Recently, applied psychological measurement researchers have become interested in the application of the generalized graded unfolding model (GGUM), a parametric item response theory model that posits an ideal point conception of the relationship between latent attributes and observed item responses. Little attention has been given to…

It is common to assume during a statistical analysis of a multiscale assessment that the assessment is composed of several unidimensional subtests or that it has simple structure. Under this assumption, the unidimensional and multidimensional approaches can be used to estimate item parameters. These two approaches are equivalent in parameter…

Spearman's factor-analytic model has been proposed as a unidimensional linear item response theory (IRT) model for continuous item responses. This article first proposes a reexpression of the model that leads to a form similar to that of standard IRT models for binary responses and discusses the item indices of difficulty discrimination and…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

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…

Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Lof test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte…

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…

Investigated the data demands associated with the marginal maximum likelihood (MML) expected a posterior (EAP) methodology and the precision of the resulting parameter estimates when data fit the underlying model through simulation. Also studied the extent to which a misspecified prior distribution would affect the item and person parameter…

Presents a general class of ordinal logit models that specifies equality and inequality constraints on sums of conditional response probabilities. Uses maximum likelihood to estimate these models, making their assumptions testable with likelihood-ratio statistics. Illustrates the proposed models with an example using reported adult crying…

The Rasch testlet model for both dichotomous and polytomous items in testlet-based tests is proposed. It can be viewed as a special case of the multidimensional random coefficients multinomial logit model (MRCMLM). Therefore, the estimation procedures for the MRCMLM can be directly applied. Simulations were conducted to examine parameter recovery…

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…

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

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)

The robustness of the likelihood ratio difference statistic to the violation of a regularity condition when used to assess differences in fit provided by pairs of latent class models was investigated. Recommendations are made regarding the use of the statistic under violation of the regularity condition. (SLD)

Two joint maximum likelihood estimation methods (LOGIST 2B and LOGIST 5) and two marginal maximum likelihood estimation methods (BILOG and ForScore) were contrasted by measuring the difference between a simulation model and a model obtained by applying an estimation method to simulation data. Marginal estimation was generally superior. (SLD)