It is demonstrated that for polytomous items the monotone likelihood ratio (MLR) holds for the partial credit model. MLR does not necessarily hold if the slopes of the item response functions vary over items or item steps. MLR also does not hold for the graded response model. (Author/SLD)

Correspondence analysis (CA) aids analysis of residuals from independence models and decomposes the departure from independence in a two-way contingency table. CA of incomplete tables is proposed that decomposes the departure from the quasi-independence model. This procedure is equivalent to the French procedure for missing data--reconstitution of…

With reference to the authors' previous paper (1985), it is proposed that loglinear analysis can be used to detect interactions in a multiway contingency table and explore the form of these interactions with correspondence analysis. Correspondence analysis assists in finding a model with restrictions on the interaction parameters. (TJH)

This paper establishes the correspondence between an item response function and a unique set of item category response functions for the partial credit model and the graded response model. Theoretical and practical implications are discussed. (SLD)

The absence of the invariant item ordering (IIO) property in two nonparametric polytomous item response theory (IRT) models is discussed, and two nonparametric models are discussed that imply an IIO. Only two parametric polytomous IRT models are found to imply an IIO. A method is proposed to investigate whether an IIO is implied with empirical…

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions, especially those related to transfer to other distributions. Results are formulated as a series of theorems and corollaries that apply to…

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having…

A new concept of weakly parallel tests, in contrast to strongly parallel tests in latent trait theory, is proposed. Some criticisms of the fundamental concepts in classical test theory, such as the reliability of a test and the standard error of estimation, are given. (Author)

In this study, the statistical properties of extended caution indices are investigated, and their relationships to Guttman scales and to item and person response curves are discussed. Further, these indices are standardized, and an example of their potential usefulness for diagnosing students' misconceptions is shown. (Author/BW)

The axioms of a three-set Guttman simplex model are presented and the effects of relaxing the axioms for one of the three sets are examined. This model can be used to define longitudinal developmental scales. (NSF)

The problem of characterizing the manifest probabilities of a latent trait model is considered. The approach taken here differs from the standard approach in that a population of examinees is being considered as opposed to a single examinee. Particular attention is given to the Rasch model. (Author/JKS)

Three counterexamples demonstrate that the Dutch Identity conjecture of P. Holland about examinee ability (1990) does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving such strong conditions are given. (Author/SLD)

Proposed a new nonlinear structural equation model with fixed covariates to deal with some complicated substantive theory and developed a Bayesian path sampling procedure for model comparison. Illustrated the approach with an illustrative example using data from an international study. (SLD)

Presented nonparametric tests for testing the validity of polytomous unidimensional ordinal probabilistic polytomous item response theory models along with procedures for testing the comonotonicity of two item sets and for item selection. Describes advantages of the new approach. (SLD)