Robustness of the School-Level Polytomous Irt Model

Abstract

Robustness of the school-level, polytomous IRT model to violations of the assumptions that (a) student ability is normally distributed within schools, (b) the within-school distribution of student ability has constant variance across schools, and (c) the mean student ability for each school is distributed normally across schools was assessed in a computer simulation study. The study considered variation of the intraclass correlation (the ratio of the variance of the school abilities to the variance of the individual abilities of the total aggregated student population, with values of 0.1, 0.3, and 0.5), the school size (ranging from 20 to 140), and the true school ability, defined as the mean of the abilities of the students in a school. When the assumptions were violated, the actual precision of estimating school ability was typically equal to or somewhat worse than the nominal precision; but in the vast majority of cases, the differences were not of practical importance.