GlmmADMB: random slopes and fixed effects

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

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]]

[[alternative HTML version deleted]]

-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.11 (GNU/Linux)

iQEcBAEBAgAGBQJVQXy0AAoJEOCV5YRblxUHyEYIAImiOMFEfUxLfcYincSo7nM+
gI7sykoIEOiY3Pg32DH2lh5/gcCi19ezWBJlQtKgA0ZVBC9PoUDN6PkD+CiR4Tq/
YghExE/axBE8/mOnkhCtqulkx6ZsVbMvq+6efPG8Xc7YEp8obNnruW56co0/1/Sr
8JRK+07HqtD9ocjcKrJ6rF0Zv175+LSBVpiT+UslbObV1/l1NxfCrBVQDIJ9AKw9
VgxSiuX7A57JlLhbSzYD/f0WSDLk9C2XbRt1S7azfcFsJBZdFXzi4R4pwsgoxXDO
9zh+XSXgCv6xqv851gz58DqI8kaloHrcCFgNdNMacWOqPnBLReQabUYJ+40tNLU=
=JtYy
-----END PGP SIGNATURE-----