GLMM

Misc

  • Packages
    • {glmmTMB}
      • Beta, Beta-Binomial, Beta-Ordinal, various extensions for Negative Binomial and Poisson, Log-Normal, Tweedie, Student-T, Gamma, Zero-Inflated, Truncated (See Manual >> nbinom2 for details)
      • Currently has an experimental implementation of fixed effect priors which can be a solution to complete separation errors, singular fits, and instability (Link).
      • Supports parallelization through OpenMP but might not be supported by Mac and has significant overhead on Windows.
    • {GLMMadaptive} - For binary/dichotomous data and count data with small counts and few repeated measurements, the accuracy of Laplace approximations (i.e. {glmmTMB}) is low. This package uses adaptive Gaussian quadrature rule which is the recommended, albeit more computationally intensive, approximation method for MLE in this situation.
      • Supported Distribution Families: Student’s-t, Beta, Zero-Inflated and Hurdle Poisson and Negative Binomial, Hurdle Log-Normal, Hurdle Beta, Gamma, and Censored Normal
      • Currently no nested or crossed random effects designs
      • Can penalize fixed effects with a student-t prior
      • Parallelization through {optimParallel} which doesn’t seem to have any OS limitations.
    • {glmmPen} (Vignette)
      • Fits high dimensional penalized generalized linear mixed models using the Monte Carlo Expectation Conditional Minimization (MCECM) algorithm.
      • Performs variable selection on both the fixed and random effects simultaneously through MCP, SCAD, or LASSO penalties.
      • Supports Binomial, Gaussian, and Poisson data with canonical links

Model Equation

  • Equation
    \[ g\{E(y_i \mid b_i)\} = \beta X_i + b_i Z_i, \]
    • \(g(⋅)\): A monotonic link function
    • \(X_i\): A design matrix for the fixed effects
    • \(\beta\): Fixed effects coefficients
    • \(Z_i\): A design matrix for the random effects that’s assumed to be a subset of \(X_i\)
    • \(b_i\): Random effects coefficients