A model of test item dependency is presented and used to illustrate the effect that violations of local independence have on the behavior of item characteristic curves. The dependency model is flexible enough to simulate the interaction of a number of factors including item difficulty and item discrimination, varying degrees of item dependence,…

The usefulness of path analysis as a means of better understanding various linear models is demonstrated. First, two linear models are presented in matrix form using linear structural relations (LISREL) notation. The two models, regression and factor analysis, are shown to be identical although the research question and data matrix to which these…

The Auto-Regressive Integrated Moving Average (ARIMA) Models, often referred to as Box-Jenkins models, are regression methods for analyzing sequential dependent observations with large amounts of data. The Box-Jenkins approach, a three-stage procedure consisting of identification, estimation and diagnosis, was used to select the most appropriate…

The models and procedures discussed in this paper are related to those presented in Bock and Aitkin (1981), where they considered the 2-parameter probit model and approximated a normally distributed prior distribution of abilities by a finite and discrete distribution. One purpose of this paper is to clarify the nature of the general EM (GEM)…

This proposal attempts to follow in Allan Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than previously realized. Birnbaum's two significant contributions to the theories of statistics and educational testing are: (1) the proof that the sufficiency and conditionality principles…

Determination of statistical power for analysis of variance procedures requires five elements: (1) significance level; (2) effect size; (3) number of means; (4) error variance; and (5) sample size. Significance levels are traditionally chosen to be 0.5, .01, or .001. Effect size is not discussed in this paper. The number of means is determined by…

The mixed model analysis of variance assumes a mathematical property known as sphericity. Several preliminary tests have been proposed to detect departures from the sphericity assumption. The logic of the preliminary testing procedure is to conduct the mixed model analysis of variance if the preliminary test suggests that the sphericity assumption…

The stepwise regression method of selecting predictors for computer assisted multiple regression analysis was compared with forward, backward, and best subsets regression, using 16 data sets. The results indicated the stepwise method was preferred because of its practical nature, when the models chosen by different selection methods were similar…

The purpose of this paper is to demonstrate how multiple linear regression provides a viable statistical methodology for dealing with meta-analysis in general, and specifically with the issues of nonindependence and design complexity, such as multiple treatments. Since the F-test and t-test are special cases of the general linear model,…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

A general model is described which can be used to represent the four common types of meta-analysis: (1) estimation of effect size by combining study outcomes; (2) estimation of effect size by contrasting study outcomes; (3) estimation of statistical significance by combining study outcomes; and (4) estimation of statistical significance by…

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

One of the important underlying assumptions of all item response theory (IRT) models is that of local independence. This assumption requires that the response to an item on a test not be influenced by the response to any other items. This assumption is often taken for granted, with little or no scrutiny of the response process required to answer…

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

Meta-analysis is a technique for combining the summary statistics from previously conducted research studies to indicate the direction of results and provide an index of the magnitude of effect size. This paper focuses on the effect of the violation of the assumption of independence (that the value of any included statistic is in no way…