Person fit statistics are considered for dichotomous item response models. The asymptotic null distribution is derived for statistics which are linear in the item responses, and in which the ability parameter is replaced by an estimate. This allows the asymptotically correct standardization of linear person fit statistics with estimated ability parameter. The fact that the ability parameter is estimated usually decreases the asymptotic variance.

The paper takes up the problem of performing all pairwise comparisons among J independent groups based on 20% trimmed means. Currently, a method that stands out is the percentile-t bootstrap method where the bootstrap is used to estimate the quantiles of a Studentized maximum modulus distribution when all pairs of population trimmed means are equal. However, a concern is that in simulations, the actual probability of one or more Type I errors can drop well below the nominal level when sample sizes are small. A practical issue is whether a method can be found that corrects this problem while maintaining the positive features of the percentile-t bootstrap. Three new methods are considered here, one of which achieves the desired goal. Another method, which takes advantage of theoretical results by Singh (1998), performs almost as well but is not recommended when the smallest sample size drops below 15. In some situations, however, it gives substantially shorter confidence intervals.

The linear logistic test model (LLTM) specifies the item parameters as a weighted sum of basic parameters. The LLTM is a special case of a more general nonlinear logistic test model (NLTM) where the weights are partially unknown. This paper is about the identifiability of the NLTM. Sufficient and necessary conditions for global identifiability are presented for a NLTM where the weights are linear functions, while conditions for local identifiability are shown to require a model with less restrictions. It is also discussed how these conditions are checked using an algorithm due to Bekker, Merckens, and Wansbeek (1994). Several illustrations are given.

While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary array M into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes in M. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.

A Monte Carlo algorithm realizing a family of nonparametric tests for the Rasch model is introduced which are conditional on the item and subject marginals. The algorithm is based on random changes of elements of data matrices without changing the marginals; most powerful tests against all alternative hypotheses are given for which a monotone characteristic may be computed from the data matrix; alternatives may also be composed. Computation times are long, but exactp-values are approximated with the quality of approximation only depending on calculation time, but not on the number of persons. The power and the flexibility of the procedure is demonstrated by means of an empirical example where, among others, indicators for increased item similarities, the existence of subscales, violations of sufficiency of the raw score as well as learning processes were found. Many of the features described are implemented in the program T-Rasch 1.0 by Ponocny and Ponocny-Seliger (1999).

This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each step h=1,...,m is characterized by a parameter bh, and, for a subject with ability θ, Pr(X ≥ h; θ) = F(θ − bh). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(X≥h;θ)=Πr=1hG(θ−dr). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.