A joint maximum likelihood estimation algorithm, based on the partial compensatory multidimensional logistic model (PCML) proposed by L. Zeng (1989), is presented. The algorithm simultaneously estimates item difficulty parameters, the strength of each dimension, and individuals' abilities on each of the dimensions involved in arriving at a correct…

A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models…

Compared three online pretest calibration scaling methods through simulation: (1) marginal maximum likelihood with one expectation maximization (EM) cycle (OEM) method; (2) marginal maximum likelihood with multiple EM cycles (MEM); and (3) M. Stocking's method B. MEM produced the smallest average total error in parameter estimation; OEM yielded…

The form of item log-likelihood surface was investigated under two-parameter and three-parameter logistic models. Results confirm that the LOGIST program procedures used to locate the maximum of the likelihood functions are consistent with the form of the item log-likelihood surface. (SLD)

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)

An approximation for the bias function of the maximum likelihood estimate of the latent trait or ability is developed for the general case where item responses are discrete, which includes the dichotomous response level, the graded response level, and the nominal response level. (SLD)

Three potential causes of scale shrinkage (measurement error, restriction of range, and multidimensionality) in item response theory vertical equating are discussed, and a more comprehensive model-based approach to establishing vertical scales is described. Test data from the National Assessment of Educational Progress are used to illustrate the…

Standard item response theory (IRT) models posit latent variables to account for regularities in students' performance on test items. They can accommodate learning only if the expected changes in performance are smooth, and, in an appropriate metric, uniform over items. Wilson's "Saltus" model extends the ideas of IRT to development that…

A confirmatory approach to assessing test structure using multidimensional item response theory (MIRT) was developed and evaluated. The approach involved adding to the exponent of the MIRT model an item structure matrix that allows the user to specify the ability dimensions measured by an item. Various combinations of item structures were fit to…

Binary or graded disagree-agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (J. S. Roberts, 1995; W. H. Van Schuur and H. A. L. Kiers, 1994). Advances in…

A plausible "s"-factor solution for many types of psychological and educational tests is one in which there is one general factor and "s - 1" group- or method-related factors. The bi-factor solution results from the constraint that each item has a non-zero loading on the primary dimension "alpha(sub j1)" and at most…

To reduce the cost of item writing and to enhance the flexibility of item presentation, items can be generated by item-cloning techniques. An important consequence of cloning is that it may cause variability on the item parameters. Therefore, a multilevel item response model is presented in which it is assumed that the item parameters of a…

A method of item factor analysis is described, which is based on Thurstone's multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm. Also assessed are the statistical significance of successive factors added to the model, provisions for guessing and omitted items, and Bayes constraints. (TJH)

Using the constant information model, constant amounts of test information, and a finite interval of ability, simulated data were produced for 8 ability levels and 20 numbers of test items. Analyses suggest that it is desirable to consider modifying test information functions when they measure accuracy in ability estimation. (SLD)

Type I error rates of the likelihood ratio test for the detection of differential item functioning (DIF) were investigated using Monte Carlo simulations. The graded response model with five ordered categories was used to generate data sets of a 30-item test for samples of 300 and 1,000 simulated examinees. All DIF comparisons were simulated by…