[R-sig-eco] multiple regression

[David Hewitt]

>>> AFAIK, the better solutions proposed for comparing the relative
>>> importance of variables use measures of e.g, SSEs or partial
>>> correlations over all possible orderings of the model; but I believe
>>> that in the face of multicollinearity you are still faced w/ problems
>>> in interpreting 'importance'.  It's just a tough problem...
>>
>> It is indeed tough, but I don't think partial correlations/SSEs are a
>> good route. What methods are you referring to in particular? I can't
>> see how this would help except in the simplest linear models.
>
> My aim wasn't to hold up those metrics as improved measures of
> importance, but rather to mention the idea calculating a metric over
> all possible orderings of the model.  E.g, see the Gromping paper I
> cited earlier in the thread, or for more seminal work:
>
> @article{1987,
> title = {Relative Importance by Averaging Over Orderings},
> author = {Kruskal, William},
> journal = {The American Statistician},
> volume = {41},
> number = {1},
> jstor_formatteddate = {Feb., 1987},
> pages = {6--10},
> abstract = {Many ways have been suggested for explicating the
> ambiguous concept of relative importance for independent variables in
> a multiple regression setting. There are drawbacks to all the
> explications, but a relatively acceptable one is available when the
> independent variables have a relevant, known ordering: consider the
> proportion of variance of the dependent variable linearly accounted
> for by the first independent variable; then consider the proportion of
> remaining variance linearly accounted for by the second independent
> variable; and so on. When, however, the independent variables do not
> have a relevant ordering, that approach fails. The primary suggestion
> of this article is to rescue the idea by averaging relative importance
> over all orderings of the independent variables. Variations and
> extensions of the idea are described.},
> year = {1987},
> publisher = {American Statistical Association}
> }

Gotcha. I think we are on the same track. If I understand things
correctly, the new methods coming out for multimodel inference and
model-averaging are the grown-up versions of this older idea. I think
Chatfield really pushed all this in the mid-1990s with his work on
model selection uncertainty.