Bayesian model averaging and weighted average least squares

Equivariance, stability, and numerical issues

G. De Luca, J.R. Magnus

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Pr¨ufer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.
Original languageEnglish
Pages (from-to)518-544
JournalThe Stata Journal
Volume11
Issue number4
Publication statusPublished - 2011

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Equivariance
Bayesian Model Averaging
Weighted Average
Model Averaging
Least Squares
Estimator
Uncertainty
Pre-test
Preliminary Test
Diagnostic Tests
Least Squares Estimator
Linear Regression Model
Econometrics
Model Selection
Regression
Likely
Computing

Cite this

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title = "Bayesian model averaging and weighted average least squares: Equivariance, stability, and numerical issues",
abstract = "In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Pr¨ufer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.",
author = "{De Luca}, G. and J.R. Magnus",
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}

Bayesian model averaging and weighted average least squares : Equivariance, stability, and numerical issues. / De Luca, G.; Magnus, J.R.

In: The Stata Journal, Vol. 11, No. 4, 2011, p. 518-544.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

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