Hi Jarrod,

I see. This now makes a lot of sense. I appreciate it.


On Sun, Aug 26, 2012 at 9:28 AM, Jackson King <jackson.king722@gmail.com>wrote:

> Hello,
>
> I am attempting to fit a multinomial logit model (3 categories) with
> random effects (across states). I have attempted to follow the advice in
> the course notes, but am a little uncertain the reason for the priors on
> the residuals, and how this is used to calculate predicted probabilities. I
> would like my covariates to predict each outcome -- cov1 predicting option3
> versus option1 and cov1 predicting option2 versus option1, rather than a
> main effect.
>
> Here is a simple version of my model
>
> j<-length(levels(data$char))
>
> I<-diag<-(j-1) #2x2 identity matrix
>
> J=matrix(rep(1, (j-1)^2), c(j-1, j-1)) #2x2 Unit Matrix
>
> IJ <- (1/3) * (diag(2) + matrix(1, 2, 2)) #Residual covriance matrix
>
> prior = list(R = list(V =IJ, fix = 1), G = list(G1 = list(V = diag(2), nu
> = 0.002))) #Why can't I use V=diag(2) for prior R?
>
>
> model<- MCMCglmm(char~-1+trait*(cov1), random=~idh(trait):state, rcov =
> ~us(trait):units, data=data, family = "categorical", prior = prior,verbose
> = TRUE)
>
>
> I find that the model converges, and the coefficients look similar to
> maximum likelihood, but then I would like to predict probabilities for
> being in each category. Typically, I think this is done by
> plogis(x/sqrt(1+c2)), so why is it necessary to multiply by the delta
> matrix (course notes p. 97)? Alternatively, if I simply use a 2x2 diagonal
> matrix for the prior for R, shouldn't I be able to use the same
> transformation -- plogis(x/sqrt(1+c2)). In short, I am a little confused
> about the IJ matrix and where it comes from. Is there a quick answer, or
> another paper that explains this? And (2) is it reasonable to predict
> probabilities from my model, based on fixed values of cov1, using this
> simple transformation above... plogis(x/sqrt(1+c2))
>
> Many thanks.
>
> Jackson
>
>

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