[R] Mixed Models: Contribution of random variable to final estimate

[Ben Bolker]

Luis Reino <luisreino <at> isa.utl.pt> writes:

> 
> Dear all,
 
> We want to test if the invasiveStatus is predicted by the amount
> (quant) of animals arriving to a country of a certain species
> (taxonid). We are using lmer to perform the model.

  In general lmer questions belong on r-sig-mixed-models at r-project.org,
but I think this
 
> The model is:
> lmer(invasiveStatus~I(log(quant+1))+I(log(inDegree+1))+
>  (1|taxonid)+(1|country),
> family=binomial,data=td)

  You don't need I() around those terms -- you only need it to
protect expressions such as x^2 that would be interpreted differently
in the formula context.

> where invasiveStatus is a binary variable, quant and inDegree are
> integer variables, and taxonid and country are factor variables.

> The fixef output is
>           (Intercept)    I(log(quant + 1)) I(log(inDegree + 1))
>           -15.6338288            0.3198074            2.1566502
 
> and the ranef output is, sorted from higher to lower, andshowing
>  only the first 10 lines,
 
> $taxonid
> T16	9.51
> T258	8.36
 [snip]

> $country
> US	3.23
> JP	2.45
> ES	2.35

[snip]

> Our problem is that the coefficients to the final estimate of
> invasiveStatus are higher for the random variables than the fixed
> ones. We think this is a result of the confound effect between
> quant, and country and taxonid. In other words, the higher the
> number of animals of a given species(taxonid) arriving to given
> country, the higher the probability of other species to arrive to
> the same country.  Are we formulating the model correctly? Is there
> a way to avoid that the contribution of the random variables is the
> most contributing part to the final estimate?  Thanks, Luis Reino

  This might be an issue of parameter scaling.
The idea is that your coefficients measure the effect of
the parameters *per unit*.  Thus the random effects are
measured in log-odds units, while the effects of quant and inDegree
are measured in units of log-odds change **per log-unit change in
the variable**, i.e. multiplying by e is expected to  make 1 log-odds
change in the outcome.  You might try scaling your variables
(see e.g. Schielzeth 2010 Methods in Ecology & Evolution).
(Of course, you can make the fixed effects look as big as you
want by scaling the predictor appropriately ...)

  It worries me a little that your intercept is so small --
suggests that the average fraction invasive when quant=0
and inDegree=0 is 3 x 10^{-7} ...

  Follow-ups to r-sig-mixed-models