Multiple regression is part of a larger statistical strategy originated by Gauss. The authors raise questions about the theory and suggest some changes that would make room for Mandelbrot and Serendipity.

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and…

In a 2010 address to the College Board, U.S. Secretary of Education Arne Duncan laid out a vision for high school that advances the Obama administration's goal of the U.S. once again leading the world in educational attainment. There is no grade in which the magnitude and complexity of this shift becomes clearer than in senior year. Historically,…

Commonality analysis is a method of partitioning variance to determine the predictive ability unique to each predictor (or predictor set) and common to two or more of the predictors (or predictor sets). The purposes of the present paper are to (a) explain commonality analysis in a multiple regression context as an alternative for middle grades…

This "Practitioner's Guide to Growth Models," commissioned by the Technical Issues in Large-Scale Assessment (TILSA) and Accountability Systems & Reporting (ASR), collaboratives of the "Council of Chief State School Officers," describes different ways to calculate student academic growth and to make judgments about the…

We discuss aspects of multivariate fMRI modeling, including the statistical evaluation of multivariate models and means for dimensional reduction. In a case study we analyze linear and non-linear dimensional reduction tools in the context of a "mind reading" predictive multivariate fMRI model.

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

In this study, we examine the role of academic preparation in the transition from community colleges to four-year institutions. We address two specific questions: To what extent do academically unprepared students transfer to four-year institutions? And, can positive experiences in community colleges diminish the role of inadequate academic…

This paper contains information concerning the following: 1. An overview of multivariate analysis of variance, and discriminant (DA) and canonical (CA) analyses. 2. An introduction to specification and measurement errors, and collinearity. 3. The sparsity of information concerning specification and measurement errors and collinearity as they…

The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…

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…

Rectifies the unsatisfactory textbook treatment of the finite-sample proprieties of estimators of regression models with a lagged dependent variable and autocorrelated disturbances. Maintains that the bias of the ordinary least squares estimator is determined by the dynamic and correlation effects. (MJP)

This report describes 12 studies dealing with the knowledge monitoring component of metacognition. It is assumed that knowledge monitoring is basic to other metacognitive activities, such as evaluating learning, selecting appropriate strategies, or planning, because distinguishing between what students know and do not know ought to be a…