The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…

Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or…

An item response model is proposed for the analysis of continuous response formats in an item response theory (IRT) framework. With such formats, respondents are asked to report their response as a mark on a fixed-length graphical segment whose ends are labeled with extreme responses. An interpolation process is proposed as the response mechanism…

A method is proposed to assess the importance of differential item functioning (DIF) by estimating the largest possible fraction of the population in which DIF does not occur, or equivalently, the smallest possible portion of the population in which DIF may occur. The approach is based on latent class (C. C. Clogg, 1981) or mixture concepts, and…

This paper presents a method for estimating certain characteristics of test items which are designed to measure ability, or knowledge, in a particular area. Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates to item parameters of the two-parameter…

Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…

Since its release in 1976, LOGIST has been the most widely used computer program for estimating the parameters of the three-parameter logistic item response model developed by A. Birnbaum. An alternative program, BILOG, developed by R. J. Mislevy and R. D. Bock (1983), has recently become available. This paper compares the approaches taken by the…

The usefulness of a latent trait model designed for use with multidimensional test data was investigated in two stages. The first stage consisted of generating simulation data to fit the multidimensional extension of the two-parameter logistic model, applying the model to the data, and comparing the resulting estimates with the known parameters.…

A mastery test is frequently described as follows: an examinee responds to n dichotomously scored test items. Depending upon the examinee's observed (number correct) score, a mastery decision is made and the examinee is advanced to the next level of instruction. Otherwise, a nonmastery decision is made and the examinee is given remedial work. This…

Two perspectives provide the theoretical framework for this study. The first provides confirmatory maximum likelihood estimates of factor loadings and factor intercorrelations; the second, and more important, provides statistical tests of hypotheses that factor structures and patterns of values are invariant for female and male adolescents. The…

Whenever one uses ordinary least squares regression, one is making an implicit assumption that all of the independent variables have been measured without error. Such an assumption is obviously unrealistic for most social data. One approach for estimating such regression models is to measure implied coefficients between latent variables for which…

An asymptotic theory is developed for a new time series model introduced in TM 502 289. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in that they have the same asymptotic distribution as the maximum likelihood estimators. (Author/RC)

Issues concerning equating test scores are discussed in an introduction, four papers, and two commentaries. Equating methods research, sampling errors, linear equating, population differences, sources of equating errors, and a circular equating paradigm are considered. (SLD)

A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. (Author/LMO)