In contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using…

The isotonic ordinal probabilistic model (ISOP) is introduced as a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal, and dichotomous variables. Fundamental theorems on dichotomous and polytomous weakly independent ordered systems are derived, and testing at the observed empirical level is discussed.…

Ordinal measurement is the rank ordering of individuals in a population. For ordinal measurement, the concept of an individual propensity distribution is his or her true score. Estimation of, as well as other aspects of the distribution, are discussed. (Author/JKS)

Introduces and discusses the rationale and procedures of two nonparametric approaches to estimating the operating characteristic of a discrete item response, or the conditional probability, given the latent trait, that the examinee's response be that specific response. (SLD)

The Lorge-Solomon approach to group problem solving situations and its extensions to trichotomous response situations are examined by use of the maximum likelihood methods. (DG)

An alternative to the uniform probability distribution model for ordinal data is considered. Implications for statistics and for test theory are discussed. (JKS)

The asymptotic posterior normality of latent variable distributions is established under very general and appropriate hypotheses, providing a probabilistic basis for assessing ability estimation/prediction accuracy in the long test case, as well as a first step in making the Dutch Identity conjecture rigorous. (SLD)

A nonparametric multicategorical model for multiple-choice data is proposed as an extension of the binary spline model of J. O. Ramsay and M. Abrahamowicz (1989). Results of two Monte Carlo studies illustrate the model, which approximates probability functions by rational splines. (SLD)