Using explicit formulas for the information matrix of maximum likelihood factor analysis under multivariate normal theory, gross and net information for estimating the parameters in a covariance structure gained by adding the associated mean structure are defined. (Author/SLD)

Describes the maximum likelihood (ML) estimation of mean and covariance structure models when data are missing. Describes expectation maximization (EM), generalized expectation maximization, Fletcher-Powell, and Fisher-scoring algorithms for parameter estimation and shows how software can be used to implement each algorithm. (Author/SLD)

Presents a simple result concerning variances of maximum likelihood (ML) estimators. The result allows for construction of residual diagrams to evaluate whether ML estimators derived from independent samples can be assumed to be equal apart from random errors. Applies this result to the polytomous Rasch model. (SLD)

Discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. In this context, proposes a family of models, called the logistic positive exponent family, that provides…

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure."…

Discusses a full-information maximum likelihood method for fitting a multidimensional latent variable model to a set of ordinal observed variables. Also discusses estimating the model, scoring persons on the latent dimensions, and goodness of fit. Applies the method to a data set of attitudes of 392 respondents toward technology. (SLD)

Provides asymptotic standard errors of the estimates of equated scores from several types of item response theory (IRT) true score equatings. Equating designs considered cover those with internal or external common items and separate or simultaneous estimation. Uses marginal maximum likelihood estimation for the estimation of item parameters. (SLD)

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…