Lecture 22
Multiple Logistic Regression

Just as in OLS regression, logistic regression can be used with more than one predictor. The analysis options are similar to regression. One can choose to select variables, as with a stepwise procedure, or one can enter the predictors simultaneously, or they can be entered in blocks.

The interpretation is similar. Slopes and odds ratios represent the "partial" prediction of the dependent variable. A slope for a given predictor represents the average change in y for each unit change in x, holding constant the effects of the other variable. For instance, we might examine the prediction of CHD by age, controlling for or holding constant the effects of gender. We might expect, for instance, that men will have greater risk of CHD, so if our sample contains men and women, we might want to "partial out" the effects of gender on CHD. The odds ratio then represents the risk of CHD given an increase of 1 year in age, controlling for or independent of gender.

Another example might be activity level (or exercise). Because people who are more active will have a lower risk of CHD, it might be hypothesized that the relationship between age and CHD is partly or completely due to declining activity levels associated with age. Thus, activity level might be considered a third variable which is responsible for our initial relationship between age and CHD. If we controlled for activity level, we might see a decline or an elimination of the predictive effect of age. The odds ratios would tell us the independent risk of activity level and age for CHD.

As with OLS regression, logistic regression can test interaction effects or curvilinear relationships. And the analysis for these proceed similarly. With interactions, a third, multiplicative term is computed which is the product of the two predictors. All three are used to predict the dependent variable. With curvilinear effects, the variable is squared to produce a new variable that tests the curvilinear relationship. It is usually recommended that the two variables (squared and not squared) are entered together to test the linear and cuvilinear relationships of the predictor to the dependent variable.

As with OLS, we also want to test the overall predictive efficiency of all predictors together. With SPSS, a researcher might have to run several logistic regression analyses to get the appropriate difference in chi-squares. For instance, if the researcher chooses to do a stepwise procedure to select the significant predictors, he or she might have to rerun the new analysis to get the difference in fit from the no predictor model and the full model containing all the predictors.

My coverage and the text's coverage of logistic regression has been an introductory one. If you would like to learn more about logistic regression, the most accessible source I have found is the following book:

Hosmer, D.W., & Lemeshow, S. (1989). Applied logistic regression. New York: Wiley & Sons.