The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

A technique to estimate variances of weighted estimates in program evaluation is discussed. BRR estimates of variance are constructed from orthogonally weighted subsamples and can provide better estimates from complex samples than can other methods. Use of BRR is illustrated in a government evaluation of a food service program. (SLD)

Supporting the use of separate analyses of measurement and structural portions of latent or mixed manifest and latent variable models, limited information (single equation) procedures are presented for estimating structural parameters. These procedures are recommended for testing specific causal hypotheses and locating specific structural model…

An extension of the discussion of loglinear models presents post hoc procedures for statistically evaluating treatment effects, contrasts, and confidence intervals, illustrating methods for main effect and interaction contrasts and paying special attention to odds ratios and their interval estimates. Procedures for treating variables as…

The problems posed for latent variable analysis by populations with different sets of parameter values are discussed. An overview of methodology to address heterogeneity is presented, including a review of structural modeling by the multiple indicator-multiple causes model and the use of the LISCOMP computer program. (SLD)

Conditions necessary and sufficient for the determination of LISREL model solutions are identified. The reasons for indeterminacy of LISREL solutions are discussed, and an index of determinacy is presented and related to the covariance matrix of latent variables. (SLD)

Problems of estimation and interpretation are discussed that arise when a statistical package, which does not incorporate a dedicated weighted least-squares (WLS) routine, performs WLS regression by misapplication of a case-weighting strategy. A strategy is offered for adjusting WLS regression estimates after a case weighting strategy has been…

Estimation theory in educational statistics and the application of hierarchical linear models are reviewed. Observations within each group vary as a function of microparameters. Microparameters vary across the population of groups as a function of macroparameters. Bayes and empirical Bayes viewpoints review examples with two levels of hierarchy.…

Misspecification of mean and covariance structures for metric endogenous variables is considered. Maximum likelihood estimation of model parameters and the asymptotic covariance matrix of the estimates are discussed. A Haussman test for misspecification is developed, which is sensitive to misspecification not detected by the test statistics…

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. Some Monte Carlo simulations illustrate the efficacy of the procedure, which performs well with or without outliers. (SLD)

The equivalence between non-parametric marginal logistic models (NMLMs) and a class of discrete marginal logistic models is examined. Parametric models offer some of the advantages of the NMLMs approach, but there are more restrictions on the manifest probabilities. (SLD)

A model is proposed for empirically testing the appropriateness of using tetrachoric correlations for a set of dichotomous variables. A testing method is proposed that uses information from trivariate marginal tables. Assumptions are tested with real and simulated data. (SLD)

This paper reports an attempt to identify appropriate and robust location estimators for situations that tend to occur among various types of empirical data. Emphasizing robustness across broad unidentifiable ranges of contamination, an attempt was made to replicate, on a somewhat smaller scale, the definitive Princeton Robustness Study of 1972 to…

In experiments with paired comparisons, judges are occasionally allowed to express indifference between alternatives. For the analysis of such data, models for paired comparisons with ties are needed. Several models with tie parameters are reviewed. All are extensions of the basic models of L. L. Thurstone (1927) and R. A. Bradley and M. E. Terry…