reproduce example for CV question

lme4_groupRE.R

## https://stats.stackexchange.com/questions/649052/selecting-the-correct-r-lme4-syntax-for-nested-models

library(lme4)
df <- data.frame(Subject = rep(factor(1:120), each = 200),
                 Group = rep(LETTERS[1:3], each = 40*200))
with(df, table(Group))
with(df, table(table(Subject)))

df$Accuracy <- simulate(~ Group + (1|Subject),
                        newdata = df,
                        newparams = list(beta = c(0, 1, 2),
                                         theta = 1),
                        family = binomial,
                        seed = 101)[[1]]

model3 <- glmer(Accuracy ~ Group + (1|Group:Subject), 
                data=df,
                family=binomial(link="logit"),
                glmerControl(optimizer = "bobyqa"), 
                na.action=na.omit)

## replace 'Group:Subject' by 'Subject'
model4 <- update(model3, . ~ . - (1|Group:Subject) + (1|Subject))

identical(car::Anova(model3), car::Anova(model4))        ## TRUE
identical(coef(summary(model3)), coef(summary(model4)))  ## TRUE