Whether the groupings in your data arise in a nested fashion (students nested in schools and schools nested in districts) or in a nonnested fashion (regions crossed with occupations), you can fit a multilevel model to account for the lack of independence within these groups. Fit models for continuous, binary, count, ordinal, and survival outcomes. Estimate variances of random intercepts and random coefficients. Compute intraclass correlations. Predict random effects. Estimate relationships that are population averaged over the random effects. And much more
Outcomes and regression estimators
Continuous, modeled as
- Linear
- Log linear
- Log gamma
- Nonlinear
- Interval-measured (interval-censored)
- Left-censored, right-censored, or both (tobit)
Binary outcomes, modeled as
- Logistic
- Probit
- Complementary log-log
Count outcomes, modeled as
- Poisson
- Negative binomia
Categorical outcomes, modeled as
- Multinomial logistic (via generalized SEM)
Ordered outcomes, modeled as
- Ordered logistic
- Ordered probit
Survival outcomes, modeled as
- 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
Bayesian estimation
- Select from many prior distributions or use default priors
- Adaptive MH sampling or Gibbs sampling with linear regression
- Postestimation tools for checking convergence, estimating functions of model parameters, computing Bayes factors, and performing interval hypotheses testing
Watch Nonlinear mixed-effects models with lags and differences
Watch Nonlinear mixed-effects models
Watch Tour of multilevel GLMs
Types of models
- Two-, three-, and higher-level models
- Nested (hierarchical) models
- Crossed models
- Mixed models
- Balanced and unbalanced designs
Types of effects
- Random intercepts
- Random coefficients (slopes)
- Variances of random effects (variance components)
- Fixed effects (regression 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
Error (residual) structures for linear models
- Independent
- Exchangeable
- Autoregressive
- Moving average
- Exponential
- Banded
- Toeplitz
- Flexible
- 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)
- Kenward–Roger
- Satterthwaite
- ANOVA
- Repeated-measures ANOVA
- Residual
Watch Small-sample inference for mixed-effects models
Constraints
- 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
- 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
Watch Multilevel models for survey data in Stata.
Multiple imputation
Postestimation Selector
- View and run all postestimation features for your command
- Automatically updated as estimation commands are run
Watch Postestimation Selector
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
Predictions
Predicted outcomes with and without effects
- Linear predictions
- Probabilities
- Counts
- Density function
- Distribution function
- Survivor function
- Hazard function
- Predict marginally with respect to random effects
- Pearson, deviance, and Anscombe residuals
Other postestimation analysis
- Estimate variance components
- Intraclass correlation coefficients (ICCs) after logistic probit, and random-effects models Updated
- 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 Updated
- Include polynomial terms
- Perform contrasts of categories/levels
Watch Introduction to Factor Variables in Stata tutorials
Marginal analysis
- Estimated marginal means
- Marginal and partial effects
- Average marginal and partial effects
- Least-squares means
- Predictive margins
- Adjusted predictions, means, and effects
- Works with multiple outcomes simultaneously
- Integrates over random effects
- Contrasts of margins
- Pairwise comparisons of margins
- Profile plots
- Graphs of margins and marginal effects
Reference