The General Linear Model: A New Perspective on Some Familiar Topics

Abstract

This paper presents an attempt to explicate some common features of several superficially diverse techniques of data analysis and to indicate how the logic of a single abstract model is relevant to each. The specific purposes are: (1) to show in a relatively intuitive fashion the mathematical relationship between analysis of variance, regression analysis, and analysis of covariance, as special cases of the general linear model: (2) to suggest types of practical applications of analysis of covariance in social reserch; and (3) to indicate some generally overlooked parallels between the general linear model, especially as formulated in analysis of covariance, and other methodological topics, including Lazarsfeld's elaboration procedure for the 2 X 2 X 2 table, ecological correlations, compositional effects, and others. A final section points out some logical problems which arise in the attempt to apply any of the techniques of this class.