Dennis Roberts wrote (after an example)
> if you are thinking about regression to the mean in the typical way ... how
> come this "regression reversal" seems to have occured?
Regression to the mean was first observed in a _stationary_ process -
one fitting a model something like
X1 = h_f + E1
X2 = h_f + E2 + E3
in which h_f is the father's "genetic height", E1 the random effects of
his environment, E2 the effect of the mother's height, and E3 the random
effect of the son's environment, with E(E1) = E(E2) = E(E3) = 0. Thus
the "regression" is not masked by anything else.
The testing example is not a stationary process, and moreover the
change is positively correlated with the first measurement. Thus it
hides the effect of regression to the mean; however, we may guess that
the size of the improvement is somewhat reduced.
-Robert Dawson
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