This doesn't answer any of my points so far as I
can see. Wanting to know about "relative importance"
and/or what happens when the model is changed
are understandable desires, although problematic
in other senses. My main concern is much narrower:
why anyone should want to trust
change of b / original b
when this measure behaves so awkwardly as
original b passes through 0. What's more, the
situation you sketch is worse when there are
lots of covariates, as the coefficients of many
might appear to be near 0.
Nick
n.j.cox@durham.ac.uk
Tim Wade
> Nick,
> One use for this type of metric could be used in a "backward deletion"
> or "change in estimate" procedure for selecting important covariates
> in a regression model. In this process a full model with an exposure
> of interest and all other potentially important covariates is fit,
> then the relative importance of each covariate is judged by how much
> of an effect its removal has on the coefficient of the exposure of
> interest. Variables that, when removed from the model, have little
> effect on the exposure coefficient are rdeleted from the final model.
> The result is a model where the effect of the exposure has been
> adjusted for confounding but with unimportant variables removed. It
> is sometimes advocated as an alternative to stepwise methods that rely
> on statistical significance.
Nick Cox
> > On a different note, why this interest in percent
> > change in coefficient as a metric?
> >
> > I make three elementary comments.
> >
> > 1. The behaviour of ratios can be complicated
> > already. This measure is a ratio calculated from
> > ratios.
> >
> > 2. Specifically, is the behaviour as the denominator
> > goes from small positive through zero to small
> > negative regarded as a feature?
> >
> > 3. There is a lack of symmetry in the calculation.
> >
> > I can imagine a practical argument that (1) and
> > (2) do not matter for the application, and (3)
> > might be irrelevant given a time order, but I wouldn't
> > put much weight on this measure.
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