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Bayesian model averaging (BMA) New

Perform Bayesian model averaging with the bma suite to account for model uncertainty in your analysis. Perform model choice, inference, and prediction. Identify influential models and important predictors. Explore model complexity, model fit, and predictive performance. Perform sensitivity analysis to the assumptions about importance of models and predictors. Generate predictions. And much more.

Learn about Bayesian model averaging and see examples of Bayesian model averaging features.

Watch Bayesian model averaging.

Also see overview examples.

Bayesian model averaging (BMA) for linear regression

  • Model priors: uniform, binomial, and beta-binomial
  • Many fixed and random g-priors
  • Grouping of predictors
  • Support of always-included predictors
  • Heredity rules for interactions
  • Support of factor variables and times-series operators
  • Automatic grouping of factor variables and interactions

Model space

  • Full model enumeration with fewer than 25 predictors
  • MC3 sampling with fixed g parameter
  • MC3 and MH sampling with random g parameter
  • Options to control MCMC sampling
  • Convergence diagnostics with sampling

BMA posterior summaries

  • Analytical posterior means and standard deviations for regression coefficients with fixed g
  • MCMC posterior means and standard deviations for regression coefficients with sampling
  • Posterior summaries for random g and the shrinkage parameter
  • Posterior model probabilities (PMPs) and cumulative PMPs
  • Posterior inclusion probabilities (PIPs) for predictors
  • Posterior model-size summaries

Simulating posterior distributions of model parameters

  • Analytical posterior distributions
  • MCMC-based posterior distributions

Model and variable-inclusion summary

  • Models ranked by PMP
  • Highest probability model (HPM)
  • Median probability model (MPM)
  • Models containing specific predictors

Posterior distributions of regression coefficients

  • Density plots for one coefficient
  • Density plots for multiple or for all coefficients
  • Analytical posterior densities
  • MCMC-sample posterior densities
  • Posterior probability of noninclusion
  • Customized graphs

Model-size distribution summaries

  • Analytical prior mean and median model size
  • Analytical posterior mean and median model size
  • Frequency posterior mean and median model size

BMA plots

  • Checking BMA convergence
  • Prior and posterior model-size distribution plots
  • Variable-inclusion maps
  • Customized graphs

Jointness measures for predictors

  • Doppelhofer—Weeks measure
  • Ley—Steel type 1 measure
  • Ley—Steel type 2 measure
  • Yule's Q measure
  • Modified Yule's Q measure

Log predictive-score (LPS)

  • Analytical LPS
  • Frequency-based LPS
  • LPS summaries
  • Entropy

BMA predictions

  • Analytical posterior predictive means and standard deviations with fixed g
  • MCMC-sample posterior predictive summaries: mean, median, standard deviation, and credible intervals
  • Predictions of simulated outcome
  • Replicates of simulated outcome
  • Log predictive-score

Postestimation Selector

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

Posterior summaries

MCSE estimation methods

  • Using effective sample size
  • Using batch means

Bayesian predictions

  • Generate predictions: simulate outcome values and their functions
  • Save all or a subset of predictions in a separate dataset
  • Save posterior summaries of predictions as variables in current dataset
  • Save a subset of MCMC replicates as variables in current dataset
  • Obtain graphical and posterior summaries, perform hypothesis tests, and more
  • Use built-in tools to create functions of predictions, or write your own Mata functions and Stata programs
  • Generate replicated data for posterior predictive checks

Model goodness of fit

  • Posterior predictive p-values
  • MCMC replicates
  • Predictions

Tools to check MCMC convergence

  • Diagnostic plots in compact form
  • Trace plots
  • Autocorrelation plots
  • Histograms
  • Density plots
  • Cumulative sum plots
  • Bivariate scatterplots
  • Produce any of the above for parameters or functions of parameters
  • Multiple separate graphs or multiple plots on one graph
  • Pause between multiple graphs
  • Customize the look of each graph

Tools to check MCMC efficiency

  • Effective sample sizes
  • Autocorrelation times
  • Efficiencies
  • Compute any of the above for parameters or functions of parameters

Additional resources

See Bayesian analysis
See Bayesian econometrics

See New in Stata 18 to learn about what was added in Stata 18.