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Multilevel mixed-effects models

Outcomes and regression estimators

  • Continuous, modeled as
    • Linear
    • Log linear
    • Log gamma
  • Binary outcomes, modeled as
    • Logistic
    • Probit
    • Complementary log-log
  • Count outcomes, modeled as
    • Poisson
    • Negative binomial
  • Categorical outcomes, modeled as
    • Multinomial logistic
      (via generalized SEM)
  • Ordered outcomes, modeled as
  • Generalized linear models (GLMs)
    • Seven families: Gaussian, Bernoulli, binomial, gamma, negative binomial, ordinal, Poisson
    • Five links: identity, log, logit, probit, cloglog

Types of models

  • Two-, three-, and higher-level models
  • Nested (hierarchical) models
  • Crossed models
  • Mixed models
  • Balanced and unbalanced designs

Types of effects

  • Random effects (variance components)
    • Random intercepts
    • Random slopes (coefficients)
  • Fixed effects (fixed coefficients)

Effect covariance structures

  • Identity—shared variance parameter for specified effects with no covariances
  • Independent—unique variance parameter for each specified effect with no covariances
  • Exchangeable—shared variance parameter and single shared covariance parameter for specified effects
  • Unstructured—unique variance parameter for each specified effect and unique covariance parameter for each pair of effects
  • Compound—any combination of the above

Residual error structures for linear models

  • Independent
  • Exchangeable
  • Autoregressive
  • Moving average
  • Banded
  • Toeplitz
  • Unstructured


  • linear constraints on fixed parameters
  • linear constraints on variance components

Survey data for linear models

  • Sampling weights
  • Weights at each level of model
  • Cluster–robust SEs to relax distributional assumptions and allow for correlated data
  • Weight rescaling

Multiple imputation

Estimates of random effects

  • BLUPs for linear models
  • Standard errors of BLUPs for linear models
  • Empirical Bayes posterior means or posterior modes
  • Standard errors of posterior modes or means


  • Predicted outcomes with and without effects
    • Linear predictions
    • Probabilities
    • Counts
  • Pearson, deviance, and Anscombe residuals

Other postestimation analysis

  • Intraclass correlation coefficients (ICCs) , logistic , and probit random-effects models
  • Linear and nonlinear combinations of coefficients with SEs and CIs
  • Wald tests of linear and nonlinear constraints
  • Likelihood-ratio tests
  • Linear and nonlinear predictions
  • Summarize the composition of nested groups
  • Adjusted predictions
  • AIC and BIC information criteria
  • Hausman tests

Factor variables

  • Automatically create indicators based on categorical variables
  • Form interactions among discrete and continuous variables
  • Include polynomial terms
  • Perform contrasts of categories/levels

Estimation methods

  • Maximum likelihood (ML)
  • Restricted maximum likelihood (REML)
  • Mean-variance or mode-curvature adaptive Gauss–Hermite quadrature
  • Nonadaptive Gauss–Hermite quadrature
  • Laplacian approximation
  • EM method starting values

Marginal analysis

  • Estimated marginal means
  • Marginal and partial effects
  • Average marginal and partial effects
  • Least-squares means
  • Predictive margins
  • Adjusted predictions, means, and effects
  • Contrasts of margins
  • Pairwise comparisons of margins
  • Profile plots
  • Graphs of margins and marginal effects

Additional resources

Watch a video overview of the multilevel modeling features added in Stata 13.

See New in Stata 13 for more about what was added in Stata 13.

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