[R-sig-ME] correlation of fixed effects coefficients all close to +/-1

[Alessandra Bielli]

Hi Phillip

Thank you so much for your explanation.

I have a couple more questions

1.In my model, the regression coefficients of each one of the categories of
my predictor are correlated, but I just have one categorical predictor.  In
case of collinearity I would usually drop one predictor, but here I only
have one and my goal is to use the model to predict the dependent variable.
What's the procedure here?

2. Is there a test or visual way to determine if I have enough data to get
good estimates?

3. A couple days ago I came across this post on Cross validated that states
that the correlation of fixed effect part of the outpout is only useful in
special cases,
https://stats.stackexchange.com/questions/57240/how-do-i-interpret-the-correlations-of-fixed-effects-in-my-glmer-output.
The post references the book
http://www.sfs.uni-tuebingen.de/~hbaayen/publications/baayenCUPstats.pdf,
page 268,

"The summary concludes with a table listing the correlations of the fixed
effects. The numbers listed here can be used to construct confidence
elipses for pairs of fixed-effects parameters, and should not be confused
with the normal correlation obtained by applying cor() to pairs of
predictor vectors in the input data. Since constructing confidence ellipses
is beyond the scope of the book we will often suppress this table".

What I understand is that the correlation matrix is useful for prediction
of future values, which is also my case, but I am not entirely sure I am
interpreting this correctly.

I really appreciate your advice!

Alessandra


On Sun, May 24, 2020 at 3:15 PM Phillip Alday <phillip.alday using mpi.nl> wrote:

> Hi,
>
> Very high correlations of the fixed-effects estimates can indicate two
> problems (which are actually just different manifestations of the same
> deeper problem):
>
> 1. Multicollinearity -- this is the same as multicollinearity in
> classical/standard/non mixed-effects regression. Basically this means
> that some of your variables are expressing the same thing and so you
> have some redundancies that could be eliminated. Perfect
> multicollinearity leads to a rank-deficient model matrix, which R will
> catch and correct, but near multicollinearity may not be caught.
>
> 2. You don't have enough data to get good estimates of all your
> coefficients.
>
> The bigger problem for your inference is that both of these problems
> will inflate your standard errors. In both cases, there isn't enough
> information to full tease apart the contribution from the different
> variables, which means that you have a lot of variability in your
> estimates and thus large standard errors.
>
> Note that some correlation between estimates is expected. If you think
> of a very simple case with the intercept and one slope/predictor then
> you'll see that if you change the intercept, then you have to change the
> slope a bit to get the line to stay close to the observed data.
>
> (Once again, I worry that I've oversimplified and said something
> horribly infelicitous, but I'm always happy to be corrected and learn
> something myself!)
>
> Best,
>
> Phillip
>
> On 11/5/20 11:42 pm, Alessandra Bielli wrote:
> > Dear list,
> >
> > I am fitting the mixed effect model:
> >  > lmer(log(percapita_day) ~ Type_residuo + (1|boatID), data=all)
> >
> >  where percapita_day is a non-negative continuous response variable (on
> the
> > log scale to have residuals normally distributed), Type_residuo is a
> > categorical explanatory variable and boatID is a random effect with 4
> > levels.
> >
> > I have found values very close to +/-1 in the correlation of fixed
> effects
> > matrix below, and after some research I learnt that the coefficients are
> > not about the correlation of the variables but the expected correlation
> of
> > the regression coefficients.
> >
> > Correlation of Fixed Effects:
> >             (Intr) Tp_rsM Tp_rsdOr Tp_rsdOt Tp_Pyc Tp_rsP Tp_rsR
> > Type_rsdMtl -0.944
> > Tp_rsdOrgnc -0.951  0.945
> > Typ_rsdOtrs -0.959  0.953  0.959
> > Tp_rsdPplyc -0.926  0.919  0.925    0.933
> > Tp_rsdPlstc -0.951  0.945  0.951    0.958    0.925
> > Type_resdRd -0.870  0.867  0.873    0.878    0.850  0.872
> > Type_rsdVdr -0.954  0.949  0.955    0.962    0.928  0.954  0.876
> >
> > However I still can't explain why all coefficients are so close to +/-1
> and
> > I was wondering if these are indicators that something is wrong with my
> > model?
> > Is that due to the presence of outlayers in the response variable (see
> > attached)?
> >
> > Thanks,
> >
> > Alessandra
> > _______________________________________________
> > R-sig-mixed-models using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>

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