This study aims to compare the results of the factor analysis performed with Frequentist and Bayesian approaches. The number of sub-dimensions of the measurement tool obtained from different methods, the variation of the items in the sub-dimensions, and the fit statistics' differentiation were examined. 778 students constitute the study sample.…

Bayesian confirmatory factor analysis (CFA) offers an alternative to frequentist CFA based on, for example, maximum likelihood estimation for the assessment of reliability and validity of educational and psychological measures. For increasing sample sizes, however, the applicability of current fit statistics evaluating model fit within Bayesian…

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…

Posterior Predictive Model Checking (PPMC) is a Bayesian model checking method that compares the observed data to (plausible) future observations from the posterior predictive distribution. We propose an alternative to PPMC in the context of structural equation modeling, which we term the Poor Persons PPMC (PP-PPMC), for the situation wherein one…

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

The usefulness of the l[subscript z] person-fit index was investigated with achievement test data from 20 exams given to more than 3,200 college students. Results for three methods of estimating ? showed that the distributions of l[subscript z] were not consistent with its theoretical distribution, resulting in general overfit to the item response…

This paper describes how item response theory (IRT) methods of test-equating could be applied to the maintenance of public examination standards in England. IRT methods of test-equating have been sparingly applied to the main public examinations in England, namely the General Certificate of Secondary Education (GCSE), the equivalent of a school…

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach.…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

It is shown that the common and unique variance estimates produced by a type of estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. A simple alternative method of specifying the Bayesian parameters required by the procedure is…

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…

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)

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…

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)