Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this article is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific…

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n x 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a…

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the…

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

A Monte Carlo evaluation of 30 internal criteria for cluster analysis was conducted using four hierarchical clustering techniques. The results indicated that a subset of internal criteria was identified which appear to be valid indices of correct cluster recovery. (Author/JKS)

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients…

Four different extensions to McNemar's problem concerning the hypothesis of equal probabilities for the unlike pairs of correlated binary variables are considered, each for testing simultaneous equality of proportions of unlike pairs in c independent populations of correlated binary variables, but each under different assumptions and/or additional…

Presents a latent variable representation for multiple-choice items and option characteristic curves, and proposes a criterion for distractors based on distractor selection ratios. Results allow for testing the criterion from observable data without specifying a parametric form for the characteristic curves. (Author/SLD)

This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the ability estimators produced by these criteria are discussed and empirically criticized. (SLD)