Developed two methods for estimating the individual level correlation coefficient that combines information from aggregate data with a small fraction of the individual level data. Results of a simulation study support the use of these methods. (SLD)

Developed a new estimator for the population squared multiple correlation using maximum likelihood estimation. Data from 72 air control school graduates demonstrate that the new estimator has greater accuracy than other estimators with values that fall within the parameter space. (SLD)

Studied the performance of rank (percentile) estimators in a basic two-stage hierarchical model capturing essential features of more complicated models commonly used to estimate effects. Simulation results highlight the need to assess whether even optimal percentile estimators perform sufficiently well to be used to evaluate teachers or schools.…

Derived an approximate test and confidence interval for coefficient alpha and used the approximate test and confidence interval to derive closed-form sample size formulas that can be used to determine the sample size needed to test coefficient alpha with desired power or to test coefficient alpha with desired precision. (SLD)

Examined alternative ways of specifying models in the complier average causal effects (CACE) estimation method when the major interest is in estimating causal effects of treatments for compliers. Explored modeling possibilities of CACE estimation in a maximum likelihood-expectation maximization framework in the presence of covariate information.…

Notes that the article reviewed contributes to the expanding literature on noncompliance by explicating the assumptions involving covariates that can be used to identify maximum likelihood estimates in place of exclusion restrictions. Notes points that require further discussion. (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)

Asserts that, in principle, an analyst should be satisfied with infinite estimates slope in logistic regression because it indicates that a predictor is perfect. Using simple approaches, hypothesis tests may be performed and confidence intervals calculated even when a slope is infinite. Some functions of parameters that are infinite are still…

Developed an item response model for characterizing test-compromise that enables the estimation of item preview and score-gain distributions. In the approach, models parameters and posterior distributions are estimated by Markov Chain Monte Carlo procedures. Simulation study results suggest that when at least some test items are known to be…

Examines the ways in which level-1 outliers can impact the estimation of fixed effects and random effects in hierarchical models (HMs). Also outlines and illustrates the use of Markov Chain Monte Carlo algorithms for conducting sensitivity analyses under "t" level-1 assumptions, including algorithms for settings in which the degrees of freedom at…

Studied the efficiency and robustness of alternative estimators of regression coefficients for three-level data. A simulation study shows that, as expected, the hierarchical model analyses produced more efficient point estimates than did analyses that ignored the covariance structure in the data, even when the normality assumption was violated.…

Considers the estimation of polynomial structural models and shows a limitation of an existing method. Introduces a new procedure, the generalized appended product indicator procedure, for nonlinear structural equation analysis. Addresses statistical issues associated with the procedure through simulation. (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)

Provides asymptotic formulas for the standard errors of parameter estimates from the NOHARM computer program for restricted and unrestricted rotated models, using large-sample theory, and a goodness-of-fit test of the model. Used simulation to show that results from NOHARM are comparable to the three-stage estimator of B. Muthen (1993). (SLD)

Conducted a meta-analysis focusing on the explanation of empirical Type I error rates for six principal classes of estimators. Generally, chi-square tests for overall model fit were found to be sensitive to nonnormality and the size of the model for all estimators, with the possible exception of elliptical estimators with respect to model size and…