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Topic: Basic GLM Question
Replies: 6   Last Post: Apr 9, 2013 2:53 PM

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David Jones

Posts: 79
Registered: 2/9/12
Re: Basic GLM Question
Posted: Apr 1, 2013 10:44 AM
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"Gary" wrote in message

On Sunday, 31 March 2013 08:00:38 UTC+2, Rich Ulrich wrote:
> On Sat, 30 Mar 2013 16:04:46 -0700 (PDT), Gary
> wrote:

> >On Saturday, 30 March 2013 15:20:56 UTC+2, SChapman wrote:
> >> Why is it that we don't try to predict individual values in Generalized
> >> Linear Model. But in a General Linear Model (Simple Linear Regression)
> >> we do try and predict individual response variable values.

> >Who is the 'we' in your statement? Are you absolutely certain that no one
> >uses generalized linear models for predictions?

> >
> >Models are built for specific purposes. Sometimes the purpose is just to
> >understand a system, sometimes it is for more practical purposes which
> >might include predictions. Maybe most of the more applied researchers
> >haven't yet caught on to the value of generalized linear models...

> Now that you mention it -- I can't remember whether I have ever
> requested "predicted values" for any of the thousands of regressions
> that I must have run since 1970. Biostatisticians in my sort of
> clinical work haven't had that sort of application where they are
> useful.
> On the other hand, I did find it useful to look at details of
> prediction when I was figuring out the peculiarites of
> discriminant function -- predicted group membership based
> on the highest observed likelihood of belonging to any
> group (even when the highest is not "high"). But even that
> was for theoretical understanding, not as a useful product
> of "applied research."

I hope I didn't offend you. I had in mind the sort of applied researcher who
just wants to figure out which credit applicant will not repay a loan
without really wanting to understand the behavioural science of loan



How you expect information about the predicted values to be supplied is a
bit of a question. For ordinary normal-theory, simple linear regression you
would traditionally get prediction limits supplied to form curves, along
with confidence limits for the mean, but I doubt anything much is provided
for multiple regression. For other distributions things are not so simple,
but still possible. It is the comparison of the predicted distributions as
the explanatory variables change that gives an impression of the practical
importance of any relationship found, rather than any technical finding of
statistical significance. For normal-theory stuff the practical importance
might perhaps be easily judged by a numerical quantity such as R^2, but for
other distributions there may be no easily understood numerical criterion.

On the question of the "we" in the original question, this might best be
modified to ask what facilities for predicted distributions (graphical
display) are provided by the major statistical packages, and whether these
are provided in via simple options.

David Jones

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