Partition for the Hosmer and Lemeshow Testmrsa¼1 mrsa¼ 0
Group Total Observed Expected Observed Expected
1 29 1 1.50 28 27.50
2 30 2 2.44 28 27.56
3 29 4 3.01 25 25.99
4 29 5 4.76 24 24.24
5 29 10 7.87 19 21.13
6 29 11 12.96 18 16.04
7 31 17 18.27 14 12.73
8 32 22 21.93 10 10.07
9 31 24 23.85 7 7.15
10 20 18 17.40 2 2.60
Hosmer and Lemeshow Goodness-of-Fit TestChi-Square DF Pr>ChiSq
2.3442 8 0.9686- Is the model being fitted a fully parameterized model?
Explain briefly. - Is the model being fitted a saturated model? Explain
briefly. - a. Is the deviance value of 157.1050 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. Why cannot you use this deviance statistic to test
whether the interaction model provides adequate fit
to the data? Explain briefly. - a. What can you conclude from the Hosmer–
Lemeshow statistic provided in the above output
about whether the interaction model has lack of fit
to the data? Explain briefly.
b. Based on the Hosmer–Lemeshow test results for
both the no-interaction and interaction models,
can you determine which of these two models is
the better model? Explain briefly.
c. How can you use the deviance values from the out-
put for both the interaction and no-interaction
models to carry out an LR test that compares these
two models? In your answer, state the null hypothe-
sis being tested, the formula for the LR statistic
using deviances, carry out the computation of the
LR test and draw a conclusion of which model is
more appropriate.
Test 341