MCMCglmm:interaction bt continuous variable and categorical random effect

Hi,
I am using MCMCglmm to fit resource selection models for wolves using logistic regression where the response variable is pixels on the landscape that are either used by, or available to, wolves.  I have named the response variable "used".  Observed locations of wolves are coded 1 and available locations for wolves (systematic locations across their home ranges) are coded 0.  My initial interest was to assess relative selection (in a use-available context) of various environmental variables which are things like slope, elevation, and distance to roads.  I'm including a random term for individual wolf to account for the unbalanced sample sizes (of observations) across individuals and a random term for pack to account for the fact that I have sampled multiple wolves within some packs.  Here is my code and prior:

prior1<-list(R=list(V=1,fix=1),G=list(G1=list(V=1,nu=0.002),G2=list(V=1,nu=0.002)))Model1<-MCMCglmm(used~slope+elevation+road,random=~wolf+pack,family="categorical",data=datum,prior=prior1)
This seems to have worked quite well and the various diagnostics indicate good chain mixing and low autocorrelation, as long as I used sufficient iterations, thinning, and burnin.  I am making population-level inference on the relative selection or avoidance of the fixed effects.  Although not my primary question, I'd be interested in confirmation that my code looks correct for the desired inference.
My real question is that I'd like to derive individual selection coefficients for each wolf in relation to a given environmental variable (i.e. road). I would then use these coefficients in a separate analysis to see how selection of roads varies in relation to various things such as availability of roads, genetic ancestry, etc.  I have thought of 2 ways to derive the individual selection coefficients for roads for each wolf:
1. I could run a separate model for each wolf and simply use the fixed effect coefficient for road from each model.  This seems valid but would be time consuming (because I have ~70 wolves) and seems to fail to take advantage of the random effect of wolf in the overall model which presumably could be used to derive an estimate of individual selection of a given resource.
2. So alternatively, I wondered if I could run the overall model, but this time include an interaction between the random effect of wolf and road (which is continuous).  I'm not sure if this valid or the best way to structure the code but here is my first try:
Model1<-MCMCglmm(used~slope+elevation,random=~wolf:road+pack,family="categorical",data=datum,prior=prior1, pr=TRUE)

Again my goal is simply to derive a coefficient of selection of roads for each individual wolf from the overall model.  Any help with this would be greatly appreciated and if anything in my explanation or question is unclear please let me know and I will try to clarify.
Many thanks in advance!
John




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Hi Joshua,

Thanks for the quick reply!  I tried the code you suggested, but I got an
error message regarding my prior.

Error in priorformat(if (NOpriorG) { :
  V is the wrong dimension for some prior$G/prior$R elements

Any thoughts on how to structure the prior for the code you suggested?

Many thanks!

John

Date: Sun, 31 Mar 2013 13:59:20 -0700
Subject: Re: [R-sig-ME] MCMCglmm:interaction bt continuous variable and
categorical random effect
From: jwiley.psych at gmail.com
To: smilodon2000 at hotmail.com
CC: r-sig-mixed-models at r-project.org

Hi John,

That is the basic idea, but I doubt you want to parameterize it quite
that way. I would suggest:

Model1 <- MCMCglmm(used ~ slope + elevation + road,
random = ~ us(1 + road):wolf + pack, family = "categorical",
data = datum, prior = prior1, pr = TRUE)

which would fit a random intercept and slope by wolf, that are allowed
to be correlated, as well as a random intercept by pack (assumed
orthogonal to the others).

Having road in the fixed effects portion will give you the overall
effect, and then the random effects bit will be shrunken deviations
from that.

Cheers,

Joshua


On Sun, Mar 31, 2013 at 1:32 PM, john benson <smilodon2000 at hotmail.com>
wrote:

Hi,
I am using MCMCglmm to fit resource selection models for wolves using
logistic regression where the response variable is pixels on the landscape
that are either used by, or available to, wolves. I have named the response
variable "used". Observed locations of wolves are coded 1 and available
locations for wolves (systematic locations across their home ranges) are
coded 0. My initial interest was to assess relative selection (in a
use-available context) of various environmental variables which are things
like slope, elevation, and distance to roads. I'm including a random term
for individual wolf to account for the unbalanced sample sizes (of
observations) across individuals and a random term for pack to account for
the fact that I have sampled multiple wolves within some packs. Here is my
code and prior:


prior1<-list(R=list(V=1,fix=1),G=list(G1=list(V=1,nu=0.002),G2=list(V=1,nu=0.002)))Model1<-MCMCglmm(used~slope+elevation+road,random=~wolf+pack,family="categorical",data=datum,prior=prior1)
This seems to have worked quite well and the various diagnostics
indicate good chain mixing and low autocorrelation, as long as I used
sufficient iterations, thinning, and burnin. I am making population-level
inference on the relative selection or avoidance of the fixed effects.
Although not my primary question, I'd be interested in confirmation that my
code looks correct for the desired inference.
My real question is that I'd like to derive individual selection
coefficients for each wolf in relation to a given environmental variable
(i.e. road). I would then use these coefficients in a separate analysis to
see how selection of roads varies in relation to various things such as
availability of roads, genetic ancestry, etc. I have thought of 2 ways to
derive the individual selection coefficients for roads for each wolf:
1. I could run a separate model for each wolf and simply use the fixed
effect coefficient for road from each model. This seems valid but would be
time consuming (because I have ~70 wolves) and seems to fail to take
advantage of the random effect of wolf in the overall model which presumably
could be used to derive an estimate of individual selection of a given
resource.
2. So alternatively, I wondered if I could run the overall model, but
this time include an interaction between the random effect of wolf and road
(which is continuous). I'm not sure if this valid or the best way to
structure the code but here is my first try:

Model1<-MCMCglmm(used~slope+elevation,random=~wolf:road+pack,family="categorical",data=datum,prior=prior1,
pr=TRUE)

Again my goal is simply to derive a coefficient of selection of roads
for each individual wolf from the overall model. Any help with this would be
greatly appreciated and if anything in my explanation or question is unclear
please let me know and I will try to clarify.
Many thanks in advance!
John




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--
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://joshuawiley.com/
Senior Analyst - Elkhart Group Ltd.
http://elkhartgroup.com