeric data frame or matrix: either only the item responses or the item responses with a group membership column. - `group`: A numeric or character vector: either a vector of group membership or a column index/name indicating group membership in `Data`. - `nfold`: Integer: the number of folds used in cross-validation. Default is 5. - `lambda`: Optional numeric vector of $\lambda$ values to be used in the penalization path. If `NULL`, a default sequence is used. ## Returns A list with the following components: - **DIFitems**: Indices of items flagged as exhibiting DIF. - **DIFpars**: Matrix of estimated DIF parameters for each item. - **crit.value**: Cross-validation criterion values (deviance) across the $\lambda$ path. - **crit.type**: The type of criterion used, here `"cv"`. - **lambda**: Vector of $\lambda$ values considered. - **opt.lambda**: The optimal $\lambda$ value selected via cross-validation. - **glmnet.fit**: Fitted `glmnet` model object. ## Details This function detects uniform differential item functioning (DIF) using a lasso-penalized logistic regression model and selects the penalty parameter $\lambda^*$ that minimizes cross-validation error. For this selected value, the function returns the estimated DIF parameters for all items and flags those with non-zero DIF effects. Note: The performance of the method depends on choices such as the number of folds and the grid of $\lambda$ values. We strongly recommend testing different configurations to assess the robustness of the results before interpretation. ## References Magis, D., Tuerlinckx, F., & De Boeck, P. (2015). Detection of Differential Item Functioning Using the Lasso Approach. Journal of Educational and Behavioral Statistics, 40(2), 111–135. https://doi.org/10.3102/1076998614559747 ## Author(s) David Magis Data science consultant at IQVIA Belux Brussels, Belgium Carl F. Falk Department of Psychology McGill University (Canada) carl.falk@mcgill.ca , [https://www.mcgill.ca/psychology/carl-f-falk](https://www.mcgill.ca/psychology/carl-f-falk) Sebastien Beland Faculte des sciences de l'education Universite de Montreal (Canada) sebastien.beland@umontreal.ca ## Examples ```r ## Not run: # With the Verbal data set data(verbal) Dat <-verbal[,1:20] Member <-verbal[,26] # Using cross-validation set.seed(1234) cv.res <- lassoDIF.CV(Dat, Member, nfold=5) cv.res # With simulated data It <- 15 # number of items ItDIFa <- NULL ItDIFb <- c(1,3) NR <- 100 # number of responses for group 1 (reference) NF <- 100 # number of responses for group 2 (focal) a <- rep(1,It) # for tests: runif(It,0.2,.5) b <- rnorm(It,1,.5) Gb <- rep(2,2) # Group value for U-DIF Ga <- 0 # Group value for NU-DIF: need to be fix to 0 for U-DIF Out1 <- SimDichoDif(It,ItDIFa,ItDIFb,NR,NF,a,b,Ga,Gb) Dat<-Out1$data[,1:15] Member<-Out1$data[,16] set.seed(1234) # appears to be sensitive to random number seed cv.res <- lassoDIF.CV(Dat, Member, nfold=5) cv.res ## End(Not run) ```

lassoDIF.CV function