Detection of Uniform and Non-Uniform Differential Item Functioning by Item Focussed Trees

Detection of differential item functioning by use of the logistic modelling approach has a long tradition. One big advantage of the approach is that it can be used to investigate non-uniform DIF as well as uniform DIF. The classical approach allows to detect DIF by distinguishing between multiple groups. We propose an alternative method that is a combination of recursive partitioning methods (or trees) and logistic regression methodology to detect uniform and non-uniform DIF in a nonparametric way. The output of the method are trees that visualize in a simple way the structure of DIF in an item showing which variables are interacting in which way when generating DIF. In addition we consider a logistic regression method in which DIF can by induced by a vector of covariates, which may include categorical but also continuous covariates. The methods are investigated in simulation studies and illustrated by two applications.Comment: 32 pages, 13 figures, 7 table

Sparser Ordinal Regression Models Based on Parametric and Additive Location-Shift Approaches

The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modelling. While proportional odds models are often too simple, non-proportional odds models are typically unnecessary complicated and seem widely dispensable. In addition, the class of location-shift models is extended to allow for smooth effects. The additive location-shift model contains two functions for each explanatory variable, one for the location and one for dispersion. It is much sparser than hard-to-handle additive models with category-specific covariate functions but more flexible than common vector generalised additive models. An R package is provided that is able to fit parametric and additive location-shift models

Transition Models for Count Data: a Flexible Alternative to Fixed Distribution Models

A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared by utilizing several real data applications.Comment: 24 pages, 8 figures, 4 table