type of test to check for linearity. It can also be used to check for a single
product representing an e¤ect modification.
Example 11.16 Refer to the data for low-birth-weight babies in Example
11.11 (Table 11.14), but this time we investigate only one covariate, the
mother’s weight. After fitting the second-degree polinomial model, we obtained
a result which indicates that thecurvature e¤ectis negligibleðp¼ 0 : 9131 Þ.
Contribution of a Group of Variables This testing procedure addresses the
more general problem of assessing the additional contribution of two or more
factors to the prediction of the response over and above that made by other
variables already in the regression model. In other words, the null hypothesis is
of the form
H 0 :b 1 ¼b 2 ¼¼bm¼ 0To test such a null hypothesis, one can perform a likelihood ratio chi-square
test withmdf:
w^2 LR¼ 2 ½lnLðbb^;allX’sÞlnLðbb^;all otherX’s withX’s under investigation deletedÞAs with the tests above for individual covariates, thismultiple contribution
procedureis very useful for assessing the importance of potential explanatory
variables. In particular, it is often used to test whether a similar group of vari-
ables, such asdemographic characteristics, is important for prediction of the
response; these variables have some trait in common. Another application
would be a collection of powersand/orproduct terms (referred to asinteraction
variables). It is often of interest to assess the interaction e¤ects collectively
before trying to consider individual interaction terms in a model, as suggested
previously. In fact, such use reduces the total number of tests to be performed,
and this, in turn, helps to provide better control of overall type I error rates,
which may be inflated due to multiple testing.
Example 11.17 Refer to the data for low-birth-weight babies in Example
11.11 (Table 11.14). With all four covariates, we consider collectively three
TABLE 11.18
Variable Coe‰cient
Standard
Error zStatistic pValueBleeding 1.6198 1.3689 1.183 0.2367
Pregnancy loss 1.7319 0.8934 1.938 0.0526
CONDITIONAL LOGISTIC REGRESSION 423