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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
  • Survival outcomes, modeled as New
    • Exponential
    • Weibull
    • Lognormal
    • Loglogistic
    • Gamma
  • 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

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

Small-sample inference in linear models (DDF adjustments) New

  • Kenward–Roger
  • Satterthwaite
  • Repeated-measures ANOVA
  • Residual


  • 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 allowing for correlated data

Survey data for generalized linear and survival models New

  • Sampling weights
  • Weights at each level of model
  • Cluster–robust SEs allowing for correlated data
  • Support the –svy– prefix for linearized variance estimation including stratification and multistage weights

Multiple imputation

Postestimation Selector New

  • View and run all postestimation features for your command
  • Automatically updated as estimation commands are run

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
    • Density function New
    • Distribution function New
    • Survivor function New
    • Hazard function New
    • Predict marginally with respect to random effects New
    • 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
Watch Introduction to Factor Variables in Stata tutorials

Marginal analysis

Additional resources

See New in Stata 14 for more about what was added in Stata 14.





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