[R] Mixed Models: Contribution of random variable to final estimate
Ben Bolker
bbolker at gmail.com
Sat Feb 2 15:35:23 CET 2013
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} ...
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