We consider the identification of a semiparametric multidimensional fixed effects item response model. Item response models are typically estimated under parametric assumptions about the shape of the item characteristic curves (ICCs), and existing results suggest difficulties in recovering the distribution of individual characteristics under…

Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the…

Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and…

The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both…

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…

Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of…

This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the…

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the…

A large class of rank tests which includes the "sign test" and Wilcoxon signed-ranks test is described. These distribution free tests provide a basis for testing various research hypotheses. Exact small sample and approximate large sample procedures are considered. Applications are presented including numerical examples. (Author/HG)

The (univariate) isotonic psychometric (ISOP) model (Scheiblechner, 1995) is a nonparametric IRT model for dichotomous and polytomous (rating scale) psychological test data. A weak subject independence axiom W1 postulates that the subjects are ordered in the same way except for ties (i.e., similarly or isotonically) by all items of a psychological…

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems is proven. Also, an additional approach is proposed. (Author/JKS)

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented. The algorithm is quick, simple and accurate. (Author)

A measure of multiple rank correlation is proposed for the situation of no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. The measure is equivalent to one proposed by Moran. (Author/JKS)

Six different algorithms to generate widely different non-normal distributions are reviewed. These algorithms are compared in terms of speed, simplicity, and generality of the technique. The advantages and disadvantages of using these algorithms are briefly discussed. (Author)