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 commensurability 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 of explanatory research, where the conditions for statistical and theoretical model commensurability are most likely to hold, the GLM has notable weaknesses and limitations.
BentlerP.M. (1980). Multivariate analysis with latent variables: Causal modelling. Annual Review of Psychology, 31, 419–45.
3.
BibbyJ.M. (1977). The general linear model: A cautionary tale. In O'MuircheartaighC.O.PayneC. (Eds.), The Analysis of Survey Data, Volume 2: Model Fitting (pp. 35–79). New York: Wiley.
4.
BoringE.G. (1923). Intelligence as the tests test it. New Republic, 34, 35–6.
5.
ChalmersA.F. (1976). What is this Thing Called Science?St Lucia: University of Queensland Press.
6.
DelamontS.HamiltonD. (1984). Revisiting classroom research: A continuing cautionary tale. In DelamontS. (Ed.), Readings on Interaction in the Classroom (pp. 3–37). London: Methuen.
7.
DraperN.R.SmithH. (1981). Applied Regression Analysis (2nd ed.). New York: Wiley.
8.
EcobR.EvansJ.HutchisonD.PlewisI. (1982). Reading between the Numbers: A Critical Guide to Educational Research. London: BSSRS Publications.
9.
EcobR.GoldsteinH. (1983). Instrumental variable methods for the estimation of test score reliability. Journal of Educational Statistics, 8, 223–41.
10.
FergusonG.A. (1981). Statistical Methods in Psychology and Education (5th ed.). New York: McGraw-Hill.
11.
GauldA.ShotterJ. (1977). Human Action and its Psychological Investigation. London: Routledge & Kegan Paul.
12.
GoldsteinH. (1980). The statistical procedures. In TizardB. (Ed.), Fifteen Thousand Hours: A Discussion (Bedford Way Papers No. 1, pp.21–5). London: University of London Institute of Education.
13.
GoldsteinH. (1984). Present position and potential developments: Some personal views on statistics in the social sciences. Journal of the Royal Statistical Society, Series A, 147 (Pt 2), 260–7.
14.
GoldsteinH. (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73, 43–56.
15.
GoldsteinH. (1987). Multilevel Models in Educational and Social Research. London: Griffin.
16.
GouldS.J. (1981). The Mismeasure of Man. Harmondsworth, Mx: Penguin.
17.
HarrisR.J. (1985). A Primer of Multivariate Statistics (2nd ed.). New York: Academic Press.
18.
HarréR.SecordP.F. (1972). The Explanation of Social Behaviour. Oxford: Basil Blackwell.
19.
HealyM.J.R.GoldsteinH. (1976). An approach to the scaling of categorized attributes. Biometrika, 63, 219–29.
20.
HeathA.CliffordP. (1981). The measurement and explanation of school outcomes. Oxford Review of Education, 7, 33–40.
21.
HoutsP.L. (Ed.). (1977). The Myth of Measurability. New York: Hart Publishing.
22.
HumeD. (1975). [Enquiries Concerning Human Understanding and Concerning the Principles of Morals] (NidditchP.H., Ed., 3rd ed.). Oxford: Clarendon Press. (Original work published 1777).
MorrisonD.F. (1976). Multivariate Statistical Methods (2nd ed.). New York: McGraw-Hill.
27.
PopkewitzT.S. (1984). Paradigm and Ideology in Educational Research. London: Falmer Press.
28.
RaudenbushS.BrykA.S. (1986). A hierarchical model for studying school effects. Sociology of Education, 59, 1–17.
29.
RutterM.MaughanB.MortimerP.OustonJ.SmithA. (1979). Fifteen Thousand Hours: Secondary Schools and their Effects on Children. West Compton House, nr Shepton Mallett, Somerset: Open Books.
30.
RyanA. (1970). The Philosophy of the Social Sciences. London: Macmillan.
31.
SalmonW.C. (1975). The Foundations of Scientific Inference. Pittsburgh, PA: University of Pittsburgh Press.
32.
ScottLong J. (1983). Covariance Structure Models: An Introduction to LISREL (Sage University Paper Series on Quantitative Applications in the Social Sciences, Series no. 07–34). Beverly Hills: Sage.
WongG.Y.MasonW.M. (1985). The hierarchical logistic regression model for multilevel analysis. Journal of the American Statistical Association, 80, 513–24.
35.
YoungM. (1980). A case study of the limitations of policy research. In TizardB. (Ed.), Fifteen Thousand Hours: A Discussion (Bedford Way Papers, No. 1, pp.29–37). London: University of London Institute of Education.
