How do I get properly accounted for nested random effects with lme4?

Question

I have a data frame with subject , wd , and group variables, and a value response variable. Each subject is assigned to one group and has 7 measurements taken over each weekday. Because each subject is completely nested within a group, I want to use a nested random effects model with subject and group , as well as adding a third random effect for wd . Currently, I am using this to do so:

model = lmer(value ~ 1+ (1|wd) + (1|group) + (1|subject), 
             data = dframe, REML = 0)

I found the code I based this off of on page 40 of this guide . I have used both REML = TRUE and REML = 0 . However, when I use VarCorr(model)$variances , I get

Groups   Name        Std.Dev.  
subject  (Intercept) 94.9534363
wd       (Intercept) 42.5931401
group    (Intercept)  0.0015608
Residual              0.9589836

This group variance conflicts with the code that I used to generate the data, which has group means of 36.9, 28.78, and -15.269. When I look at "residuals" for the predicted random effects (using ranef ) vs. true random effects, I get residuals with very high correlation to the group they are in (if I modeled residuals ~ group , the R-squared value would be over 0.9).

How do I properly fit a nested random effects model in R? I prefer to use lme4, but any package will suffice.

Here is the code I used to generate the data:

library(dplyr)
generate_data <- function(n = 10, g = 3, seed = 1, mean.overall = 300,
                          sigma.g = 50, sigma.wd = 50, 
                          sigma.subject = 100, sigma. = 30) {
    set.seed(seed)
    means.wd = rnorm(7) * sigma.wd
    means.g = rnorm(g) * sigma.g
    means.subject = rnorm(n*g) * sigma.subject
    dframe = data.frame(subject = rep(1:(g*n), each = 7),
                        wd = rep(1:7, g*n), 
                        group = rep(1:g, each = (7*n)))
    dframe = mutate(dframe,
       value = mean.overall + means.wd[wd] +    
           means.subject[subject] + means.g[group] + rnorm(7*g*n),
       subject = factor(subject, levels = 1:(n*g)),
       wd = factor(wd), 
       group = factor(group, levels = 1:g))
    dframe$value = round(pmax(5,dframe$value))
    truefx = list(wd = means.wd, group = means.g, 
                  subject = means.subject)
    list(data = dframe, effects = truefx)
}

dframe = generate_data()$data

Answer 1

I'd guess that you want group as a fixed effect, as there's only a couple levels. Also the nesting of weekday within subject feels unneeded as there's only one observation for each subject/weekday combination. If so, all you should need is

lmer(value ~ group + (1|subject), data = dframe)

It's not clear that weekday is truly nested in subject though; if these were all the same weekdays for all subjects, something else might be more appropriate. That's a better question for stats.stackexchange.com though.

If you really did want to nest these, something like this might work.

lmer(value ~ (1|group/subject/wd), data = dframe)