It is a well-known problem in testing the fit of models to multinomial data that the full underlying contingency table will inevitably be sparse for tests of reasonable length and for realistic sample sizes. Under such conditions, full-information test statistics such as Pearson's X[superscript 2] and the likelihood ratio statistic G[superscript…

In this study, the Trends in International Mathematics and Science Study 2007 data were used to build mathematics achievement models of fourth graders in two East Asian school systems: Hong Kong and Singapore. In each school system, eight variables at student level and nine variables at school/class level were incorporated to build an achievement…

Despite the growing popularity of diagnostic classification models (e.g., Rupp, Templin, & Henson, 2010) in educational and psychological measurement, methods for testing their absolute goodness-of-fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics…