[R-sig-Geo] Correlation between covariates and intercept (spatstat)

[Virginia Morera Pujol]

Hello,

You are right, what changes is the coefficient of the covariate, but it's
effect (coef+covariate value) is the same in both models, and selecting the
"significant covariates" won't be much of a problem as I only have 2
covariates in my model.

Thank you very much for your kind help!

Virginia Morera
PhD Student
Department of Animal Biology
University of Barcelona

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2016-04-17 12:36 GMT+02:00 Adrian Baddeley <adrian.baddeley at curtin.edu.au>:

> Virginia Morera Pujol <morera.virginia at gmail.com> writes:
>
> > In trying a spatial model with spatstat I am running into a conceptual
> > problem. It might be more of a general modelling doubt than a specific
> > spatial problem, but I hope someone can help.
>
> > I am running a ppm() model that includes two covariates (as pixel
> images),
> > one is primary productivity at sea, and the other is distance to a point
> > that is not included in the pattern window. That means there is no 0
> value,
> > the range of values goes from 400 to 1400 approx.  When I run the model
> and
> > look at the var-covar matrix using 'vcov(model, what = "corr")' , there
> is
> > a very strong correlation (around -0.85) between the intercept and this
> > covariate. I am not sure that this is a problem, but [...]
>
> This is about the correlation between *estimates* of the model
> coefficients - in this case, the correlation between the estimated
> intercept and the estimated coefficient of the distance covariate.
> Extremely high correlations could cause problems with the identifiability
> of the model, but this is probably not a problem here. Moderately high
> correlations suggest that the t-tests for individual parameters (given in
> the printout for the model) are not independent. If we want to select the
> 'significant' covariates, we shouldn't use the model printout to discard
> more than one variable at a time.
>
> >  I have tried a couple of things just in case:
>
> > 1/ centering the covariate values around the mean just changes the sign
> of
> > the correlation (from -0.85 to +0.85 approx).
>
> > 2/ normalizing the covariate values, so the values go from 0 to 1 makes
> the
> > correlation between this covariate and the intercept almost 1 (0.99) It
> > also makes the effect of this covariate three orders of magnitude higher
> > than the effect of the other covariate, which didn't happen before and
> was
> > not expected from the data.
>
> Such transformations will change the correlation. Roughly speaking, that's
> because when you add a constant to the distance covariate, you are adding a
> multiple of the intercept onto the covariate.
>
> When you say the 'effect' of the covariate has increased, do you mean the
> coefficient of the covariate has increased, or the *effect term* (=
> coefficient x covariate value) has increased? I'd be surprised if this
> happens - the models should be equivalent as regards their fitted
> intensity, etc.
>
> Adrian Baddeley
>
>
> Prof Adrian Baddeley DSc FAA
> Department of Mathematics and Statistics
> Curtin University, Perth, Western Australia
>

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