Martin Feldkircher

What it does

  • Which set of the covariates is appropriate to explain variation of the response variable? Are my results robust to in- / exclusion of additional explanatory variables? In addressing these issues Bayesian model averaging (BMA) has become a popular alternative to model selection. The BMS (Bayesian Model Sampling) package implements Bayesian model averaging for R.

Why BMS?

  • The BMS package excels in offering a range of widely used prior structures coupled with efficient MCMC algorithms
  • to sort through the model space.
  • It allows for uniform and binomial-beta priors on the model space as well as informative prior inclusion probabilities. Via these customized model priors one can thus fuse prior beliefs into the otherwise purely agnostic analysis, that is prevalent in the applied literature using BMA.
  • The BMS package also provides various specifications for Zellner's g prior including the so-called hyper-g priors advocated in Liang et al. (2008); Ley and Steel (2010); Feldkircher and Zeugner (2009). The sensitivity of BMA results to the specification of Zellner's g prior is well documented in the literature (Feldkircher and Zeugner 2011).
  • The package comes along with numerous graphical tools to analyze posterior coefficient densities, the posterior model size or predictive densities. It also includes a graphical representation of the model space via an image plot.
  • The BMS homepage provides (video-) tutorials on the usage of BMS as well as several extensions covered in the "BMS-blog" section. These include the use of model averaging for panel data, BMA in the context of the spatial autoregressive (SAR) model , implementation of the jointness measure (Doppelhofer and Weeks, 2009) and spatial filtering (Crespo Cuaresma and Feldkircher, 2012).


  • The package is fully described covering a range of hands-on examples in: Bayesian Model Averaging Employing Fixed and Flexible Priors - The BMS Package for R, together with Stefan Zeugner. In: Journal of Statistical Software , Vol. 68(4), pp. 1-37, 2015.

Software reviews

  • Amini and Parmeter (2011) and Amini and Parmeter (2012) carry out a comparison of R software packages that implement Bayesian model averaging, in particular the packages BAS (Merlise Clyde 2012) and BMA (Adrian Raftery and Jennifer Hoeting and Chris Volinsky and Ian Painter and Ka Yee Yeung 2012). Amini and Parmeter (2012) conclude that BMS is the only among its competitors that is able the reproduce empirical results in Fernandez et al. (2001); Doppelhofer and Weeks (2009) and the working paper version of Masanjala and Papageorgiou (2008). See also Blazejowski and Kwiatkowski (2015) for a more recent comparison.

BMS Add-ons and Tutorials

  • A Tutorial
  • spatBMS_0.0.tar.gz (works only with R<=2.11)
  • (works only with R<=2.11)
  • spatBMS_0.1.tar.gz (works only with R>2.11)
  • (works with R>2.11)
  • References

    • Amini SM, Parmeter CF (2011). Bayesian Model Averaging in R. Journal of Economic and Social Measurement, 36:4, pp. 253-287
    • Amini SM, Parmeter CF (2012). Comparisons of Model Averaging Techniques: Assessing Growth Determinants. Journal of Applied Econometrics, Vol. 27:5, 1099-1255.
    • Babecký, Havránek, Matěju, Rusnák, Šmidková, and Vašiček (2013); Leading Indicators of Crisis Incidence: Evidence from Developed Countries. Journal of International Money and Finance, Vol. 35, pp1-19.
    • Blazejowski and Kwiatkowski (2015); Bayesian Model Averaging and Jointness Measures for gretl. Journal of Statistical Software, Vol. 68(5), pp1-19.
    • Chipman H (1996). Bayesian Variable Selection with Related Predictors. Canadian Journal of Statistics, 24, pp. 17-36
    • Crespo Cuaresma J, Doppelhofer G, Feldkircher M (2014). The determinants of economic growth in European regions. Regional Studies, Vol. 48, Nr. 1, pp. 44-67.
    • Crespo Cuaresma J, Feldkircher M (2013). Spatial Filtering, Model Uncertainty and the Speed of Income Convergence in Europe. Journal of Applied Econometrics, Vol. 28, Issue 4, pp. 720-741.
    • Doppelhofer G, Weeks M (2009). Jointness of Growth Determinants. Journal of Applied Econometrics, 24(2), 209-244
    • Feldkircher M (2012). Forecast Combination and Bayesian Model Averaging - A Prior Sensitivity Analysis. Journal of Forecasting, 31, 361-376.
    • Fernández C, Ley E, Steel MF (2001). Model Uncertainty in Cross-Country Growth Regressions. Journal of Applied Econometrics, 16, 563-576
    • Giannone D, Lenza M, Reichlin L (2011). Market Freedom and the Global Recession. IMF Economic Review, 59, 111-135
    • Horváth R (2013). Does Trust Promote Growth? Journal of Comparative Studies, Vol. 41:3, pp. 777-788.
    • Horváth R (2011). Research & development and growth: A Bayesian model averaging analysis. Economic Modelling, 28:6, 2669-2673
    • Horváth, Rusnák, Šmidková, and Zapal (2011). Dissent voting behavior of central bankers: what do we really know?. Economic Modelling, 28:6, 2669-2673
    • Masanjala WH, Papageorgiou C (2008). Rough and Lonely Road to Prosperity: A Reexamination of the Sources of Growth in Africa Using Bayesian Model Averaging. Journal of Applied Econometrics, 23, 671–682.
    • Adrian Raftery and Jennifer Hoeting and Chris Volinsky and Ian Painter and Ka Yee Yeung (2012). BMA: Bayesian Model Averaging. recent R package version.
    • Merlise Clyde (2012). BAS: Bayesian Adaptive Sampling for Bayesian Model Averaging. recent R package version .