A Monte Carlo study determined the Inverse Scree Test's shape with various numbers of true groups and under different conditions of distribution shape and sample size. Six simulated distributions of 3,000 subjects each and 1 with 1,500 were created. Findings suggest relative distribution independence, number independence, and modest…

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that equating the asymptotic standard error of the communality estimate to the unique variance estimate is not correct for the unstandardized case. Monte Carlo simulations illustrate the study. (SLD)

Three heuristic methods of assessing the dimensionality of binary item pools were evaluated in a Monte Carlo investigation. The indices were based on (1) the local independence of unidimensional tests; (2) patterns of second-factor loadings derived from simplex theory; and (3) the shape of the curve of successive eigenvalues. (SLD)

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

Factors affecting a lower-bound estimate of internal consistency reliability, Cronbach's coefficient alpha, are explored. Theoretically, coefficient alpha is an estimate of the correlation between two tests drawn at random from a pool of items like the items in the test under consideration. As a practical matter, coefficient alpha can be an index…

The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…

The validity of the assumptions under which the ordinal true score test theory was derived was examined using (1) simulation based on classical test theory; (2) a long empirical test with data from 321 sixth graders; and (3) an extensive simulation with 480 datasets based on the 3-parameter model. (SLD)