Complex Latent Variable Modeling in Educational Assessment

Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with powerful simulation-based estimation techniques are discussed. Furthermore, it is shown how the Bayes factor can be used to test relevant hypotheses in assessment using the College Basic Academic Subjects Examination (CBASE) data

Item Response Modeling of Multivariate Count Data With Zero Inflation, Maximum Inflation, and Heaping

Questionnaires that include items eliciting count responses are becoming increasingly common in psychology. This study proposes methodological techniques to overcome some of the challenges associated with analyzing multivariate item response data that exhibit zero inflation, maximum inflation, and heaping at preferred digits. The modeling framework combines approaches from three literatures: item response theory (IRT) models for multivariate count data, latent variable models for heaping and extreme responding, and mixture IRT models. Data from the Behavioral Risk Factor Surveillance System are used as a motivating example. Practical implications are discussed, and recommendations are provided for researchers who may wish to use count items on questionnaires

Modeling Socially Desirable Responding and Its Effects

The impact of socially desirable responding or faking on noncognitive assessments remains an issue of strong debate. One of the main reasons for the controversy is the lack of a statistical method to model such response sets. This article introduces a new way to model faking based on the assumption that faking occurs due to an interaction between person and situation. The technique combines a control group design with structural equation modeling and allows a separation of trait and faking variance. The model is introduced and tested in an example. The results confirm a causal nfluence of faking on means and covariance structure of a Big 5 questionnaire. Both effects can be reversed by the proposed model. Finally, a real-life criterion was implemented and predicted by both variance sources. In this example, it was the trait but not the faking variance that was predictive. Implications for research and practice are discussed

Multilevel IRT Modeling in Practice with the Package mlirt

Variance component models are generally accepted for the analysis of hierarchical structured data. A shortcoming is that outcome variables are still treated as measured without an error. Unreliable variables produce biases in the estimates of the other model parameters. The variability of the relationships across groups and the group-effects on individuals' outcomes differ substantially when taking the measurement error in the dependent variable of the model into account. The multilevel model can be extended to handle measurement error using an item response theory (IRT) model, leading to a multilevel IRT model. This extended multilevel model is in particular suitable for the analysis of educational response data where students are nested in schools and schools are nested within cities/countries.\u

The Use of Loglinear Models for Assessing Differential Item Functioning Across Manifest and Latent Examinee Groups

Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set