Fit a negative binomial GLMM for count imputation

Fits a negative binomial generalized linear mixed model (GLMM) to longitudinal count data using glmmTMB::glmmTMB() with family = nbinom2(link = "log"). The fitted model and the estimated dispersion parameter \(k\) (where Var(Y) = \(\mu + k\mu^2\)) are returned for use in subsequent imputation steps. This mirrors PROC GLIMMIX with dist=negbin link=log in SAS.

Usage

fit_nb_glmm(data, formula, replicate_col = NULL)

Arguments

data: Data frame of observed (non-missing) records.
formula: A two-sided formula specifying fixed and random effects, e.g. count ~ base + trt + visit + (1 | id). The left-hand side should be the outcome variable; rows with a missing outcome should be excluded before calling this function (see impute_nb()).
replicate_col: Character or NULL. Column in data identifying bootstrap replicates. The model is fitted separately within each unique value. If NULL (default), all rows form a single fit.

Value

A named list—one element per unique replicate—where each element contains:

model: The fitted glmmTMB object.
k: Estimated NB dispersion \(k\) (= glmmTMB::sigma(model)).

When replicate_col = NULL, the list has a single element named "1".

Details

The dispersion parameter follows the parameterisation used throughout gsDesignNB: \(k\) such that \(\text{Var}(Y) = \mu + k\mu^2\). This matches glmmTMB's nbinom2 family, where glmmTMB::sigma() returns \(k\) directly.

Examples

if (FALSE) { # \dontrun{
# Requires glmmTMB
obs_data <- long_data[!is.na(long_data$count), ]
fits <- fit_nb_glmm(
  data    = obs_data,
  formula = count ~ baseline + trt + visit + (1 | id)
)
fits[["1"]]$k  # estimated dispersion
} # }