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…

Normal theory maximum likelihood (ML) is by far the most popular estimation and testing method used in structural equation modeling (SEM), and it is the default in most SEM programs. Even though this approach assumes multivariate normality of the data, its use can be justified on the grounds that it is fairly robust to the violations of the…

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript…

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 optimum weighting of variables to predict a dependent-criterion variable is an important problem in nearly all of the social and natural sciences. Although the predominant method, multiple regression analysis (MR), yields optimum weights for the sample at hand, these weights are not generally optimum in the population from which the sample was…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…