Developed a sandwich-type covariance matrix to evaluate parameters and provide a rescaled statistic to evaluate a hypothesized general multilevel model. A simulation study with a two-level factor model implies that the rescaled statistic is preferable. (SLD)

A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The probability integrals over the partitioned cubes forms a k-dimensional contingency table with ordered categories. A loglinear model with main effects plus two-way interactions provides an approximation for…

The accuracy of Kendall's chi square approximation (M. Kendall, 1962) to circular triad distributions was assessed by comparing estimated indices to enumerated values across upper and lower tails of cumulative proportions of circular triad distributions. In general, the approximation was found to be quite good, and its use is discussed. (SLD)

A model for preferential and triadic choice is derived in terms of weighted sums of central F distribution functions. It is a probabilistic generalization of Coombs' (1964) unfolding model from which special cases can be derived easily. This model for binary choice can be easily related to preference ratio judgments. (SLD)

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…

Derives the asymptotic normal distribution of the maximum likelihood estimator of Cronbach's alpha (under normality) for the case when no assumptions are made about the covariances among items. Also considers the asymptotic distribution for the special case of compound symmetry and when compared to the exact distribution. (Author/SLD)

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments such as might occur in educational research. Three applications illustrate the approach. (SLD)

Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…

The posterior distribution of the bivariate correlation is analytically derived given a data set where "X" is completely observed, but "Y" is missing at random for a portion of the sample. Interval estimates of the correlation are constructed from the posterior distribution in terms of the highest density regions. (SLD)

This paper demonstrates that two major tests for two-by-two tables, Fisher's exact and Pearson's chi-square tests, are highly related from a Bayesian perspective. A formal similarity is demonstrated in small samples, and reasons for the relationship are discussed. (SLD)

Two ideal-point probabilistic choice models from the external analysis of preferences are presented that allow for more flexible distributions of ideal-points. The first extends the probit model of W. Kamakura and R. Srivastava. The second is based on simplifying assumptions that lead to a multidimensional histogram of ideal-points. (SLD)

A general procedure is provided for comparing correlation coefficients between optimal linear composites. It allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from Monte Carlo…

Two-dimensional euclidean planes and additive trees are two of the most common representations of proximity data for multidimensional scaling. Guidelines for comparing these representations and discovering properties that could help identify which representation is more appropriate for a given data set are presented. (Author/JKS)

The frequencies of "m" independent "p-way" contingency tables are analyzed by a model that assumes that the ordinal category data in each of "m" groups are generated from a latent continuous multivariate normal distribution. The model permits analysis of several groups of individuals simultaneously. (TJH)

Presents a hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The approach combines the flexibility of semiparametric latent class models that assume common parameters for each subpopulation and the parsimony of random effects models that assume normal distributions for the regression parameters.…