Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

In sequential mastery testing (SMT), assessment via computer is used to classify examinees into one of two mutually exclusive categories. Unlike paper-and-pencil tests, SMT has the capability to use variable-length stopping rules. One approach to shortening variable-length tests is stochastic curtailment, which halts examination if the probability…

Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Lof test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte…

A reliability study is illustrated in which subjects are judged on a dichotomous trait by different sets of judges, possibly unequal in number. A kappa-like measure of reliability is proposed, its correspondence to an intraclass correlation coefficient is pointed out, and a test for its statistical significance is presented. (Author/CTM)

Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total…

Four indexes of agreement between ratings of a person that correct for chance and are interpretable as intraclass correlation coefficients for different analysis of variance models are investigated. Relationships among the estimators are established for finite samples, and the equivalence of these estimators in large samples is demonstrated. (SLD)

Type I error rates were examined for several fit indices available in GGUM2000: extensions of Infit, Outfit, Andrich's X(2), and the log-likelihood ratio X(2). Infit and Outfit had Type I error rates much lower than nominal alpha. Andrich's X(2) had Type I error rates much higher than nominal alpha, particularly for shorter tests or larger sample…

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)