How can one simulate quantities of interest from the posterior density in MCMCglmm?

Question

I would like to simulate quantities of interest from a model estimated with MCMCglmm more or less the way Zelig package does. In Zelig you can set the values you want for the independent values and software calculates the result for the outcome variable (expected value, probability, etc). An example:

# Creating a dataset:
set.seed(666)
df <- data.frame(y=rnorm(100,20,20),z=rnorm(100,50,70))

# Loading Zelig
library(Zelig)

# Model
m1.zelig <- zelig(y~z, data=df, model="ls")
summary(m1.zelig)

# Simulating z = 10
s1 <- setx(m1.zelig, z = 10)
simulation <- sim(m1.zelig, x = s1)
summary(simulation)

As we can see, if z = 10 y is approximately 17.

# Same model with MCMCglmm
library(MCMCglmm)
m1.mcmc <- MCMCglmm(y~z, data=df, family = "gaussian", verbose = FALSE)
summary(m1.mcmc)

Is there any way to simulate z = 10 with the posterior distribution estimated by MCMCglmm and get the expected value of y? Thank you very much!

Answer 1

You can simulate, but not as easily as in Zelig. You have to know a little more about the structure of the model you're fitting and the way the parameters are stored in the MCMCglmm object.

Set up data and fit:

set.seed(666)
df <- data.frame(y=rnorm(100,20,20),z=rnorm(100,50,70))
library(MCMCglmm)
m1.mcmc <- MCMCglmm(y~z, data=df, family = "gaussian", verbose=FALSE)

The most common protocol in R for prediction and simulation is to set up a new data frame with the same structure as the original data:

predframe <- data.frame(z=10)

Construct the model matrix for the linear model:

X <- model.matrix(~z,data=predframe)

Now use the chains of coefficients stored in the Sol ("solution") component of the MCMCglmm object; for convenience, I've set this up as a matrix calculation.

predframe$y <- X %*% t(m1.mcmc$Sol)

If you want to simulate for more complicated models (linear or generalized linear mixed models) then you'll need to work a little harder (handle random effects and inverse-link functions appropriately) ...