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

[Phillip Alday]

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
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