Page 439 - Applied Statistics with R

17.3. WORKING WITH LOGISTIC REGRESSION 439

## age 0.062416 0.009723 6.419 1.37e-10 ***
## ldl:famhistPresent 0.314311 0.114922 2.735 0.00624 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 596.11 on 461 degrees of freedom
## Residual deviance: 477.46 on 455 degrees of freedom
## AIC: 491.46
##
## Number of Fisher Scoring iterations: 5

Based on the -test seen in the above summary, this interaction is significant.
The effect of LDL on the probability of CHD is different depending on family
history.

17.3.7.2 Polynomial Terms

Let’s take the previous model, and now add a polynomial term.

chd_mod_int_quad = glm(chd ~ alcohol + ldl + famhist + typea + age + ldl:famhist + I(ldl^2),
data = SAheart, family = binomial)
summary(chd_mod_int_quad)

##
## Call:
## glm(formula = chd ~ alcohol + ldl + famhist + typea + age + ldl:famhist +
## I(ldl^2), family = binomial, data = SAheart)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8953 -0.8311 -0.4556 0.9276 2.5204
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.096747 1.065952 -5.720 1.07e-08 ***
## alcohol 0.003842 0.004350 0.883 0.37716
## ldl 0.056876 0.214420 0.265 0.79081
## famhistPresent -0.723769 0.625167 -1.158 0.24698
## typea 0.036248 0.012171 2.978 0.00290 **
## age 0.062299 0.009788 6.365 1.95e-10 ***
## I(ldl^2) -0.001587 0.015076 -0.105 0.91617
## ldl:famhistPresent 0.311615 0.117559 2.651 0.00803 **