# Find DIF in Generalized Partial Credit Models Performs GPCMlasso, a method to identify DIF in Generalized Partial Credit Models. A joint parametric model is set up based on an IRT model chosen by the user. Several variables can be considered simultaneously. For each pair between variable and item, a parametric DIF effect is introduced which indicates DIF if the respective parameter is selected (estimated to be unequal zero). Parameter selection is done using a lasso-type penalization term. package ## Examples ```r data(tenseness_small) ## formula for simple model without covariates form.0 <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~0")) ###### ## fit simple RSM where loglikelihood and score function are evaluated parallel on 2 cores rsm.0 <- GPCMlasso(form.0, tenseness_small, model = "RSM", control= ctrl_GPCMlasso(cores=2)) rsm.0 ## Not run: ## formula for model with covariates (and DIF detection) form <- as.formula(paste("cbind(",paste(colnames(tenseness_small)[1:5],collapse=","),")~.")) ###### ## fit GPCM model with 10 different tuning parameters gpcm <- GPCMlasso(form, tenseness_small, model = "GPCM", control = ctrl_GPCMlasso(l.lambda = 10)) gpcm plot(gpcm) pred.gpcm <- predict(gpcm) trait.gpcm <- trait.posterior(gpcm) ###### ## fit RSM, detect differential step functioning (DSF) rsm.DSF <- GPCMlasso(form, tenseness_small, model = "RSM", DSF = TRUE, control = ctrl_GPCMlasso(l.lambda = 10)) rsm.DSF plot(rsm.DSF) ## create binary data set tenseness_small_binary <- tenseness_small tenseness_small_binary[,1:5][tenseness_small[,1:5]>1] <- 2 ###### ## fit and cross-validate Rasch model set.seed(1860) rm.cv <- GPCMlasso(form, tenseness_small_binary, model = "RM", cv = TRUE, control = ctrl_GPCMlasso(l.lambda = 10)) rm.cv plot(rm.cv) ## End(Not run) ``` ## References Schauberger, Gunther and Mair, Patrick (2019): A Regularization Approach for the Detection of Differential Item Functioning in Generalized Partial Credit Models, **Behavior Research Methods**, [https://link.springer.com/article/10.3758/s13428-019-01224-2](https://link.springer.com/article/10.3758/s13428-019-01224-2) ## See Also `GPCMlasso` ## Author(s) Gunther Schauberger gunther.schauberger@tum.de

GPCMlasso-package