inla.pmarginal() question

[Drew N]

Hello,

I'm following Ch2 in the Bayesian Inference with INLA book for working with marginal posterior.

For this part, is there a way to scale the code to hypothesis test for all fixed effects (or ones we care about)?

In order to know whether covariate x1 has a (positive) association with the response, the probability of its coefficient being higher than one can be computed:

1 - inla.pmarginal(0, m1$marginals.fixed$x1)

I'd appreciate any help with this, thank you!

Best,

Andrew

[Helpdesk (Haavard Rue)]

something like this. its not strictly correct from the Bayesian point of view,
but you can kind of do this to check if all coeffs are zero. easist if the
covariates are kind of centered.


n <- 100
x <- rnorm(n)
xx <- rnorm(n)
xxx <- rnorm(n)
y <- 1 + rnorm(n)

r <- inla(y ~ 1 + x + xx + xxx,
data = data.frame(y, x, xx, xxx),
family = "gaussian",
control.fixed = list(correlation.matrix = TRUE))

S <- r$misc$lincomb.derived.covariance.matrix
## remove the contribution from the intercept
S <- S[2:4, 2:4]
est <- r$summary.fixed$mean[2:4]
## this should be chisq_3 when there is no effects (about...)
sq <- as.numeric(est %*% solve(S) %*% est)
## some rough p-value (whatever it mean here)
1-pchisq(sq, df = 3)

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[Drew N]

Thank you for your reply Dr. Rue. Apologies as I am more accustomed to tidyverse syntax, but would a lapply function work with inla.pmarginal()? I'm interested in using inla.pmarginal() to obtain the probability of positive and negative associations with reference to 0.  

[Håvard Rue]

the summary(result), or result$summary.fixed will also compute the quantiles,
which you can check contains 0 or not. this is what you want?

hr...@r-inla.org

[Drew N]

This is what I was looking for: lapply(model$marginals.fixed,function(x){inla.pmarginal(0,x)})

The probability of association for the coefficients in the model.