A new diagnostic tool for the identification of differential item functioning (DIF) is proposed. Classical approaches to DIF allow to consider only few subpopulations like ethnic groups when investigating if the solution of items depends on the membership to a subpopulation. We propose an explicit model for differential item functioning that includes a set of variables, containing metric as well as categorical components, as potential candidates for inducing DIF. The ability to include a set of covariates entails that the model contains a large number of parameters. Regularized estimators, in particular penalized maximum likelihood estimators, are used to solve the estimation problem and to identify the items that induce DIF. It is shown that the method is able to detect items with DIF. Simulations and two applications demonstrate the applicability of the method.

Most common analysis tools for the detection of differential item functioning (DIF) in item response theory are restricted to the use of single covariates. If several variables have to be considered, the respective method is repeated independently for each variable. We propose a regularization approach based on the lasso principle for the detection of uniform DIF. It is applicable to a broad range of polytomous item response models with the generalized partial credit model as the most general case. A joint model is specified where the possible DIF effects for all items and all covariates are explicitly parameterized. The model is estimated using a penalized likelihood approach that automatically detects DIF effects and provides trait estimates that correct for the detected DIF effects from different covariates simultaneously. The approach is evaluated by means of several simulation studies. An application is presented using data from the children's depression inventory. Keywords Differential item functioning • DIF • Generalized partial credit model • Regularization • Lasso • GPCMlasso

The return of the Eurasian Lynx to Central Europe has led to a number of conflicts. A primary subject of discussion involves its predation on other wildlife species. Here, we investigated the influence of lynx on its main prey, Roe Deer, in the Bavarian Forest National Park in south-eastern Germany. We compared the survival rates of deer before and after reintroduction of lynx. The analysis is based on data from 1984 to 1988 and 2005 to 2008 of 88 and 99 radio-collared Roe Deer, respectively. During the first period, 35 deer deaths were documented; during the second period, 41 deaths were documented. The causes of death in the second period were lynx 44%, road kill 15%, hunting 12%, and other causes 29%. We used the Cox model to determine the influence of covariables on the hazard rate, which made it possible to consider interactions between the variables. The resulting model includes the four main effects sex, age, presence of lynx, and severity of first winter, and the three interactions-presence of lynx:sex, age:severity of first winter, and sex:severity of first winter, which had a statistically significant influence on Roe Deer survival.

In the modeling of ordinal responses in psychological measurement and survey-based research, response styles that represent specific answering patterns of respondents are typically ignored. One consequence is that estimates of item parameters can be poor and considerably biased. The focus here is on the modeling of a tendency to extreme or middle categories. An extension of the partial credit model is proposed that explicitly accounts for this specific response style. In contrast to existing approaches, which are based on finite mixtures, explicit person-specific response style parameters are introduced. The resulting model can be estimated within the framework of generalized mixed linear models. It is shown that estimates can be seriously biased if the response style is ignored. In applications, it is demonstrated that a tendency to extreme or middle categories is not uncommon. A software tool is developed that makes the model easy to apply.