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

Answers to Practice Exercises

Practice Exercises

1. TheVvariables should include theCvariables HS, CT,
   AGE, and SEX and any functions of these variables
   that have some justification based on previous
   research or theory about risk factors for surgical
   wound infection. The simplest choice is to choose the
   Vs to be theCs themselves, so that at least every
   variable already identified as a risk factor is controlled
   in the simplest way possible.


2. TheWvariables should include some subset of theVs,
   or possibly all theVs, plus those functions of theVs
   that have some support from prior research or theory
   about effect modifiers in studies of surgical wound
   infection. Also, consideration should be given, when
   choosing theWs, of possible statistical problems, e.g.,
   collinearity, that may arise if the size of the model
   becomes quite large and the variables chosen are
   higher order product terms. Such statistical problems
   may be avoided if theWs chosen do not involve very
   high-order product terms and if the number ofWs
   chosen is small. A safe choice is to choose theWstobe
   theVs themselves or a subset of theVs.


3. logit P(X)¼aþbHTþg 1 HSþg 2 CTþg 3 AGE
   þg 4 SEXþd 1 HTHSþd 2 HTCT
   þd 3 HTAGEþd 4 HTSEX.
   This model is HWF because given any interaction
   term in the model, both of its components are also in
   the model (as main effects).


4. If HTAGESEX is added to the model, the new
   model willnotbe hierarchically well formulated
   because the lower order component AGESEX is not
   contained in the original nor new model.


5. A test for HTAGESEX in the above model is
   dependent on coding in the sense that different test
   results (e.g., rejection vs. nonrejection of the null
   hypothesis) may be obtained depending on whether
   HT is coded as (0, 1) or (1, 1) or some other coding.
   Such a test should not be carried out because any test
   of interest should be independent of coding, reflecting
   whatever the real effect of the variable is.


6. A test for HTAGE in the model of Exercise 3 is
   independent of coding because the model is
   hierarchically well formulated and the HTAGE
   term is a variable of highest order in the model. (Tests
   for lower order terms like HT or HS are dependent on
   the coding even though the model in Exercise 3 is
   hierarchically well formulated.)


7. A test for the variable AGE is inappropriate because
   there is a higher order term, HTAGE, in the model,
   so that a test for AGE is dependent on the coding of the

Answers to Practice Exercises 201