Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Variable Abbreviation Coding

Type of hospital HT 1 ¼public, 0¼private
Size of hospital HS 1 ¼large, 0¼small
Degree of
contamination

CT 1 ¼contaminated,
0 ¼clean
Age AGE continuous
Sex SEX 1 ¼female, 0¼male

1. State the logit form of a no interaction model that
   includes all of the above predictor variables.


2. State the logit form of a model that extends the model
   of Exercise 1 by adding all possible pairwise products
   of different variables.


3. Suppose you want to carry out a (global) test for
   whether any of the two-way product terms (considered
   collectively) in your interaction model of Exercise 2 are
   significant. State the null hypothesis, the form of the
   appropriate (likelihood ratio) test statistic, and the dis-
   tribution and degrees of freedom of the test statistic
   under the null hypothesis of no interaction effects in
   your model of Exercise 2.

Suppose the test for interaction in Exercise 3 is nonsignif-

icant, so that you felt justified to drop all pairwise products

from your model. The remaining model will, therefore,

contain only those variables given in the above listing.

4. Consider a test for the effect of hospital type (HT)
   adjusted for the other variables in the no interaction
   model. Describe the likelihood ratio test for this effect
   by stating the following: the null hypothesis, the for-
   mula for the test statistic, and the distribution and
   degrees of freedom of the test statistic under the null
   hypothesis.


5. For the same question as described in Exercise 4, that
   is, concerning the effect of HT controlling for the other
   variables in the model, describe the Wald test for this
   effect by providing the null hypothesis, the formula for
   the test statistic, and the distribution of the test statistic
   under the null hypothesis.


6. Based on the study description preceding Exercise 1,
   do you think that the likelihood ratio and Wald test
   results will be approximately the same? Explain.


7. Give a formula for a 95% confidence interval for the
   odds ratio describing the effect of HT controlling for
   the other variables in the no interaction model.

Practice Exercises 157