Average biases, root mean squared errors (RMSE), coverage probabilities of 95% confidence intervals and mean confidence interval widths (CI) for negative binomial GLLVM estimates based on the plain R and the TMB implementations for the variational approximation and the Laplace approximation methods.

The true model parameters were obtained by fitting a negative binomial GLLVM with two environmental covariates for the testate amoebae data with counts of m = 48 species recorded at n = 50, 120, 190 and 260 sites. Parameter β0 refers to the species specific intercepts, βpH and βtemp to the coefficients of water pH and water temperature and log ϕ to the log transformed dispersion parameters.