Brian S. Everitt A Handbook of Statistical Analyses using SPSS

Competing models in a logistic regression can be formally
compared by a likelihood ratio (LR) test, a score test or by
Wald’s test. Details of these tests are given in Hosmer and
Lemeshow (2000).
The three tests are asymptotically equivalent but differ in finite
samples. The likelihood ratio test is generally considered the
most reliable, and the Wald test the least (see Therneau and
Grambsch, 2000, for reasons), although in many practical applications
the tests will all lead to the same conclusion.
This is a convenient point to mention that logistic regression and the
other modeling procedures used in earlier chapters, analysis of variance and
multiple regression, can all be shown to be special cases of the generalized
linear model formulation described in detail in McCullagh and Nelder (1989).
This approach postulates a linear model for a suitable transformation of the
expected value of a response variable and allows for a variety of different
error distributions. The possible transformations are known as link functions.
For multiple regression and analysis of variance, for example, the link
function is simply the identity function, so the expected value is modeled
directly, and the corresponding error distribution is normal. For logistic
regression, the link is the logistic function and the appropriate error distribution
is the binomial. Many other possibilities are opened up by the
generalized linear model formulation — see McCullagh and Nelder (1989)
for full details and Everitt (2002b) for a less technical account.
9.3 Analysis Using SPSS
Our analyses of the Titanic data in Table 9.1 will focus on establishing
relationships between the binary passenger outcome survival (measured
by the variable survived with “1” indicating survival and “0” death) and
five passenger characteristics that might have affected the chances of
survival, namely:
Passenger class (variable pclass, with “1” indicating a first class
ticket holder, “2” second class, and “3” third class)
Passenger age (age recorded in years)
Passenger gender (sex, with females coded “1” and males coded “2”)
Number of accompanying parents/children (parch)
Number of accompanying siblings/spouses (sibsp)
Our investigation of the determinants of passenger survival will proceed
in three steps. First, we assess (unadjusted) relationships between survival
© 2004 by Chapman & Hall/CRC Press LLC