Derives three reliability estimates for the Bayes modal estimate (BME) and the maximum-likelihood estimate (MLE) of theta in computerized adaptive tests (CATs). Computes the three reliability estimates and the true reliabilities of both BME and MLE for seven simulated CATs. Results show the true reliabilities for BME and MLE to be nearly identical…

This paper presents a row-column (RC) association model in which the estimated row and column scores are forced to be in agreement with a priori specified ordering. Two efficient algorithms for finding the order-restricted maximum likelihood (ML) estimates are proposed and their reliability under different degrees of association is investigated by…

The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are: the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically distribution-free procedure. When data are normally distributed and the model structure…

This simulation study compared maximum likelihood (ML) estimation with weighted least squares means and variance adjusted (WLSMV) estimation. The study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors, based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3, 4, 5, and 6 categories. There was no…

Latent variable models exist with continuous, categorical, or both types of latent variables. The role of latent variables is to account for systematic patterns in the observed responses. This article has two goals: (a) to establish whether, based on observed responses, it can be decided that an underlying latent variable is continuous or…

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…

A method is proposed to assess the importance of differential item functioning (DIF) by estimating the largest possible fraction of the population in which DIF does not occur, or equivalently, the smallest possible portion of the population in which DIF may occur. The approach is based on latent class (C. C. Clogg, 1981) or mixture concepts, and…

This paper presents a method for estimating certain characteristics of test items which are designed to measure ability, or knowledge, in a particular area. Under the assumption that ability parameters are sampled from a normal distribution, the EM algorithm is used to derive maximum likelihood estimates to item parameters of the two-parameter…

Lord's bias function and the weighted likelihood estimation method are effective in reducing the bias of the maximum likelihood estimate of an examinee's ability under the assumption that the true item parameters are known. This paper presents simulation studies to determine the effectiveness of these two methods in reducing the bias when the item…

The usefulness of a latent trait model designed for use with multidimensional test data was investigated in two stages. The first stage consisted of generating simulation data to fit the multidimensional extension of the two-parameter logistic model, applying the model to the data, and comparing the resulting estimates with the known parameters.…

A method is proposed for partially analyzing additive ipsative data (PAID). Transforming the PAID according to a developed equation preserves the density of the transformed data, and maximum likelihood estimation can be carried out as usual. Simulation results show that the original structural parameters can be accurately estimated from PAID. (SLD)

Examined the relative performance of two commonly used methods of parameter estimation in factor analysis, maximum likelihood (ML) and ordinary least squares (OLS) through simulation. In situations with a moderate amount of error, ML often failed to recover the weak factor while OLS succeeded. Also presented an example using empirical data. (SLD)

A simulation study explored the effect of population distribution on maximum likelihood estimation (MLE) and expected a posteriori (EAP) estimation in computerized adaptive testing based on the rating scale model of D. Andrich (1978). The choice between EAP and MLE for particular situations is discussed. (SLD)

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. (SLD)

A unidimensional model for responses to statements that have an unfolding structure was constructed from the cumulative Rasch model for ordered response categories. A joint maximum likelihood estimation procedure was investigated. Analyses of data from a small simulation and a real data set show that the model is readily applicable. (SLD)