The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model.

A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models.

Effect of Purification Procedures on DIF Analysis in IRTPRO.

Purification of the test has been a well-accepted procedure in enhancing the performance of tests for differential item functioning (DIF). As defined by Lord, purification requires reestimation of ability parameters after removing DIF items before conducting the final DIF analysis. IRTPRO 3 is a recently updated program for analyses in item response theory, with built-in DIF tests but not purification procedures. A simulation study was conducted to investigate the effect of two new methods of purification. The results suggested that one of the purification procedures showed significantly improved power and Type I error. The procedure, which can be cumbersome by hand, can be easily applied by practitioners by using the web-based program developed for this study.