The authors examine the asymptotic effect of omitting a random coefficient in the multilevel model and derive expressions for the change in (a) the variance components estimator and (b) the estimated variance of the fixed effects estimator. They apply the method of moments, which yields a closed form expression for the omission effect. In…

Birnbaum's three-parameter logistic function has become a common basis for item response theory modeling, especially within situations where significant guessing behavior is evident. This model is formed through a linear transformation of the two-parameter logistic function in order to facilitate a lower asymptote. This paper discusses an…

Rationale and procedures for conducting process analysis in evaluation research are discussed. Two different procedures for estimating mediation are discussed, as well as procedures for examining whether a treatment exerts its effects, in part, by altering mediating process that produces outcome. Benefits of process analysis in evaluation research…

Proposes a class of locally dependent latent trait models for responses to psychological and educational tests. Focuses on models based on a family of conditional distributions, or kernel, that describes joint multiple item responses as a function of student latent trait, not assuming conditional independence. Also proposes an EM algorithm for…

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…

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

Confirmatory maximum likelihood factor analysis was used to determine how accurately each of several hypothesized combinations of first-order and/or higher-order factors could describe the covariation within selected sub-matrices taken from the total correlation matrix originally analyzed by M. O'Sullivan et al. (1965). Focus was on evaluating the…

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…

Using a 21-statement attitude-type instrument, an iterative procedure for improving confirmatory model fit is demonstrated within the context of the EQS program of P. M. Bentler and maximum likelihood factor analysis. Each iteration systematically eliminates the poorest fitting statement as identified by a variable fit index. (SLD)

Generalizing Boolean matrix decomposition to a larger class of matrix decomposition models is demonstrated, and probability matrix decomposition (PMD) models are introduced as a probabilistic version of the larger class. An algorithm is presented for the computation of maximum likelihood and maximum a posteriori estimates of the parameters of PMD…

The success of applications of item response theory (IRT) depends upon the properties of the estimates of model parameters. Many theoretical properties of these estimates have been extensively studied. However, the properties of estimates obtained empirically from real data depend not only on the theoretical results, but also on the data and the…

Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if…

A model is presented for item responses when different examinees use different strategies to arrive at their answers and when only those answers, not choice or strategy or subtask results, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of solution strategies, responses are modeled…

Describes and assesses missing data methods currently used to analyze data from matrix sampling designs implemented by the National Assessment of Educational Progress. Several improved methods are developed, and these models are evaluated using an EM algorithm to obtain maximum likelihood estimates followed by multiple imputation of complete data…

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…