Flavours aside, Maarten, I disagree that this gives the average over
cohorts. It is not an average. It is the probability of an `average' person.
a) This is exactly my point. Taking average heights yields the average
of a physical property. That no one exists who has that height is not
important. If, on the other hand, you wish to construct such a person,
for whatever reason, and I cannot think of one, fine. It is not
necessary since you have the average height. Life, of course, gets silly
when we think of a person with average binary covariates: half-dead, etc...
b) Why it would "be a better description of the typical predicted
probability" goes back to why an average is a good predictor of a
variable. Same context. You want a "typical" probability. Each person
has a probability fitted to her/him. This is just like any other
characteristic (height, weight etc...). Take the average of these, like
any good statistician, to describe the typical, however you take averages.
m.p.
Maarten Buis wrote:
Marcello:
A reasonable argument can be made for Stijn's position, if the
mean changes over cohorts, e.g. the proportion of mothers that
are working. It would show the change over cohorts, including
the change in the distribution of working status of the
mothers. In this sense this approach has a clear "population
average flavour".
There are however clearly some issues with this approach:
a) It is true that the person with average values on the
explanatory variables cannot exist, but we almost never think
the "average person" is a real individual. This is just a
construct that helps us summarize what we see.
b) It is true that the predicted probability for an
individual with average values on the explanatory variables is
different from the average predicted probability, but I don't
see why one would be a better description of the typical
predicted probability than the other.
Maarten
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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