Comparing Attitudes Across Groups: An IRT-Based Item-Fit Statistic for the Analysis of Measurement Invariance:

Questionnaires for the assessment of attitudes and other psychological traits are crucial in educational and psychological research, and item response theory (IRT) has become a viable tool for scaling such data. Many international large-scale assessments aim at comparing these constructs across countries, and the invariance of measures across countries is thus required. In its most recent cycle, the Programme for International Student Assessment (PISA 2015) implemented an innovative approach for testing the invariance of IRT-scaled constructs in the context questionnaires administered to students, parents, school principals, and teachers. On the basis of a concurrent calibration with equal item parameters across all groups (i.e., languages within countries), a group-specific item-fit statistic (root mean square deviance [RMSD]) was used as a measure for the invariance of item parameters for individual groups. The present simulation study examines the statistic's distribution under different types and extents of (non)invariance in polytomous items. Responses to five 4-point Likert-type items were generated under the generalized partial credit model (GPCM) for 1,000 simulees in 50 groups each. For one of the five items, either location or discrimination parameters were drawn from a normal distribution. In addition to the type of noninvariance, the extent of noninvariance was varied by manipulating the variation of these distributions. The results indicate that the RMSD statistic is better at detecting noninvariance related to between-group differences in item location than in item discrimination. The study's findings may be used as a starting point to sensitivity analysis aiming to define cutoff values for determining (non)invariance.