LabStats

  Introduction This post is the practical follow‑up to When Linear Mixed Models Don’t Converge , where I discussed the theoretical reasons why convergence issues often arise in linear mixed models. Here, we move from theory to practice: simulated examples, diagnostic tools, interpretation of singular fits, and practical modeling alternatives. If you haven’t read the first part yet, you may want to start there for the conceptual foundations. Figure. Conceptual map showing how model complexity and available information interact Legend of Figure 1. Green = identifiable models; yellow = risk of singularity; red = non‑identifiable models. A Concrete Example Using R: When a Random-Slope Model Becomes Singular Let’s simulate a simple dataset with only 8 groups and a very small random‑slope variance. This is a classic scenario where the model converges numerically but is statistically non‑identifiable. ```r set.seed(123) n_groups <- 8 n_per_group <- 20 group <- factor(rep(1:n_gro...

  Introduction   Linear mixed-effects models (LMMs) have become a standard tool for analyzing correlated or hierarchical data across many applied fields, including biostatistics, psychology, ecology, and toxicology. Their appeal lies in the ability to model both population-level effects (fixed effects) and sources of variability associated with grouping or experimental structure (random effects) within a single coherent framework.   However, practitioners frequently encounter warning messages when fitting LMMs, such as “failed to converge,” “boundary (singular) fit,” or “Hessian not positive definite.” These warnings are often treated as technical nuisances or software-specific quirks, and it is tempting to either ignore them or attempt minor numerical fixes (e.g., changing optimizers or increasing iteration limits). Such warnings usually signal deeper statistical issues related to model identifiability and data support.   Convergence problems are especia...