I am interested in calculating the degrees of freedom for predictor variables in mixed effects (or multi-level) models using the Kenward-Roger approximation (described in this paper here).

Using a function (get_Lb_ddf()) to "Get adjusted denomintor degress freedom for testing Lb=0 in a linear mixed model where L is a restriction matrix," I obtain one value.

My question is, Do these Kenward-Roger approximation degrees of freedom apply to all of the predictor variables in the model?

I ask, because, naïvely, it seems odd to me for a data-level and a group-level predictor, for example, to have the same degrees of freedom.


Based on how this is implemented in the lmerTest package (link https://cran.r-project.org/web/packages/lmerTest/index.html), each coefficient is associated with its own degrees of freedom. Here is a chunk of code to estimate them using the Kenward-Rogers approximation:


fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)

get_kr_df <- function(model_object) {
    L <- diag(rep(1, length(fixef(model_object))))
    L <- as.data.frame(L)
    out <- purrr::map_dbl(L, pbkrtest::get_Lb_ddf, object = model_object)
    names(out) <- names(fixef(model_object))


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