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/
-----------------------------------------
--- Marcello Pagano wrote:
This is bad statistical practise, Stijn. Knowing average, or fitted
probabilities for mean covariates tells you something you don't really
need to know--for example, if you code males=0 and females=1 and you
have 30% males in your sample, what's the point of determining the
expected probability for someone with gender 0.7?
We have been seduced by linear models into being lazy; there it does not
matter when we take the mean. But with a non-linear model, such as the
logistic, when you take the means is critical. What you may want to do
in the above example is find the expected probability for males and the
expected probability for females. Then if you want to find an overall
mean, take a weighted combination of these two expected probabilities;
with weights 0.3 and 0.7, if you trust your sample, or, for example,
weights 0.5 and 0.5, if you know better. With more than one covariate,
life gets even more interesting if you try and capture interactions!
But this is very easy to do well with the tools we have in Stata. If
you want to read more about this, take a look at,
Chang, I., Gelman, R. and Pagano, M. Corrected group prognostic curves
and summary statistics. Journal of Chronic Diseases 1982; 35 :669--674.
m.p.
Stijn Ruiter wrote:
> Dear all,
> I tried to make a graph using postgr3, but did not succeed plotting
> expected probabilities (estimated with logit) by a specific variable
> (say, Z) holding all other variables at the group mean given Z. Using
> the x() option followed by rest(grmean) allows to hold the other
> variables constant at the group mean given X, but this is not what I
> intended to do.
> More specifically, I want to plot expected probabilities over time (so,
> "postgr3 year") holding all covariates constant at the year-specific
> means. Is this somehow possible?
> Kind regards,
> Stijn
>
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