The relative
importance of predictors
is reflected in the regression coefficients of a regression
model. Interpretation is relatively straightforward for dichotomous
variables: the regression coefficient indicates what the effect
is of a characteristic's presence, versus its absence. For example,
when males are compared to females, the coefficient indicates
the difference between males and females, adjusted for the covariables
included in the model.
For continuous
predictors, the coefficient still indicates the effect of a
change in one unit on the outcome. A predictor may cover a wide
range, e.g. age between 20 and 65 years, and have a small coefficient
per unit, per year, for instance. For comparability we may then
contrast the effects at the 75th and 25th percentile, or code
the predictor in more relevant units, e.g. age in decades. To
see an illustration of the relative importance of predictors,
see Example 1: Gallstones
and Example 2: HELP Survival
Model at the end of this chapter.
The importance
of a predictor can be expressed by the standardized regression
coefficient, the p-value,
or the amount of explained variation. These measures are determined
by the magnitude of the regression coefficient and the spread
in the predictor. For example, a rare characteristic may not
be statistically significant (p-value not smaller than the conventional
criterion of 5%), despite a similar regression coefficient as
a more frequent characteristic.