By Scott Menard
Emphasizing the parallels among linear and logistic regression, Scott Menard explores logistic regression research and demonstrates its usefulness in interpreting dichotomous, polytomous nominal, and polytomous ordinal established variables. The publication is geared toward readers with a historical past in bivariate and a number of linear regression.
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Extra resources for Applied Logistic Regression Analysis (Quantitative Applications in the Social Sciences)
43-47). 2, there was some evidence of nonlinearity in the relationship between frequency of marijuana use and exposure to delinquent friends. One possible transformation that could be used to model this nonlinearity is a logarithmic transformation 6 of the dependent variable, FRQMRJ5. This is done by adding 1 to FRQMRJ5 and then taking the natural logarithm. 72 is the base of the natural logarithm. 32. 1, it is evident that the slope is still positive but the numerical value of the slope has changed (because the units in which the dependent variable is measured have changed from frequency to logged frequency).
The Score statistic, AIC, and the Schwartz criterion are provided in SAS PROC LOGISTIC. The Score statistic, discussed in Hosmer and Lemeshow (1989), is, like GM, a test of the statistical significance of the combined effects of the independent variables in the model. The AIC and the Schwartz criterion, briefly discussed in Bollen (1989), are two related indices used for comparing models, rather than providing absolute tests of adequacy of fit. It is possible to compare the AIC or the Schwartz criterion for the fitted model with the AIC or Schwartz criterion for the model with only the intercept, but this provides little more information than GM or DM.
Chapter 4 looks at regression diagnostics but in Page vi a logistic context. Those who have studied ordinary regression diagnostics will find the list of problems familiar: omitted relevant variables, included irrelevant variables, nonlinearity, nonadditivity, collinearity, and outliers. Chapter 5 explores logistic regression when the dependent variable is polytomous, rather than dichotomous. Methodological work, as well as published research examples, emphasizes the simple case of the two-category dependent variable, but, obviously, the situation of a dependent variable with three or more categories is common and deserves more application.