Consider the conventional multilevel model Y=C[gamma]+Zu+e where [gamma] represents fixed effects and (u,e) are multivariate normal random effects. The continuous outcomes Y and covariates C are fully observed with a subset Z of C. The parameters are [theta]=([gamma],var(u),var(e)). Dempster, Rubin and Tsutakawa (1981) framed the estimation as a…

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…

L. A. Goodman's loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. Three-way tables and generalizations of correspondence analysis are deduced, and a generalized version of Goodman's algorithm is used to estimate scores in all cases. (Author/TJH)

The Bock and Aitkin Marginal Maximum Likelihood/EM (MML/EM) approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. This paper provides the essential mathematical details of a MML/EM solution and shows its use in obtaining consistent item parameter estimates. (TJH)

A stochastic multidimensional scaling procedure is presented for analysis of three-mode, three-way pick any/"J" data. The procedure fits both vector and ideal-point models and characterizes the effect of situations by a set of dimension weights. An application in the area of consumer psychology is discussed. (SLD)

Describes algorithms used in the computer program LOGIMO for obtaining maximum likelihood estimates of the parameters in loglinear models. These algorithms are also useful for the analysis of loglinear item-response theory models. Presents modified versions of the iterative proportional fitting and Newton-Raphson algorithms. Simulated data…

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)

The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are estimation bias due to measurement error and the estimation of the effects of the individual's hierarchical social milieu. This paper…

Covariance structures associated with linear structural equation models are discussed. Algorithms for computing maximum likelihood estimates (namely, the EM algorithm) are reviewed. An example of using likelihood ratio tests based on complete and incomplete data to improve the fit of a model is given. (SLD)

An extension is proposed for the network algorithm introduced by C.R. Mehta and N.R. Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. A simulation study indicates the efficiency of the algorithm. (SLD)

Combining Rasch and latent class models is presented as a way to overcome deficiencies and retain the positive features of both. An estimation algorithm is outlined, providing conditional maximum likelihood estimates of item parameters for each class. The model is illustrated with simulated data and real data (n=869 adults). (SLD)

This study examined the application of the marginal maximum likelihood-EM algorithm to the parameter estimation problems of the normal ogive and logistic polytomous response models for Likert-type items. A rating scale model, based on F. Samejima's (1969) graded response model, was developed. (TJH)

In this paper, algorithms are described for obtaining the maximum likelihood estimates of the parameters in log-linear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

A probabilistic item response theory (IRT) model is developed for pair-comparison design in which the unfolding principle governing the choice process uses a discriminant process analogous to Thurstone's Law of Comparative Judgment. A simulation study demonstrates the feasibility of estimation, and two examples illustrate the implications for…