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

6. a. What can you conclude from the Hosmer–
   Lemeshow statistic provided in the above output
   about whether the model has lack of fit to the
   data? Explain briefly.
   b. Why does the output shown under “Partition for the
   Hosmer and Lemeshow Test” involve only 6 groups
   rather than 10 groups, and why is the degrees of
   freedom for the test equal to 4? Explain briefly.
   c. What two models are actually being compared by
   the Hosmer–Lemeshow statistic of 0.9474? Explain
   briefly.
   d. How can you choose between the two models
   described in part c?
   e. Does either of the two models described in part c
   perfectly fit the data? Explain briefly.

Additional questions using the same Evans County data

described at the beginning of these exercises consider

SAS output provided below for the following (interac-

tion) logistic model:

Logit PðXÞ¼aþb 1 CATþg 1 AGEþg 2 ECGþg 3 AGEECG

þd 1 CATAGEþd 2 CATECG

þd 3 CATAGEECG

Deviance and Pearson Goodness-of-Fit Statistics

Criterion Value DF Value/DF Pr>ChiSq

Deviance 0.0000 0 · ·

Pearson 0.0000 0 · ·

Number of unique profiles: 8

Model Fit Statistics

Criterion Intercept Only

Intercept and

Covariates

2 Log L 438.558 417.226

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate

Std

Error

Wald

Chi-Sq Pr>ChiSq

Intercept 1 2.7158 0.2504 117.6116 <.0001

cat 1 0.7699 1.0980 0.4917 0.4832

age 1 0.7510 0.3725 4.0660 0.0438

ecg 1 0.7105 0.4741 2.2455 0.1340

catage 1 0.00901 1.1942 0.0001 0.9940

catecg 1 0.3050 1.3313 0.0525 0.8188

ageecg 1 0.4321 0.7334 0.3471 0.5557

cae 1 0.0855 1.5245 0.0031 0.9553

336 9. Assessing Goodness of Fit for Logistic Regression