unexpected behavior in rlkjcorr

[rmcelreath]

unexpected behavior in rlkjcorr

[rmcelreath]

I think this is the expected behavior. eta=1 is uniform over matrices, not correlations. So even with K=3, you'll see concentration of mass around rho=0, just because it's not possible to build valid matrices with independent correlations.

library(rethinking)
R <- rlkjcorr(1e4,K=3,eta=1)
plot( R[,1,2] , R[,1,3] , col=col.alpha("black",0.2) , pch=16 )

The Stan functions behave the same way:

mc <- "
parameters{
    corr_matrix[3] Rho;
}
model{
    Rho ~ lkj_corr(1);
}"
m <- stan(model_code=mc,chains=1,warmup=100,iter=1e4)
R <- extract.samples(m)$Rho
plot( R[,1,2] , R[,1,3] , col=col.alpha("black",0.2) , pch=16 )

[jgabry]

Indeed, even in 3 dimensions the space of possible correlation
matrices looks like a stuffed Dorito rather than a full cube.

On Thursday, January 21, 2016, Richard McElreath [email protected]
wrote:

Closed #17 #17.

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[davharris]

Ah, you're right. I mis-remembered or misunderstood the Stan documentation. Sorry for the false alarm.

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