Transformation of the response

As mentioned on the previous page, it is much easier to interpret the parameters when parallel lines are fitted to different groups than when their slopes are different, but the data or the context may not justify such a simplification.

However parallel lines can sometimes be used after a nonlinear transformation is applied to the response. This is especially justified if there is skewness in the marginal distribution of the response or noticeable curvature in the relationship in each group. The following example illustrates.

Body fat and BMI

The diagram below again shows a scatterplot of Body fat and BMI for the AIS athletes.

Select Separate lines from the pop-up menu.

The diagram below is similar but uses the natural logarithm of body fat as the response variable.

Select Parallel lines to fit a model with parallel lines for males and females. Observe that:

We can now concisely summarise the difference between males and females.

ln(%Body fat) is (1.192 - 0.391) = 0.801 higher for females than for males with the same BMI.

From the properties of logarithms, we can express this more clearly as follows:

%Body fat of females is e0.810 = 2.23 times that of males with the same BMI.