Confidence interval of random effects with lmer

Question

I am using lmer from lme4 package to calculate confidence interval for variance component .

When I fit the model there is warning messages :

fit <- lmer(Y~X+Z+X:Z+(X|group),data=sim_data)
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

I searched a lot to understand why does the error occur and finally come to a decision that there is difference between error and warning in the R world .

I want to compute confidence interval for the model parameters and run the code which shows error :

 confint.merMod(fit,oldNames=FALSE)
 Computing profile confidence intervals ...
 Error in if (all(x[iu <- upper.tri(x)] == 0)) t(x[!iu]) else t(x)[!iu] : 
 missing value where TRUE/FALSE needed

Is there another way to obtain CI of random effects with lmer?

EDIT :

simfun <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
    N <- sum(rep(n_j,J))  
    x <- rnorm(N)         
    z <- rnorm(J)        

    mu <- c(0,0)
    sig <- matrix(c(sig2_0,sig01,sig01,sig2_1),ncol=2)
    u   <- rmvnorm(J,mean=mu,sigma=sig)

    b_0j <- g00 + g01*z + u[,1]
    b_1j <- g10 + g11*z + u[,2]

    y <- rep(b_0j,each=n_j)+rep(b_1j,each=n_j)*x + rnorm(N,0,0.5)
    data <- data.frame(Y=y,X=x,Z=rep(z,each=n_j),group=rep(1:J,each=n_j))
  } 

noncoverage <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
    dat <- simfun(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1)
    fit <- lmer(Y~X+Z+X:Z+(X|group),data=dat)
 }

comb1 = replicate(1000,noncoverage(10,5,1,.3,.3,.3,(1/18),0,(1/18)))
comb26 = replicate(1000,noncoverage(100,50,1,.3,.3,.3,(1/8),0,(1/8)))

If you get convergence warnings you can expect trouble in some subsequent analyses. confint is one of the functions that usually don't work in such a case. You should be wary and shouldn't trust this model. Investigate why it didn't converge. — Roland
we probably need to figure out the root cause of the warnings (although good for you for understanding the error/warning distinction). Have you read the ?convergence manual page, especially the stuff below "If you do see convergence warnings" ?) Can you post more info on your problem (i.e. reproducible example)? — Ben Bolker

jknowles jknowles · Accepted Answer · 2015-08-13T14:24:41

It depends on what you are looking for from the confidence intervals exactly, but the function sim in the arm package provides a great way to obtain repeated samples from the posterior of an lmer or glmer object to get a sense of the variability in the coefficients of both the fixed and random terms.

In the merTools package, we've written a wrapper that simplifies the process of extracting these values and interacting with them:

library(merTools)
randomSims <- REsim(fit, n.sims = 500)
# and to plot it
plotREsim(REsim(fit, n.sims = 500))

There are a number of other tools for exploring these in merTools. If you want the actual resulting simulations though, you're better off using arm::sim.

Confidence interval of random effects with lmer

EDIT :

4 Answers