Biostatistics

576 CHAPTER 11 REGRESSION ANALYSIS: SOME ADDITIONAL TECHNIQUES
0.65
0.60
0.55
0.50
Estimated probability
0.45
0.40
0.35
0.30
0.25
0.20
0.15
30
40
50
60
70
80
90 100
FIGURE 11.4.3 Estimated probabilities of attendance for ages within the study for
Example 11.4.2.
&
Multiple Logistic Regression Practitioners often are interested in the relationships
of several independent variables to a response variable. These independent
variables may be either continuous or discrete or a combination of the two.
Multiple logistic models are constructed by expanding Equations (11.4.1) to (11.4.4).
If we begin with Equation 11.4.4, multiple logistic regression can be represented as
p
ln ¼ b
1 p 0 þ b 1 x 1j þ b 2 x 2j þþb k x kj (11.4.6)
Using the logit transformation, we now have
p ¼
exp b 0 þ b 1 x 1j þ b 2 x 2j þþb k x kj
1 þ exp b 0 þ b 1 x 1j þ b 2 x 2j þþb k x kj
(11.4.7)
EXAMPLE 11.4.3
Consider the data presented in Review Exercise 24. In this study by Fils-Aime et al. (A-21),
data were gathered and classified with regard to alcohol use. Subjects were classified
as having either early (< 25 years) or late (> 25 years) onset of excessive alcohol use.