Hierarchical linear modeling (HLM) is often used to estimate the effects of socioeconomic status (SES) on academic achievement at different levels of an educational system. However, if a prior academic achievement measure is missing in a HLM model, biased estimates may occur on the effects of student SES and school SES. Phantom effects describe…

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL…