Variance-covariance matrix for random effect from GAM with mgcv package

Question

Random effect and variance-covariance matrix of random effect with lme4 package are extracted as following:

library(lme4)
fm1 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
fm1.rr <- ranef(fm1,condVar=TRUE)
fm1.pv <- attr(rr[[1]],"postVar")

I wonder how I can do this with mgcv? 'gam.vcomp' function does extract the estimated variance components, but not for each level of random effect.

library(mgcv)
fm2 <- gam(Reaction ~ Days + s (Subject, bs="re"), data = sleepstudy, method = "REML")
gam.vcomp(fm2)

Does mgcv::random.effects() or nlme::ranef() do what you need? Must admit I'm less familiar with mgcv. If not can you post a small sample of your data, perhaps with dput()? See stackoverflow.com/questions/5963269/… for help — Phil
You should explain in more detail what you expect. You do get an estimate of the "standard deviation" around the smoothing spline for Subject. @Phil: The questioner loaded the data into his workspace because it is in hte lme4 package. You need to execute: data(sleepstudy, package="lme4") if you didn't run the first bit of code. You will also need to use data=sleepstudy, since gam's second argument is not data. — IRTFM
Thank you. In lme4 example I get random effect and an estimate of standard deviation for each level of variable Subject, i.e. 18 random effects and 18 variances. In mgcv I get only 1 estimate around the spline. Basically I want to get same output with mgcv as it is produced by lme4. Am I missing something? The reason I want to use mgcv is because my real model contains a few other types of splines as well as random effects. — olyashevska

olyashevska olyashevska · Accepted Answer · 2018-01-11T14:57:44

library(lme4)
data(sleepstudy)

fm1 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
fm1.rr <- ranef(fm1,condVar=TRUE)$Subject[,1]
fm1.pv <- sqrt(attr(ranef(fm1,condVar=TRUE) [['Subject']],"postVar")[1,1,])

library(mgcv)
fm2 <- gam(Reaction ~ Days + s (Subject, bs="re"), 
data = sleepstudy,   method = "REML")

To extract random effect for each Subject

idx <-grep("Subject", names(coef(fm2)))
fm2.rr<-coef(fm2)[idx]
attributes(fm2.rr)<-NULL

We can see that random effects in both models are identical as expected.

To extract variance-covariance matrix for random effect and calculate an error we use parameter Vp which is a Bayesian posterior covariance matrix:

fm2.pv <-sqrt(diag(fm2$Vp))[idx]

Or frequentist estimated covariance matrix Ve

fm2.pv <-sqrt(diag(fm2$Ve))[idx]

We can see that random effect errors estimated with mgcv slightly differ that those estimated with lme4 model. Errors based on a Bayesian posterior covariance matrix are larger, whereas based on a frequentist matrix are smaller.

Variance-covariance matrix for random effect from GAM with mgcv package

2 Answers