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Qual Quant (2009) 43:5974
DOI 10.1007/s11135-007-9077-3
ORIGINAL PAPER
Ottar Hellevik
Published online: 16 February 2007 Springer Science+Business Media B.V. 2007
Abstract The article argues against the popular belief that linear regression should not be used when the dependent variable is a dichotomy. The relevance of the statistical arguments against linear analyses, that the tests of signicance are inappropriate and that one risk getting meaningless results, are disputed. Violating the homoscedasticity assumption seems to be of little practical importance, as an empirical comparison of results shows nearly identical outcomes for the two kinds of signicance tests. When linear analysis of dichotomous dependent variables is seen as acceptable, there in many situations exist compelling arguments of a substantive nature for preferring this approach to logistic regression. Of special importance is the intuitive meaningfulness of the linear measures as differences in probabilities, and their applicability in causal (path) analysis, in contrast to the logistic measures.
Keywords Logistic regression Binary variables Signicance tests
1 Introduction
In analyses of survey data it is not unusual that the dependent variable is a dichotomy. When the research problem requires a multivariate solution, regression analysis is very convenient for handling large numbers of independent variables.1 Today it seems to be a common belief that with a binary dependent variable (dichotomy coded
1 This opportunity is sometimes overexploited, however. A regression analysis of binary variables does not have access to information that is lacking in the corresponding tabular analysis. When more variables may be included in the regression analysis, this is due to the distributional assumptions on which the regression analysis is based. With a large number of variables one runs the risk that an estimate reects the model more than the data. (Rubin 1997; Rothman and Greenland 1998).
O. Hellevik (B)
Department of Political Science, University of Oslo, P.O. Box 1097, 0317, Blindern, Oslo, Norway e-mail: [email protected]
Linear versus logistic regression when the dependent variable is a dichotomy
60 O. Hellevik
01) ordinary linear regression cannot be used.2 Logistic regression is a prerequisite for an article to be considered for publication in a serious scientic journal, one hears.
Two statistical arguments are given for this rejection of linear regression. One is that with linear coefcients we risk meaningless results, since a predicted probability...