In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be…

The problem of factor score indeterminacy implies that the factor and the error scores cannot be completely disentangled in the factor model. It is therefore proposed to compute Harman's factor score predictor that contains an additive combination of factor and error variance. This additive combination is discussed in the framework of classical…

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

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)

This paper presents a new stochastic multidimensional scaling vector threshold model designed to analyze "pick any/n" choice data. A maximum likelihood procedure is formulated to estimate a joint space of both individuals and stimuli. The non-linear probit type model is described, and a Monte Carlo analysis is performed. (TJH)

A plausible "s"-factor solution for many types of psychological and educational tests is one in which there is one general factor and "s - 1" group- or method-related factors. The bi-factor solution results from the constraint that each item has a non-zero loading on the primary dimension "alpha(sub j1)" and at most…

A modification index is presented to aid in reformulating hypothetical models rejected after analysis of empirical data. This index is an improvement over the one in the LISREL V computer program in that it takes into account changes in all parameters of the model when one parameter is freed. (SLD)

A method of item factor analysis is described, which is based on Thurstone's multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm. Also assessed are the statistical significance of successive factors added to the model, provisions for guessing and omitted items, and Bayes constraints. (TJH)

A procedure for evaluating a variety of rater reliability models is presented. A multivariate linear model is used to describe and assess a set of ratings. Parameters are represented in terms of a factor analytic model, and maximum likelihood methods test the model parameters. Illustrative examples are presented. (SLD)

A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…