The commensurability of the general linear model in the context of educational and psychosocial research

In explanatory research, as opposed to exploratory research, data analysis is meant to shed light on substantive theory. The potential for accomplishing this goal is predicated, among other things, on the use of statistical models that are commensurate with the theoretical model specifications to which they are applied. This paper discusses the commensura-bility conditions applying to the general linear model (GLM) and examines some of the more serious limitations entailed by the widespread and often uncritical use of the GLM, particularly in exploratory educational and psychosocial ex post facto research. By an examination of the statistical properties of the GLM and the use of illustrative examples from a recent and well-known work in educational research, it is argued that, even in the context ofexplanatory research, where the conditions for statistical and theoretical model commensurability are most likely to hold, the GLM has notable weaknesses and limita-tions. Among the statistical models available to educational and psychosocial researchers, the general linear model (GLM) is possibly the simplest (at least at the prima facie level) and most popular (Bibby, 1977; Draper & Smith, 1981; Morrison, 1976