- Test for the significance of the factor selected in step 2 and determine,
according to a certain predetermined criterion, whether or not to delete
this factor from the model. - Repeat steps 2 and 3 for those variables still in the model. At any sub-
sequent step, if none meets the criterion in step 3, no more variables are
removed in the model and the process is terminated.
Stepwise regression procedure. Stepwise regression is a modified version
of forward regression that permits reexamination, at every step, of the
variables incorporated in the model in previous steps. A variable entered
at an early stage may become superfluous at a later stage because of its
relationship with other variables now in the model; the information it
provides becomes redundant. That variable may be removed if meeting
the elimination criterion, and the model is re-fitted with the remaining
variables, and the forward process goes on. The entire process, one step
forward followed by one step backward, continues until no more variables
can be added or removed.
Criteria For the first step of the forward selection procedure, decisions are
based on individual score test results (chi-square, 1 df). In subsequent steps,
both forward and backward, the ordering of levels of importance (step 2)
and the selection (test in step 3) are based on the likelihood ratio chi-square
statistic:
w^2 LR¼ 2 ½lnLðbb^;all otherX’sÞlnLðbb^;all otherX’s with oneXdeletedÞExample 9.8 Refer to the data set on prostate cancer of Example 9.1 (Table
9.1) with all five covariates: x-ray, stage, grade, age, and acid. This time we
perform a stepwise regression analysis in which we specify that a variable has
to be significant at the 0.10 level before it can enter into the model and that a
variable in the model has to be significant at the 0.15 for it to remain in the
model (most standard computer programs allow users to make these selections;
default values are available). First, we get these individual score test results
for all variables (Table 9.8). These indicate that x-ray is the most significant
variable.
TABLE 9.8
Variable Scorew^2 pValue
X-ray 11.2831 0.0008
Stage 7.4383 0.0064
Grade 4.0746 0.0435
Age 1.0936 0.2957
Acid 3.1172 0.0775334 LOGISTIC REGRESSION