Chapter 2: The Multiple Logistic Regression Model
In Chapter 1 we introduced the logistic regression model in the context of a model containing a single variable. As in the case of linear regression, the strength of the logistic regression model is its ability to handle many variables, some of which may be on different measurement scales. In this chapter, we generalize the model to one with more than one independent variable (i.e., the multivariable or multiple logistic regression model). Central to the consideration of the multiple logistic models is estimating the coefficients and testing for their significance. We use the same approach discussed in Chapter 1 for the univariable setting. An additional modeling consideration, which is introduced in this chapter, is using design variables for modeling discrete, nominal scale, independent variables. In all cases, we assume that there is a predetermined collection of variables to be examined. We consider statistical methods for selecting variables in Chapter 4.
2.2 The Multiple Logistic Regression Model
Consider a collection of independent variables denoted by the vector . For the moment we assume that each of these variables is at least interval scaled. Let the conditional probability that the outcome is present be ...