chapter  13
16 Pages

Comparing Regression Coefficients

This example illustrates that it is in general not possible to compare regression coefficients directly, because a regression coefficient β j describes the effect of changing the covariate Xj by one unit, and hence its size depends on the scale we use to measure the covariate. For example, in Table 13.1 the regression coefficient of Experience is −0.024, which looks rather small. However, if we use Decades in Practice, we obtain a 10-fold value (i.e., −0.249) which looks more impressive. (For the same reason, the effect of Age looks small in most applications, because we are used to measure age in years, and the effect of being older 1 year is usually small.)

So if we want to compare regression coefficients, we must ensure that they are measured on comparable scales or that we express them in a comparable manner. One approach is to consider the difference between a subject for whom the covariate x j is equal to the 10% percentile of the distribution of Xj and a subject for whom the covariate is equal to the 90% percentile. This can be easily achieved by multiplying

covariate βˆ 95%CI Experience

(Number of years in practice) −0.024 [−0.057,0.0074] Workload (Number of

surgery consultations/year/GP) −0.00012 [−0.00033,0.000083] Counselling (Number of

counsellings/year/100 patients) −0.98 [−1.94,−0.03] Drug prescription (Number of patients

covariate βˆ 95%CI Experience −0.48 [−1.10,0.14] Workload −0.47 [−1.23,0.30] Counselling −0.61 [−1.21,−0.02] Drug prescription 1.49 [0.52,2.47]

the observed regression coefficient β j with the observed difference Δ j between the 90% percentile and the 10% percentile.