Collapsing categories is a commonly used data reduction technique; however, to date there do not exist principled methods to determine whether collapsing categories is appropriate in practice. With ordinal responses under the partial credit model, when collapsing categories, the true model for the collapsed data is no longer a partial credit…

The examination of cross-classified category data is common in evaluation and research, with Karl Pearson's family of chi-square tests representing one of the most utilized statistical analyses for answering questions about the association or difference between categorical variables. Unfortunately, these tests are also among the more commonly…

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an…

CEFA 3.02(Browne, Cudeck, Tateneni, & Mels, 2008) is a factor analysis computer program designed to perform exploratory factor analysis. It provides the main properties that are needed for exploratory factor analysis, namely a variety of factoring methods employing eight different discrepancy functions to be minimized to yield initial…

Bounds are established for log odds ratios (log cross-product ratios) involving pairs of items for item response models. First, expressions for bounds on log odds ratios are provided for one-dimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model. Results are…

Examines the elements involved in fitting a bibliometric model to empirical data, proposes a consistent methodology for applying Lotka's law, and presents the results of an empirical test of the methodology. The results are discussed in terms of the validity of Lotka's law and the suitability of the proposed methodology. (49 references) (CLB)

A Rasch measurement model can be constructed to meet the requirements of rank ordered data. If multiple rankings of the same objects are available, then the parameters of the objects can be estimated, along with their standard errors and also with statistics summarizing the fit of the data to the measurement model. This paper summarizes the…

The purpose of this research is to demonstrate that a systematic approach to the graphical analysis of Rasch model residuals can lead to an increased understanding of ordered response data, and that residual patterns do change in predictable ways, and that summary statistics need not be the only piece of evidence for assuring the fit between model…

The usefulness of the general Rasch model for multidimensional data, from the most simple formulations to the more complex versions of the model, is explored. Also investigated was whether the parameters of the models could be readily interpreted. Models investigated included: (1) the vector model; (2) the product term model; (3) the vector and…

Five papers published in a special edition of Human Factors, August 1973 are examined in an attempt to explain and illustrate the characteristics and applications of central-composite designs in the context of response-surface methodology (RSM). A detailed analysis is provided to show that the experimental papers (1) fail to illustrate the most…

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.…

An error in the data analysis for a study reported in a 1988 paper by Kail is cited. The paper postulated a model that explained individual differences in the speed of processing on cognitive tasks. Reanalysis of the data suggested that support for the original conclusions is considerably weaker than reported. (LB)

Presentation of quantitative research on the family often suffers from a tendency to interpret findings on a statistical rather than substantive basis. Advocates the use of data analysis that lends itself to an intuitive understanding of the nature of the findings, the strength of the association, and the import of the result. (JPS)

Working from a common data base and hypothesized model, this paper demonstrates and compares the EQS and LISREL computer program strategies in the analysis of a second-order factor model. Program similarities and differences are noted with respect to: (1) preliminary analyses of the data; (2) treatment of data that are not multivariately normal;…

A basic methodological approach in developmental studies is the collection of longitudinal data. Behavioral data cen take at least two forms, qualitative (or discrete) and quantitative. Both types are fallible. Measurement errors can occur in quantitative data and measures of these are based on error variance. Qualitative or discrete data can…