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

Partition for the Hosmer and Lemeshow Test

mrsa¼1 mrsa¼ 0
Group Total Observed Expected Observed Expected
1 29 1 0.99 28 28.01
2 31 5 1.95 26 29.05
3 29 2 2.85 27 26.15
4 29 5 5.73 24 23.27
5 30 10 9.98 20 20.02
6 31 12 14.93 19 16.07
7 29 16 17.23 13 11.77
8 29 20 19.42 9 9.58
9 29 22 21.57 7 7.43
10 23 21 19.36 2 3.64

Hosmer and Lemeshow Goodness-of-Fit Test

Chi-Square DF Pr>ChiSq

7.7793 8 0.4553

Questions about the above output begin on the follow-
ing page.

1. Is data listing used for the above analysis in events
   trials (ET) format or in subject-specific format?
   Explain briefly.


2. How many covariate patterns are there for the model
   being fitted? Why are there so many?


3. Is the model being fitted a fully parameterized model?
   Explain briefly.


4. Is the model being fitted a saturated model? Explain
   briefly.


5. a. Is the deviance value of 159.2017 shown in the
   above output calculated using the deviance formula
   Devð^bÞ¼ 2 lnðL^c=L^maxÞ;
   whereL^c¼ML for current model andL^max¼ML
   for saturated model? Explain briefly.
   b. The deviance value of 159.2017 is obtained by com-
   paring log likelihood values from two logistic mod-
   els, one of which is the (no-interaction) model being
   fitted. Describe the other logistic model, called, say,
   Model 2. (Hint: You should answer this question
   without explicitly stating the independent variables
   contained in Model 2.)
   c. How can the deviance value of 159.2017 be calcu-
   lated using the difference between two log likeli-
   hood values obtained from the two models
   described in part b? What are the values of these
   two log likelihood functions?

Test 339