Thanks a lot Chris,
I will try that one and see what happens. However, if someone knows how to run multinomials with random effects I will be very greatful!

Quoting Chris Howden:

> I'm not neccsarily advocating this. But another way is to use 3
> logistic models with random effects.   One for wether they choose big
> acorn, one for small, one for both. Then compare the parameters of all
> 3 to see if there are any differences.
>
> Chris Howden
> Founding Partner
> Tricky Solutions
> Tricky Solutions 4 Tricky Problems
> Evidence Based Strategic Development, IP Commercialisation and
> Innovation, Data Analysis, Modelling and Training
>
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> On 07/06/2012, at 3:00, "MORAN LOPEZ, TERESA" 
> <tmoranlopez@mncn.csic.es> wrote:
>
>> Dear all,
>> I am a phD student working on animal behavior under different 
>> predation risk. We have conducted an experiment in which acorn 
>> selection by jays was evaluated in savanna vs forest-type  
>> landscapes.  We placed 8 feeders in two different forests and 8 
>> feeders in two different savannas.
>> My response variable is factorial, acorn choice (big, small, both).  
>> In my design I have spatial pseudorreplication within Areas.  I have 
>> not found multinom function which allows fitting random effects. 
>> However, MCMCglmm package allows incorporating them using Bayesian 
>> Methods. I am new using Bayesian Methods so it has taken me a lot of 
>> effort to partially understand these models implementation. However, 
>> once I have run my model I am not sure about output interpretation 
>> and most importantly how to convert fix effect parameters into 
>> probabilities.
>>
>> I have tried three different things: to convert my data in binomial 
>> (ignoring  infrequent acorn choice “both”) and run mixed model lmer. 
>>  Pros: I can include random effects , Cons: I lose an infrequent but 
>> informative level of the response.
>>
>> Keep categorical responses and run multinom function without random 
>> effects.  Pros: I can fit my response variable as categorical and 
>> keep all levels. Cons: I am ignoring spatial autocorrelation 
>> (however, when running binomial models acorn choice variation 
>> between areas was much more lower than between risk levels).
>> +
>> Run MCMCglmm model with random effects. Pros:  I can keep both 
>> spatial autocorrelation and all levels of the response factor. Cons: 
>> Not sure about  model implementation and interpretation. Low sample 
>> size.
>>
>>
>> Which option is the most accurate?
>>
>> Thanks a lot! I am really stucked with my data.
>>
>> Here I post my MCMCglmm model which is the one I have more doubts
>>
>> #head(choice)-dataset with choice as factor  (b=big, s=small, bt=both)
>>   RISK       Area             CHOICE
>> LOW        Sopie                  b
>> LOW       Sopie                  b
>> LOW      Sopie                   b
>> LOW  Anchurones                  s
>> LOW  Anchurones                  bt
>> LOW  Anchurones                  b
>>
>> I have read package tutorial and Hadfield notes (though I have not 
>> read all the chapter of Hadfield course notes). Besides I have used 
>> information posted  Jaeger lab blog: 
>> http://hlplab.wordpress.com/2009/05/07/multinomial-random-effects-models-in-r/
>>
>> I am not very sure about random effects priors but I believe the 
>> rest of them are ok.
>> k <- length(levels(choice$CHOICE))
>> I<- diag(k-1)
>> J <- matrix(rep(1, (k-1)^2), c(k-1, k-1))
>> #Constraints to variance-covariance matrix
>>
>> prior = list(R = list(fix=1, V =(1/k) * (I + J), n=k), G = list(G1 = 
>> list(V =diag(2), n=2)))
>>
>> #R priors, Hadfield manual suggests that structure. Are they right?  
>> NOT SURE ABOUT RANDOM PRIORS.
>>
>> M<- MCMCglmm(CHOICE~ -1+ trait + RISK,
>>              random = ~ us(trait):Area,
>>              rcov = ~ us(trait):units,
>>              prior = prior,
>>              family = "categorical",
>>              data = choice)
>>
>> #-1+trait following Hadfield suggestions in order to estimate 
>> interception if every outcome.
>> us(trait):-----  since we are not sure of independence assumptions. 
>> Is model function allright?
>>
>> My model runs but I find it very difficult to interpret my summary
>>
>> summary(M)
>>
>> Iterations = 3001:12991
>> Thinning interval  = 10
>> Sample size  = 1000
>>
>> DIC: 44.21802
>>
>> G-structure:  ~us(trait):Area
>>
>>                         post.mean l-95% CI u-95% CI eff.samp
>> CHOICE.bt:CHOICE.bt.Area    14.622   0.1881    64.46    7.278
>> CHOICE.s:CHOICE.bt.Area      3.274 -11.1431    19.29  116.593
>> CHOICE.bt:CHOICE.s.Area      3.274 -11.1431    19.29  116.593
>> CHOICE.s:CHOICE.s.Area       5.071   0.1416    15.82  127.395
>>
>> R-structure:  ~us(trait):units
>>
>>                          post.mean l-95% CI u-95% CI eff.samp
>> CHOICE.bt:CHOICE.bt.units    0.6667   0.6667   0.6667        0
>> CHOICE.s:CHOICE.bt.units     0.3333   0.3333   0.3333        0
>> CHOICE.bt:CHOICE.s.units     0.3333   0.3333   0.3333        0
>> CHOICE.s:CHOICE.s.units      0.6667   0.6667   0.6667        0
>>
>> Location effects: CHOICE ~ -1 + trait + RISK
>>
>>               post.mean l-95% CI u-95% CI eff.samp pMCMC
>> traitCHOICE.bt   -4.5042 -11.8926   0.3824    15.18 0.052 .
>> traitCHOICE.s    -2.0187  -6.3370   1.3569    84.55 0.200
>> RISKRAÑA          1.9095  -2.3541   8.2421    56.13 0.336
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> posterior.mode(M$Sol)
>>
>> traitCHOICE.bt   traitCHOICE.s       RISKRAÑA
>>     -2.594132      -1.836527             1.554387
>>
>> #Since there is not any intercept I can´t apply plogis() in order to 
>> get probabilities of choice in different areas.
>>
>>
>> Sorry that I have that many  questions and thanks a lot!!!
>>
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>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
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