The predictive analysis approach to adaptive testing originated in the idea of statistical predictive analysis suggested by J. Aitchison and I.R. Dunsmore (1975). The adaptive testing model proposed is based on parameter-free predictive distribution. Aitchison and Dunsmore define statistical prediction analysis as the use of data obtained from an…

The real problems of contextual analysis concern the conceptualization of contextual effects, the kinds of data with which to estimate them, and the selection and implementation of appropriate statistical techniques. This paper focuses on detection; specifically, an approach to contextual analysis based on the estimation and interpretation of a…

In a situation where the population distribution of latent trait scores can be estimated, the ordinary maximum likelihood estimator of latent trait scores may be improved upon by taking the estimated population distribution into account. In this paper empirical Bayes estimators are compared with the liklihood estimator for three samples of 300…

The effect of prior information in Bayesian estimation is considered, mainly from the standpoint of objective testing. In the estimation of a parameter belonging to an individual, the prior information is, in most cases, the density function of the population to which the individual belongs. Bayesian estimation was compared with maximum likelihood…

A joint Bayesian estimation procedure for estimating parameters in the three-parameter logistic model is developed. Simulation studies show that the Bayesian procedure (1) ensures that the estimates stay in the parameter space and (2) produces better estimates than the joint maximum likelihood procedure. (Author/BS)

A general approach is proposed for modeling the structure of a r x s contingency table and for drawing marginal inferences about all parameters (e.g., interaction effects) in the model. The main approach is relevant whenever rs minus r minus s plus 1 is greater than or equal to 5. Military aptitude test data is used as illustration. (Author/LMO)

An alternative to the Rasch model is introduced. It characterizes strength of response according to the ratio of ability and difficulty parameters rather than their difference. Joint estimation and marginal estimation models are applied to two test data sets. (SLD)

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…

Assuming vectors of item responses depend on ability through a fully specified item response model, this paper presents maximum likelihood equations for estimating the population parameters without estimating an ability parameter for each subject. Asymptotic standard errors, tests of fit, computing approximations, and details of four special cases…

The purpose of this study was to examine the potential effect of false assumptions regarding the motivation of examinees on item calibration and test construction. A simulation study was conducted using data generated by means of several models of examinee item response behaviors (the three-parameter logistic model alone and in combination with…

The precision of item parameter estimates can be increased by taking advantage of dependencies between the latent proficiency variable and auxiliary examinee variables such as age, courses taken, and years of schooling. Score gains roughly equivalent to two to six additional item responses can be expected in typical educational and psychological…

To facilitate meta-analysis of diverse study findings, a mixed linear model with fixed random effects is presented and illustrated with data from teacher expectancy experiments. The standardized effect size is viewed as random and the variation among effect sizes is modeled as a function of study characteristics. (Author/BS).

Type I error rates of F. M. Lord's chi square test for differential item functioning were investigated using Monte Carlo simulations with marginal maximum likelihood estimation and marginal Bayesian estimation algorithms. Lord's chi square did not provide useful Type I error control for the three-parameter logistic model at these sample sizes.…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…