Discusses a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model. Presents a unified maximum likelihood method for estimating the parameters of the generalized latent trait model and discusses the scoring of individuals on the latent dimensions.…

Explored are two theoretical approaches that attempt to cope with omitted responses, that is, when an examinee omits (fails to respond to) an item and therefore the item response formula cannot be used. Preliminary considerations are discussed, and it is shown that a conveniently simple application of equivalent items leads to internal…

The dynamic linear model or Kalman filtering model provides a useful methodology for predicting the past, present, and future states of a dynamic system, such as an object in motion or an economic or social indicator that is changing systematically with time. Recursive likelihood methods for adaptive Kalman filtering and smoothing are developed.…

The polytomous unidimensional Rasch model with equidistant scoring (rating scale model) is extended so that two parameters are linearly decomposed into certain basic parameters. A conditional maximum likelihood estimation procedure and a likelihood ratio test are presented in the context of the extended model (linear rating scale model). (SLD)

Computerized adaptive testing procedures (CATPs) based on the graded response method (GRM) of F. Samejima (1969) and the partial credit model (PCM) of G. Masters (1982) were developed and compared. Both programs used maximum likelihood estimation of ability, and item selection was conducted on the basis of information. Two simulated data sets, one…

A method for determining invariant item parameters is presented, along with a scheme for obtaining test scores which are interpretable in terms of a common metric. The method assumes a unidimensional latent trait and uses a three parameter normal ogive model. The assumptions of the model are explored, and the methods for calculating the proposed…

Effects of test length, sample size, and assumed ability distribution were investigated in a multiple replication Monte Carlo study under the 1-parameter (1P) and 2-parameter (2P) logistic graded model with five score levels. Accuracy and variability of item parameter and ability estimates were examined. Monte Carlo methods were used to evaluate…

Optimal appropriateness indices, recently introduced by Levine and Drasgow (1984), provide the highest rates of detection of aberrant response patterns that can be obtained from item responses. These optimal appropriateness indices are used to study three important problems in appropriateness measurement. First, the maximum detection rates of two…

A procedure for obtaining maximum likelihood trait estimates from number-correct (NC) scores for the three-parameter logistic model is presented. It produces an NC score to trait estimate conversion table. Analyses in the estimated true score metric confirm the conclusions made in the trait metric. (Author/DWH)

New legislation in 1972 shifted the emphasis of the California Assessment Program (CAP) from traditional every pupil achievement testing to a more efficient multiple-matrix testing design, under which a broad spectrum of skills could be surveyed without undue expenditure of educational resources. Scale score reporting was introduced to the grade 6…

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

The analysis of fit of data to a measurement model for graded responses is described. The model is an extension of Rasch's dichotomous model to formats which provide more than two levels of response to items. The model contains one parameter for each person and one parameter for each "step" in an item. A dichotomously-scored item…

Maximum likelihood and Bayesian procedures are presented for item selection and scoring of multidimensional adaptive tests. A demonstration with simulated response data illustrates that multidimensional adaptive testing can provide equal or higher reliabilities with fewer items than are required in one-dimensional adaptive testing. (SLD)

A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. Each item may have a different response function where each item response may be explained by one or more latent traits. Item response functions may follow a partial credit model (D. Andrich, 1978; and G. N.…

Dichotomous search strategies (DSSs) for computerized adaptive testing are similar to golden section search strategies (GSSSs). Each middle point of successive search regions is a testing point. After each item is administered, the subject's obtained score is compared with the expected score at successive testing points. If the subject's obtained…