Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT)…

Teaching quality is the lifeline of the higher education. Many universities have made some effective achievement about evaluating the teaching quality. In this paper, we establish the Students' evaluation of teaching (SET) discriminant analysis model and algorithm based on principal component clustering analysis. Additionally, we classify the SET…

General formulas are derived for assessing local influence under restrictions in which the first derivatives are still zeros, and then these results are applied to factor analysis, as the usually used restriction in factor analysis satisfies the conditions. (SLD)

The Schmid-Leiman (J. Schmid and J. M. Leiman, 1957) decomposition of a hierarchical factor model converts the model to a constrained case of a bifactor model with orthogonal common factors that is equivalent to the hierarchical model. This article discusses the equivalence of the hierarchical and bifactor models. (Author/SLD)

Demonstrated that the extra-factor phenomenon (the two-dimensional solution produced when linear factor analysis is applied to a set of unfoldable items) arises because the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model and the unidimensional quadratic factor model is not distinguishable from the…

A general linear model framework is used to suggest that structure coefficients ought to be interpreted in structural equation modeling confirmatory factor analysis (CFA) studies in which factors are correlated. Two heuristic data sets make the discussion concrete, and two additional studies illustrate the benefits of CFA structure coefficients.…

PARAFAC is a generalization of principal components analysis in a factor score matrix and in a factor loadings matrix. How PARAFAC behaves when applied to positive manifold data is examined, and a constrained PARAFAC method is offered for use when PARAFAC does not produce a positive manifold solution. (SLD)

The factor structure of the "KeyMath--Revised Normative Update" (KMR-NU) "Form A" was analyzed using data from a sample of 130 students. The KMR-NU is composed of 13 subtests that are purported to measure three important aspects of math ability: Basic Concepts, Operations, and Applications. A confirmatory factor analysis…

The power of the likelihood ratio test in multiple group confirmatory factor analysis under partial measurement invariance was studied in a population study with a six-variable, two-factor model where a specification error existed for one group. Results are discussed in terms of strategies of multiple group modeling. (SLD)

Simple modifications of principal component methods are described that have distinct advantages for structural analysis of relations among educational and psychological variables. The methods are contrasted theoretically and empirically with conventional principal component methods and with maximum likelihood factor analysis. (Author/GK)

Canonical correlation and redundancy analysis are two approaches to analyzing the interrelationships between two sets of measurements made on the same variables. A component method is presented which uses aspects of both approaches. An empirical example is also presented. (Author/JKS)

The issue of indeterminacy in factor analysis and the debate between the proposed alternative solution and posterior moment position are explored in an article and 14 commentaries and rebuttals in two rounds. Implications for applied work involving factor analysis are discussed. (SLD)

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…