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

d. For group 5, term involving cases:

(109.98)^2 /9.98¼0.00004

term involving noncases:

(2020.02)^2 /20.02¼0.00002

e. 20 terms in the sum, with 10 terms for cases

(mrsa¼1) and 10 terms for noncases (mrsa¼0).

8. No. The model is not fully parameterized, since it
   contains eight parameters whereas the number of
   covariate patterns is 186.


9. No. The model does not perfectly predict the case/
   noncase status of each of the 289 subjects in the data.


10. a. The deviance value of 157.1050 is not calculated
    using the deviance formula
    Devð^bÞ¼ 2 lnðL^c=L^maxÞ:
    In particular 2 lnL^c¼ 277 : 221 and 2 lnL^max¼ 0 ,
    so Devð^bÞ¼ 277 : 221.
    b. G¼no. of covariate patterns¼186 is large relative
    ton¼289.


11. a. The HL test has aP-value of 0.9686, which is highly
    nonsignificant. Therefore, the HL test indicates
    that the model does not have lack of fit.
    b. Although the Hosmer-Lemeshow test for the
    interaction model is more nonsignificant
    (P¼0.9686) than the Hosmer-Lemeshow test for
    the no-interaction model (P¼0.4553), both models
    adequately fit the data and these twoP-values are
    not sufficient to conclude which model is preferable.
    c. Perform a (LR) test of hypothesis that compares
    interaction and no-interaction models.
    H 0 :d 1 ¼d 2 ¼d 2 ¼0 in the interaction model;
    LR¼ 2 lnL^no interactionð 2 lnL^interactionÞ
    ¼ 279 : 317  277 : 221 ¼ 2 : 096
    ¼DevModel 1 DevModel 2 ¼ 159 : 2017  157 : 1050
    ¼ 2 : 0967 ;

which has approximately a chi-square distribution

with 3 d.f. underH 0. TheP-value satisfies

0.50<P<0.60, which indicates thatH 0 should

not be rejected. Conclusion: No-interaction

model is preferred.

Chapter 10 1. a.

True (Observed) Outcome

cp 5 0.30 Y¼ 1 Y¼ 0

Predicted Y¼ 1 nTP¼ 98 nFP¼ 68

Outcome Y¼ 0 nFN¼ 16 nTN¼ 107

n 1 ¼ 114 n 0 ¼ 175

Chapter 10 681