One of the important underlying assumptions of all item response theory (IRT) models is that of local independence. This assumption requires that the response to an item on a test not be influenced by the response to any other items. This assumption is often taken for granted, with little or no scrutiny of the response process required to answer…

To assess the effects of correlated abilities on test characteristics, and to explore the effects of correlated abilities on the use of a multidimensional item response theory model which does not explicitly account for such a correlation, two tests were constructed. One had two relatively unidimensional subsets of items, the other had all…

Critics have occasionally asserted that the number of factors in the 16PF tests is too large. This study discusses factor-analytic methodology and reviews more than 50 studies in the field. It concludes that the number of important primaries encapsulated in the series is no fewer than the stated number. (Author/JAZ)

Factor analysis is the traditional method for studying the dimensionality of test data. However, under common conditions, the factor analysis of tetrachoric correlations does not recover the underlying structure of dichotomous data. The purpose of this paper is to demonstrate that the factor analyses of tetrachoric correlations is unlikely to…

DIMTEST is a statistical test procedure for assessing essential unidimensionality of binary test item responses. The test statistic T used for testing the null hypothesis of essential unidimensionality is a nonparametric statistic. That is, there is no particular parametric distribution assumed for the underlying ability distribution or for the…

Multidimensional item response data were created. The strength of a general factor, the number of common factors, the distribution of items loadingon common factors, and the number of items in simulated tests were manipulated. LOGIST effectively recovered both item and trait parameters in nearly all of the experimental conditions. (Author/JAZ)

The TESTFACT computer program and full-information factor analysis of test items were used in a computer simulation conducted to correct for the guessing effect. Full-information factor analysis also corrects for omitted items. The present version of TESTFACT handles up to five factors and 150 items. A preliminary smoothing of the tetrachoric…

Although perfectly scalable items rarely occur in practice, Guttman's concept of a scale has proved to be valuable to the development of measurement theory. If the score distribution is uniform and there is an equal number of items at each difficulty level, both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous…