[R-sig-ME] GlmmADMB: random slopes and fixed effects

Thu Apr 30 02:52:04 CEST 2015

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On 15-04-29 07:58 PM, Ken Beath wrote:
> A random effect for a slope means that the slopes have a random 
> distribution about the fixed effect. For example if the fixed
> effect is 5 then the slopes for each species will be distributed
> around this value. So one species may have a slope of 4 and another
> 5.6. Why it is sensible to have a fixed effect is that it is
> usually not realistic for the mean slope to be zero, that is to
> have the random slopes distributed around zero. That would imply
> that some slopes are negative.

   I would frame it slightly differently ...

   In the absence of evidence to the contrary (see
example(ranef.merMod) for some ways of plotting the random effects), I
would probably encourage you to retain species as a random effect,
while perhaps simplifying the random effect (as suggested by Thierry
Onkelinx below). Perhaps you can add some species-level covariates
(average body mass, habitat preference -- perhaps that's what 'trait'
is?) -- it's the *deviations* from the species-level predictions based
on fixed effects, on the log scale, that need to be Normal, not the
species-level predictions themselves.

   It's fine to have negative slopes -- that would just imply that the
expected response decreased when the covariate increased.  What's
unusual about a model that contains a random effect without the
corresponding fixed effect is that it assumes the average effect
across groups is exactly zero.  The only contexts I can think of in
which this makes sense are (1) if the data have already manipulated so
that the expected effect is standardized to zero (e.g. meta-analyses);
(2) as a null model for testing whether the average effect is non-zero.

> 
> On 29 April 2015 at 23:56, Genevieve Perkins
> <genevieve.c.perkins at gmail.com> wrote:
> 
>> Hi Thierry, Thanks for the response and great advice.
>> 
>> I have 25 species, 59 sites and total of 1475 observations
>> (including absences). I didn't mention in the post, but I
>> centered all my predictor variables prior to fitting the model
>> (except trait,which is coded as -1 or +1 for ease of
>> interpretation).
>> 
>> I am able to run the model both with and without fixed affects :
>> 
>> fitn <- glmmadmb(bird.abund ~ Cats + trait + Cat:trait + Veg +
>> Pop + (1 + Veg + Pop + Cats|Species), data = bdata, family=
>> "nbinom").
>> 
>> The parameters for the random slope do not have normal
>> distributions, so I will take your advice and also include these
>> as fixed effects.
>> 
>> Could you suggest any references which explain how random slopes
>> are treated. I have mainly been using Zurr, Gelman and Hill,
>> chapters from Ecological Statistics (eds. Fox et al.) and online
>> postings.
>> 
>> Thanks again!
>> 
>> 
>> 
>> 
>> 
>> On 29 April 2015 at 03:51, Thierry Onkelinx
>> <thierry.onkelinx at inbo.be> wrote:
>> 
>>> Dear Genevieve,
>>> 
>>> An observation level random effect (OLRE) is used in a poisson
>>> or
>> binomial
>>> glmm to model the overdispersion. The negative binomial
>>> distribution has
>> a
>>> parameter that handles the overdispersion. So you don't need
>>> the ORLE.
>>> 
>>> Note that the as.formula() is not required.
>>> 
>>> Random slopes assume that the parameters follow a normal
>>> distribution
>> with
>>> zero mean. When the overall slope is not zero, this assumption
>>> is
>> violated
>>> when the variable is not used as a fixed effect.
>>> 
>>> Note that you better center random slopes to get more stable
>>> estimates.
>> Do
>>> you have enough data to fit such a complex model? The variance
>>> covariance matrix of the Species random effect requires 10
>>> parameters. I would
>> strive
>>> for >100 observations per species and >10 species.
>>> 
>>> Best regards,
>>> 
>>> ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek /
>>> Research Institute for Nature
>> and
>>> Forest team Biometrie & Kwaliteitszorg / team Biometrics &
>>> Quality Assurance Kliniekstraat 25 1070 Anderlecht Belgium
>>> 
>>> To call in the statistician after the experiment is done may be
>>> no more than asking him to perform a post-mortem examination:
>>> he may be able to
>> say
>>> what the experiment died of. ~ Sir Ronald Aylmer Fisher The
>>> plural of anecdote is not data. ~ Roger Brinner The combination
>>> of some data and an aching desire for an answer does not ensure
>>> that a reasonable answer can be extracted from a given body of
>> data.
>>> ~ John Tukey
>>> 
>>> 2015-04-28 22:41 GMT+02:00 Genevieve Perkins < 
>>> genevieve.c.perkins at gmail.com>:
>>> 
>>>> Hello,
>>>> 
>>>> I am a masters student new to the world of GLMMs. I have
>>>> developed a
>> mixed
>>>> model using the glmmADMB package and I have been scouring the
>>>> literature and help files, and trying to find an answer to my
>>>> questions with no success.
>>>> 
>>>> I want to estimate the effect of cats on bird abundance for
>>>> birds with particular traits (all traits are binary coded
>>>> (0,1); Specifically I am looking at the interaction
>>>> estimate.
>>>> 
>>>> I included species as a random effect, and I wanted the
>>>> species response to vary with Vegetation (Veg) and Population
>>>> (Pop). I also added a random level observation term.
>>>> 
>>>> Model 1: fitn <- glmmadmb(as.formula(bird.abund ~ Cat + trait
>>>> + Cat:trait + (1 + Veg + Pop + Cat|Species) + (1|ID)), data =
>>>> bdata,family=
>> "nbinom")
>>>> 
>>>> 
>>>> I noticed however that if I include Veg and Pop as fixed
>>>> effects (model
>> 2)
>>>> my model estimate for cats at the fixed effect level and
>>>> species level also change.
>>>> 
>>>> Model 2: fitn <- glmmadmb(as.formula(bird.abund ~ Cats +
>>>> trait + Cat:trait + Veg + Pop + (1 + Veg + Pop +
>>>> Cats|Species) + (1|ID)), data = bdata, family= "nbinom")
>>>> 
>>>> 
>>>> My questions are: 1)  Is it possible to include varying slope
>>>> coefficients (ie: Veg and
>> Pop)
>>>> in a GLMM model without including them as fixed effects? (I
>>>> couldn't
>> find
>>>> any examples of this format)
>>>> 
>>>> 2) How are the estimates for the random effects treated
>>>> without a corresponding fixed effect in Glmmadmb. I was
>>>> guessing they may be pooled to a group mean of zero, but I
>>>> was not able to find this information in the glmmadmb 
>>>> literature.
>>>> 
>>>> All suggestions greatly appreciated! Thanks
>>>> 
>>>> [[alternative HTML version deleted]]
>>>> 
>>>> _______________________________________________ 
>>>> R-sig-mixed-models at r-project.org mailing list 
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>> 
>>> 
>>> 
>> 
>> [[alternative HTML version deleted]]
>> 
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> 
> 
> 

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