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

Response Styles in Rating Scales: Simultaneous Modeling of Content-Related Effects and the Tendency to Middle or Extreme Categories

Heterogeneity in response styles can affect the conclusions drawn from rating scale data. In particular, biased estimates can be expected if one ignores a tendency to middle categories or to extreme categories. An adjacent categories model is proposed that simultaneously models the content-related effects and the heterogeneity in response styles. By accounting for response styles, it provides a simple remedy for the bias that occurs if the response style is ignored. The model allows to include explanatory variables that have a content-related effect as well as an effect on the response style. A visualization tool is developed that makes the interpretation of effects easily accessible. The proposed model is embedded into the framework of multivariate generalized linear model, which entails that common estimation and inference tools can be used. Existing software can be used to fit the model, which makes it easy to apply

Tree-structured scale effects in binary and ordinal regression

In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity. In particular since it has been demonstrated that misleading effects can occur if one ignores the presence of a scaling component, it is important to account for potential scaling effects in the regression model, which is not possible in available recursive partitioning methods. The proposed recursive partitioning method yields two trees: one for the location and one for the scaling. They show in a simple interpretable way how variables interact to determine the binary or ordinal response. The developed algorithm controls for the global significance level and automatically selects the variables that have an impact on the response. The modeling approach is illustrated by several real-world applications

Response Styles in the Partial Credit Model

In the modelling 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 modelling 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