This paper examines the estimation of two-stage clustered RCT designs in education research using the Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the…

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 jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Examples are given to demonstrate the feasibility of the method. (Author/JKS)

A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects…

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

A simplification of Lord and Wingersky's method for computing the asymptotic variance-covariance matrix of maximum likelihood estimates for item and person parameters under some restrictions on the estimates is presented. Computation of the error variance-covariance matrix for the item parameters in the Rasch model is described. (NSF)

Formulas are derived for the bias in the maximum likelihood estimators (MLE) of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. Most typically the bias of an MLE is about one-tenth of its standard error. It is very seldom more…

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…

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for common situations. Difficulties in using maximum likelihood estimation with the three parameter model are discussed. (Author/JKS)

This article illustrates a method for fitting straight lines to data that is resistant to outliers and might therefore sometimes be preferred to the customary least squares procedure.

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)

Two methods, direct maximum likelihood (ML) and the expectation maximization (EM) algorithm, can be used to obtain ML parameter estimates for structural equation models with missing data (MD). Although the 2 methods frequently produce identical parameter estimates, it may be easier to satisfy missing at random assumptions using EM. However, no…

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…

This LISREL study examines the robustness of the maximum likelihood estimates under varying degrees of measurement model misspecification. A true model containing five latent variables (two endogenous and three exogenous) and two indicator variables per latent variable was used. Measurement model misspecification considered included errors of…