R help - Feb 2013 - Mixed Models: Contribution of random variable to final estimate

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.

The model is:
lmer(invasiveStatus~I(log(quant+1))+I(log(inDegree+1))+(1|taxonid)+(1|country),
family=binomial,data=td),

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
T388	8.24
T961	7.98
T76	7.48
T470	7.46
T108	7.17
T84	7.15
T292	6.91
T189	6.65
...
$country
US	3.23
JP	2.45
ES	2.35
IT	2.14
BM	1.63
IL	1.41
SI	1.39
LB	1.06
FR	1.05
VE	0.996
...

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


	[[alternative HTML version deleted]]

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