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

Partition for the Hosmer and Lemeshow Test
Event Nonevent
Group Total Observed Expected Observed Expected
1 274 17 18.66 257 255.34
2 59 7 5.60 52 53.40
3 122 15 14.53 107 107.47
4 57 9 8.94 48 48.06
5 39 9 7.85 30 31.15
6 58 14 15.41 44 42.59

Hosmer and Lemeshow Goodness-of-Fit Test

Chi-Square DF Pr>ChiSq

0.9474 4 0.9177

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

1. Is data listing described above in events trials (ET)
   format or in subject-specific (SS) format? Explain
   briefly.


2. How many covariate patterns are there for the model
   being fitted? Describe them.


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 0.9544 shown in the above
   output calculated using the deviance formula

Devðb^Þ¼ 2 lnðL^c=L^maxÞ;

whereL^c¼ML for current model andL^max¼ML

for saturated model? Explain briefly.

b. State the logit form of two logistic models that can

be used to calculate the deviance value of 0.9544.

Hint: One of these models is the model being fitted.

c. How can the deviance value of 0.9544 be calculated

using the difference between two log likelihood

values obtained from the two models stated in part

b? What are the values of these two log likelihood

functions?

d. What is actually being tested using this deviance

statistic? Explain briefly.

e. How can you justify that this deviance statistic is

approximately chi-square under the null hypothesis

that the fitted model has adequate fit to the data?

Practice Exercises 335