A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects…

Continuation ratio logits are used to model the possibilities of obtaining ordered categories in a polytomously scored item. This model is an alternative to other models for ordered category items such as the graded response model and the generalized partial credit model. The discussion includes a theoretical development of the model, a…

The Solomon four-group design (R. Solomon, 1949) is a very useful experimental design to investigate the main effect of a pretest and the interaction of pretest and treatment. Although the design was proposed half a century ago, no proper data analysis techniques have been available. This paper describes how data from the Solomon four-group design…

Presents a preliminary empirical test of a maximum likelihood approach to using relevance data for training information retrieval parameters. Discusses similarities to language models; the unification of document-oriented and query-oriented views; tests on data sets; algorithms and scalability; and the effectiveness of maximum likelihood…

Missing data analyses have received considerable recent attention in the methodological literature, and two "modern" methods, multiple imputation and maximum likelihood estimation, are recommended. The goals of this article are to (a) provide an overview of missing-data theory, maximum likelihood estimation, and multiple imputation; (b) conduct a…

This article organizes models for categorical item response data into three distinct classes. "Difference models" are appropriate for ordered responses, "divide-by-total" models for either ordered or nominal responses, and "left-side added" models for multiple-choice responses with guessing. Details of the taxonomy…

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for common situations. Difficulties in using maximum likelihood estimation with the three parameter model are discussed. (Author/JKS)

This article illustrates a method for fitting straight lines to data that is resistant to outliers and might therefore sometimes be preferred to the customary least squares procedure.

In this study, we examine the role of academic preparation in the transition from community colleges to four-year institutions. We address two specific questions: To what extent do academically unprepared students transfer to four-year institutions? And, can positive experiences in community colleges diminish the role of inadequate academic…

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a…

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure."…

Discusses a full-information maximum likelihood method for fitting a multidimensional latent variable model to a set of ordinal observed variables. Also discusses estimating the model, scoring persons on the latent dimensions, and goodness of fit. Applies the method to a data set of attitudes of 392 respondents toward technology. (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)

When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited.…

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…