R: obtain coefficients&CI from bootstrapping mixed-effect model results

Question

The working data looks like:

set.seed(1234)
df <- data.frame(y = rnorm(1:30), 
                 fac1 = as.factor(sample(c("A","B","C","D","E"),30, replace = T)),
                 fac2 = as.factor(sample(c("NY","NC","CA"),30,replace = T)),
                 x = rnorm(1:30))

The lme model is fitted as:

library(lme4)
mixed <- lmer(y ~ x + (1|fac1) + (1|fac2), data = df)

I used bootMer to run the parametric bootstrapping and I can successfully obtain the coefficients (intercept) and SEs for fixed&random effects:

mixed_boot_sum <- function(data){s <- sigma(data)
c(beta = getME(data, "fixef"), theta = getME(data, "theta"), sigma = s)}

mixed_boot <- bootMer(mixed, FUN = mixed_boot_sum, nsim = 100, type = "parametric", use.u = FALSE)

My first question is how to obtain the coefficients(slope) of each individual levels of the two random effects from the bootstrapping results mixed_boot ?

I have no problem extracting the coefficients(slope) from mixed model by using augment function from broom package, see below:

library(broom)
mixed.coef <- augment(mixed, df)

However, it seems like broom can't deal with boot class object. I can't use above functions directly on mixed_boot.

I also tried to modify the mixed_boot_sum by adding mmList( I thought this would be what I am looking for), but R complains as：

Error in bootMer(mixed, FUN = mixed_boot_sum, nsim = 100, type = "parametric",  : 
  bootMer currently only handles functions that return numeric vectors

Furthermore, is it possible to obtain CI of both fixed&random effects by specifying FUN as well?

Now, I am very confused about the correct specifications for the FUN in order to achieve my needs. Any help regarding to my question would be greatly appreciated!

Answer 1

My first question is how to obtain the coefficients(slope) of each individual levels of the two random effects from the bootstrapping results mixed_boot ?

I'm not sure what you mean by "coefficients(slope) of each individual level". broom::augment(mixed, df) gives the predictions (residuals, etc.) for every observation. If you want the predicted coefficients at each level I would try

mixed_boot_coefs <- function(fit){
   unlist(coef(fit))
}

which for the original model gives

mixed_boot_coefs(mixed)
## fac1.(Intercept)1 fac1.(Intercept)2 fac1.(Intercept)3 fac1.(Intercept)4 
##        -0.4973925        -0.1210432        -0.3260958         0.2645979 
## fac1.(Intercept)5           fac1.x1           fac1.x2           fac1.x3 
##        -0.6288728         0.2187408         0.2187408         0.2187408 
##           fac1.x4           fac1.x5 fac2.(Intercept)1 fac2.(Intercept)2 
##         0.2187408         0.2187408        -0.2617613        -0.2617613 
##  ...

If you want the resulting object to be more clearly named you can use:

flatten <- function(cc) setNames(unlist(cc),
                                outer(rownames(cc),colnames(cc),
                                      function(x,y) paste0(y,x)))

mixed_boot_coefs <- function(fit){
   unlist(lapply(coef(fit),flatten))
}

When run through bootMer/confint/boot::boot.ci these functions will give confidence intervals for each of these values (note that all of the slopes facW.xZ are identical across groups because the model assumes random variation in the intercept only). In other words, whatever information you know how to extract from a fitted model (conditional modes/BLUPs [ranef], predicted intercepts and slopes for each level of the grouping variable [coef], parameter estimates [fixef, getME], random-effects variances [VarCorr], predictions under specific conditions [predict] ...) can be used in bootMer's FUN argument, as long as you can flatten its structure into a simple numeric vector.