Studied whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. An example illustrates that neither the factor loading estimates nor the standard error estimates possess scale…

A possible method is developed for computing the asymptotic sampling variance-covariance matrix of joint maximum likelihood estimates in item response theory when both item parameters and abilities are unknown. For a set of artificial data, results are compared with empirical values and with the variance-covariance matrices found by the usual…

An evaluation of the variation of item estimates was conducted for the multidimensional extension of the logistic item response theory (MIRT) model. The empirically determined standard errors (SEs) of marginal maximum likelihood estimation (MMLE)/Bayesian item estimates from 40 items from the ACT Assessment (Form 24b, 1985) were obtained when the…

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)

Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the…

The analytically derived expected asymptotic standard errors (SEs) of maximum likelihood (ML) item estimates can be predicted by a mathematical function without examinees' responses to test items. The empirically determined SEs of marginal maximum likelihood estimation/Bayesian item estimates can be obtained when the same set of items is…

Actual kurtotic and skewed data and varied sample sizes and estimation methods demonstrated that normal theory maximum likelihood and generalized least square estimators were fairly consistent and almost identical. Standard errors tended to underestimate the estimator's true variation but the problem was not serious for large samples. (SLD)

Examined the relative performance of two commonly used methods of parameter estimation in factor analysis, maximum likelihood (ML) and ordinary least squares (OLS) through simulation. In situations with a moderate amount of error, ML often failed to recover the weak factor while OLS succeeded. Also presented an example using empirical data. (SLD)

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. (SLD)

Given known item parameters for a test, unbiased estimators are derived for an examinee's ability parameter, his or her proportion correct true score for the variances of these parameters and for the parallel forms reliability of the maximum likelihood estimator of the ability parameter. (Author/JKS)

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. Least squares estimation procedures are compared to maximum likelihood procedures. The conclusion, based on the data used in this study, is that two of the procedures seem to work well. (Author/JKS)

A Monte Carlo approach was used to examine bias in the estimation of indirect effects and their associated standard errors. Results illustrate the adverse effects of nonnormality on the accuracy of significance tests in latent variable models estimated using normal theory maximum likelihood statistics. (SLD)

Pseudo-Maximum Likelihood (p-ML) and Asymptotically Distribution Free (ADF) estimation methods for estimating dynamic factor model parameters within a covariance structure framework were compared through a Monte Carlo simulation. Both methods appear to give consistent model parameter estimates, but only ADF gives standard errors and chi-square…

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…

Error indices (bias, standard error of estimation, and root mean square error) obtained on different scales of measurement under different test termination rules in a computerized adaptive test (CAT) context were examined. Four ability estimation methods were studied: (1) maximum likelihood estimation (MLE); (2) weighted likelihood estimation…