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…

Basic philosophical and statistical issues in structural equation modeling (SEM) are reviewed, including model conceptualization, identification, and parameter estimation and data-model-fit assessment and model modification. These issues should be addressed before the researcher uses any of the new generation of SEM software. (SLD)

An efficient procedure is described for specifying and estimating parameters of general mixed models that contain both hierarchical and crossed random factors. The approach, using a model formulated for purely hierarchical structured data, is illustrated for the continuous response linear model with extensions to generalized linear, nonlinear, and…

A general approach is proposed to avoid improper solutions in structural equation models. The constrained estimation approach presented, which is based on an adaptation of a globally convergent method for nonlinear programming, has worked well in all trials. (SLD)

Describes the development and evaluation of the statistical models used to produce indirect state estimates for schools, teachers, students, and graduates from the Private School Survey of the National Center for Education Statistics for the 1991-92 and 1993-94 school years. (SLD)

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…

The source of an event-related brain potential (ERP) is estimated from multivariate measures of ERP on the head under several mathematical and physical constraints on the parameters of the source model. Statistical aspects of estimation are discussed, and new tests are proposed. (SLD)

Section Pre-Equating (SPE) is a method used to equate test forms that consist of multiple separately timed sections. SPE does not require examinees to take two complete forms of the test. Instead, all of the old form and one or two sections of the new form are administered to each examinee, and missing data techniques are employed to estimate the…