How to change variance-covariance matrix in mixed models?

Question

I'm currently trying to do power calculation using SIMR package in R. To start off, I first created the following model which defines my study design with simulated output y:

model1 <- glmer(y ~ (a*b) +
                        (1 + (a*b)|subj), family="binomial",
                        data = simulated.df, 
                        control = glmerControl(optCtrl = list(maxfun = 1e+9)))

I would now like to adjust the variance-covariance matrix of this model based on my pilot data. The varcorr matrix of my pilot data is as follows:

#> VarCorr(m_pilot)
  #Groups   Name             Std.Dev. Corr                
  #subj     (Intercept)      0.11582                      
  #a1                        0.12624  -0.254              
  #b1                        0.12239  -0.080  0.563       
  #a1:b1                     0.10523   0.267 -0.600 -0.337

How can I change the varcorr matrix of my stimulated model (model1) to the varcor matrix from my pilot data?

I would be very grateful for any help.

Maria

Answer 1

In general the simr package takes a fitted model as input, so I'm not quite sure why you don't just pass m_pilot to doSim() ...

More generally, the covariance matrices in lme4 are parameterized as the (scaled) Cholesky factor. That is, suppose you have a fitted model m. Then you can get the parameters expected by [g]lmer (or by the simulate.formula method in lme4) directly via getME(m, "theta"), or — if you have the covariance matrix (e.g. vc <- VarCorr(m)[[1]]), then

cc <- chol(vc)
cc2 <- c(t(cc)[lower.tri(cc, diag = TRUE)])

will get the unscaled Cholesky factor, and cc2/sigma(m) will get the scaled Cholesky factor (sigma(m) is 1 for binomial and Poisson models)

Answer 2

You should be able to copy the variance-covariance matrix from one model to the other with:

VarCorr(model1) <- VarCorr(m_pilot)