[R-sig-ME] what about "zero-inflated" predictors (Ben Bolker)

[Edwin Lebrija Trejos]

Dear Ben,
sorry for not replying and thanking you for your answer before. I was relocating. 
> 
> The reason that there's very little attention given to the
> distribution of the predictors is that in general the definition
> of standard statistical models such as GLMMs **does not say anything
> about the distribution of the predictors**. In particular, as far
> as I am aware your statement that "in classic regression my data
> would certainly invalidate the analysis" is not true -- at least
> if we're only talking about the distribution of the predictor.
> 
> The main importance of the distribution of the predictor is that
> it affects the power of the test -- obviously if most of your
> predictor data are zeros, they won't give you very much information
> about how the response changes as a function of the response.
 
I went too far on the generalization of my thought. I was thinking on a related problem that was commonly addressed during my statistical training: that a few extreme values of the predictor accompanied by a very different response (considered outliers) could falsely imply a linear relationship. The point you raise is clear and simple (yet I had not thought about it).

> I haven't read Sheater's book, but the purpose of transforming the
> predictor in this context is to take a response that is *not*
> log-odds-linear on the original scale of the predictor, but (e.g.)
> might be log-odds-linear when the predictor is on a log scale.

Yes, this is the way to express it.

> Thus the transformation is *not* fixing a problem with the
> distribution of the predictor, but rather with the linearity
> of the response.
Even if not as crucial as the assumptions on the distribution of the response variable (or rather the model residuals), I beleive this is an important correction to come-up with an appropriate model and, therefore, study conclusions. I "discovered" this in Sheater´s book by looking for something else.

> As always I'm happy to be corrected by others on the list ...

Thanks again for your helpful response. It´s so important to backup the level of science we (non-statistitians) are doing.

> 
> 
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