The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter [theta] is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given…

Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into…

We demonstrate the use of a multidimensional extension of the latent Markov model to analyse data from studies with repeated binary responses in developmental psychology. In particular, we consider an experiment based on a battery of tests which was administered to pre-school children, at three time periods, in order to measure their inhibitory…

Scalability coefficients play an important role in Mokken scale analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling…

Multinomial processing tree models are widely used in many areas of psychology. Their application relies on the assumption of parameter homogeneity, that is, on the assumption that participants do not differ in their parameter values. Tests for parameter homogeneity are proposed that can be routinely used as part of multinomial model analyses to…

The utility of the jackknife for constructing confidence intervals and testing hypotheses about the disattenuated correlation is evaluated for small samples. Results of computer simulations support the claim that the jackknife can be used to construct confidence intervals but has limited utility for testing hypotheses about the disattenuated…

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)

Exact conditional tests of independence in cross-classification tables are formulated based on chi square and other statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for table dimensions and sample sizes for which the tests are economically implemented on a computer are…

The Z-variance and Box-Scheffe tests for homogeneity of variance are both relatively simple to perform and readily utilized in complex, multi-factor designs. The Z-variance test is not robust against non-normality; the Box-Scheffe test is robust against non-normality but is not nearly as powerful as the Z-variance test. (Author/BJG)

The treatment of covariance matrices given by McDonald (1974) can be readily modified to cover hypotheses prescribing zeros and equalities in the correlation matrix rather than the covariance matrix, still with the convenience of the closed-form Least Squares solution and the classical Newton method. (Author/RC)

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. A variety of results are given here for the more complex case in which the specified values are not necessarily zero. (Author/JKS)

Four approximate statistical tests are considered for repeated measurement designs in which observations are multivariate normal with arbitrary variance-covariance matrices. (Author/JKS)

Individuals are classified in a cross-classification table where two behavioral observations on each individual determine the classification. The problem is to test certain structural models assumed to underlie the cross-classified observations. A minimum chi-square test procedure is proposed. (Author)

A variety of distributional assumptions for dissimilarity judgments in multidimensional scaling are considered, with the lognormal distribution being favored for most situations. Procedures for maximum likelihood estimation in this setting are described and examples are presented. (Author/JKS)