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

d. Why is the deviance value of 159.2017 not

distributed approximately as a chi-square variable

under the null hypothesis that the no-interaction

model provides adequate fit?

6. a. What can you conclude from the Hosmer–Leme-
   show statistic provided in the above output about
   whether the model has lack of fit to the data?
   Explain briefly.
   b. What two models are actually being compared by
   the Hosmer–Lemeshow statistic of 7.7793? Explain
   briefly.
   c. How can you choose between the two models
   described in part b?
   d. Does either of the two models described in part c
   perfectly fit the data? Explain briefly.


7. Consider the information shown in the ouput under the
   heading “Partition for the Hosmer and Lemeshow Test.”
   a. Briefly describe how the 10 groups shown in the
   output under “Partition for the Hosmer and Leme-
   show Test” are formed.
   b. Why does not each of the 10 groups have the same
   total number of subjects?
   c. For group 5, describe how the expected number of
   cases (i.e., mrsa¼1) and expected number of non-
   cases (i.e., mrsa¼0) are computed.
   d. For group 5, compute the two values that are
   included as two of the terms in summation formula
   for the Hosmer–Lemeshow statistic.
   e. How many terms are involved in the summation
   formula for the Hosmer–Lemeshow statistic?

Additional questions consider SAS output provided

below for the following logistic model:

Logit PðXÞ¼aþb 1 PREVHOSPþg 1 AGEþg 2 GENDER

þg 3 PAMUþd 1 PRHAGEþd 2 PRHGEN

þd 2 PRHPAMU

Deviance and Pearson Goodness-of-Fit Statistics

Criterion Value DF Value/DF Pr>ChiSq

Deviance 157.1050 178 0.8826 0.8683

Pearson 159.8340 178 0.8979 0.8320

Model Fit Statistics

Criterion Intercept Only Intercept and Covariates

2 Log L 387.666 277.221

340 9. Assessing Goodness of Fit for Logistic Regression