The properties of nonmetric multidimensional scaling one explored by specifying statistical models, proving statistical consistency, and devloping hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. (Author/LMO)

The Pearson and likelihood ratio statistics are frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or non-subsuming relation. A subsuming relation exists when the parameters of the reduced model form a subset of those…

A Monte Carlo study was made of the recovery of cluster structure in binary data by five hierarchical techniques, with a view to finding which data structure factors influenced recovery and to determining differences between clustering methods with respect to these factors. (LMO)

A five by five covariance matrix representing longitudinal measurements at five occasions is used to illustrate that markedly different types of learning curves may generate indistinguishable covariance structures. An excellent fit of a simplex structure can be misleading. Common uses of covariance structure models for growth studies are…

Since computer programs have been available for estimating and testing linear causal models, these models have been used increasingly in the behavioral sciences. This paper discusses the problem that very different causal structures may fit the same set of data equally well. (Author/LMO)

Rasch model equatings of multilevel achievement test data before and after the deletion of misfitting persons were compared. Rasch equatings were also compared with an equating obtained using the equipercentile method. No basis could be found in the results for choosing between the two Rasch equatings. (Author/LMO)

A statistical test is described which determines homogeneity of effect size of an experiment series. An overall fit statistic is partitioned into between-class fit statistic and within-class fit statistic. These statistics permit assessment of differences between effect sizes for different classes and homogeneity of effect size within classes.…

A joint Bayesian estimation procedure for estimating parameters in the three-parameter logistic model is developed. Simulation studies show that the Bayesian procedure (1) ensures that the estimates stay in the parameter space and (2) produces better estimates than the joint maximum likelihood procedure. (Author/BS)

A general approach is proposed for modeling the structure of a r x s contingency table and for drawing marginal inferences about all parameters (e.g., interaction effects) in the model. The main approach is relevant whenever rs minus r minus s plus 1 is greater than or equal to 5. Military aptitude test data is used as illustration. (Author/LMO)

This article extends both the logic and the statistical procedures used in a recent analysis of Hyde's data on gender differences in cognitive abilities by Rosenthal and Rubin. The logic of a "model fitting" approach to meta-analysis is described. Relevant statistical procedures and goodness-of-fit tests are illustrated. (Author/BS)

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make…

Several multivariate statistical methodologies have been proposed to ensure objective and quantitative evaluation of the multitrait-multimethod matrix. The paper examines the performance of confirmatory factor analysis and covariance component models. It is shown, both empirically and formally, that confirmatory factor analysis is not a reliable…

This paper is part of a series of applied statistics monographs intended to provide supplementary reading for applied statistics students. In the present paper, derivations of the unbiased standard error of estimate for both the raw score and standard score linear models are presented. The derivations for raw score linear models are presented in…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…