The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

This study investigated personality correlates of early adolescents' tendency to either defend victims of bullying or to avoid involvement in bullying situations. Participants were 591 Dutch fifth- and sixth-grade students (X-bar[subscript age] = 11.42 years). Hierarchical regression models were run to predict these students' peer-reported…

Sharing user information between systems is an area of interest for every field involving personalization. Recommender Systems are more advanced in this aspect than Intelligent Tutoring Systems (ITSs) and Intelligent Learning Environments (ILEs). A reason for this is that the user models of Intelligent Tutoring Systems and Intelligent Learning…

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

In order to make parallel analysis more accessible to researchers employing principal component techniques, regression equations are presented for the logarithms of the latent roots of random data correlation matrices with unities on the diagonal. (Author/LMO)

The extension of regression estimation and poststratification to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISTREL framework. (Author/LMO)

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. An example is presented to demonstrate potential problems in other approaches to maximum likelihood factor analysis. (Author/JKS)

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

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…

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Canonical weights and structure correlations are used to construct low dimensional views of the relationships between two sets of variables. These views, in the form of biplots, display familiar statistics: correlations between pairs of variables, and regression coefficients. (SLD)

A constrained component analysis method, which bears a formal resemblance to the confirmatory factor analysis methods developed by K. G. Joreskog (1969) and others, is presented. In confirmatory factor analysis, the constraints allow the testing of formally structural hypotheses within a model that is falsifiable, even in its "just…

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of diagonal elements. This paper reviews both fields; points out various small errors; and presents a methodological comparision of factor analysis and…

Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum likelihood and least squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood ratio…