Log linear models are proposed for the analysis of structural relations among multidimensional developmental contingency tables. Model of quasi-independence are suggested for testing specific hypothesized patterns of development. Transitions in developmental categorizations are described by Markov models applied to successive contingency tables. A…

A goodness of fit test presented by Andersen (EJ 143 939) is shown to be incorrect. The correct test is described and a re-analysis of Andersen's data is provided. (Author/CTM)

Graham Douglas' claims (TM 503 496) that the X2-test statistics of the paper, "Paired Comparisons with Individual Differences" (EJ 143 939), are incorrect are acknowledged to be justified (Author/CTM)

A Bradley-Terry type model for paired comparisons is considered which allows for individual parameters and corresponding parameters for the choice-alternatives. Model is applied to data from a Danish investigation of blue collar attitudes towards alternative social gains. Model is compared to one suggested by Schonemann and Wang. (RC)

This paper presents an index of goodness-of-fit for comparing m models over n trials. The index allows for differentiated weighting of the trials as to their importance in the comparison of the models. Several possible weighting schemes are suggested and the conditions on the weights which assure asymptotic normality of the index distribution are…

Estimation is by means of iterative convergence to maximum likelihood estimates, and two approaches to assessing fit of the model to sample data are discussed. Relation of this general probabilistic model to other, more restricted models is explored and three cases of the general model are applied to exemplary data. (Author/RC)

Traditionally, confirmatory factor analytic models are tested against a null model of total independence. Using randomly generated factors in a matrix of 46 aptitude tests, this approach is shown to be unlikely to reject even random factors. An alternative null model, based on a single general factor, is suggested. In addition, an index of model…

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 probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…

A multitrait-multimethod matrix containing two methods of measuring 12 personality traits was analyzed and confirmatory factor analysis was applied to the data. Although unexplained variance remained, method factors and a general personality factor significantly improved the fit of a model containing only trait factors. (Author/RL)

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

A study was conducted to compare the quality of the item parameter estimates obtained from the ANCILLES and LOGIST estimation procedures using goodness of fit as a criterion. Statistics used to compare the fit included a chi-square statistic and a mean square deviation statistic. Other analyses performed included comparisons of the distributions…

The Rasch simple logistic model is used to examine the relative item parameter values of a personality inventory with respect to populations cross-classified by sex and country. While items conform to the model within each of the populations, half the items show significant discrepancies among the populations. (Author/RL)

The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set…

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…