Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information concerning parameters is incorporated in the analysis. An interactive algorithm is developed to obtain the Bayesian estimates. A numerical example is presented. (Author/JKS)

These errata correct several typographical errors affecting five equations presented in the authors' paper in 1987. (TJH)

Extends joint maximum likelihood estimation for the hyperbolic cosine model to the situation in which the units of items are allowed to vary. Describes the four estimation cycles designed to address four important issues of model development and presents results from two sets of simulation studies that show reasonably accurate parameter recovery…

The sampling interpretation of confidence intervals and hypothesis tests is discussed in the context of conditional maximum likelihood estimation. Three different interpretations are discussed, and it is shown that confidence intervals constructed from the asymptotic distribution under the third sampling scheme discussed are valid for the first…

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

Derives the asymptotic normal distribution of the maximum likelihood estimator of Cronbach's alpha (under normality) for the case when no assumptions are made about the covariances among items. Also considers the asymptotic distribution for the special case of compound symmetry and when compared to the exact distribution. (Author/SLD)

Conventional wisdom in missing data research dictates adding variables to the missing data model when those variables are predictive of (a) missingness and (b) the variables containing missingness. However, it has recently been shown that adding variables that are correlated with variables containing missingness, whether or not they are related to…

In practical applications of item response theory (IRT), item parameters are usually estimated first from a calibration sample. After treating these estimates as fixed and known, ability parameters are then estimated. However, the statistical inferences based on the estimated abilities can be misleading if the uncertainty of the item parameter…

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the…

The standard error of the maximum likelihood ability estimator is commonly estimated by evaluating the test information function at an examinee's current maximum likelihood estimate (a point estimate) of ability. Because the test information function evaluated at the point estimate may differ from the test information function evaluated at an…

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…

This paper presents an expository development of James-Stein estimation with substantial emphasis on exact results for nonnormal location models. The themes of the paper are: (1) the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; (2) the amount of…

A study involving 256 adolescents focused on differences in results on androgyny from administration of the Bem Sex Role Inventory (BSRI). The subjects ranged in age from nine to 17 years. The subject group was 75% male and 25% female. Confirmatory and second-order factor analyses of the data were used. Results based on confirmatory maximum…

The situation of nonrandomly missing data has theoretically different implications for item parameter estimation depending on whether joint maximum likelihood or marginal maximum likelihood methods are used in the estimation. The objective of this paper is to illustrate what potentially can happen, under these estimation procedures, when there is…

In a LISREL-IV analysis, a method of specifying a priori the variances of the latent variables for interpretability is demonstrated. The potential confusion of the metric of the latent variables is discussed, since many of the parameter estimates are a function of the metric. (Author/CM)