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«Abstract. Bayesian model averaging has increasingly witnessed applications across an array of empirical contexts. However, the dearth of available ...»

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BMA IN R 17 Raftery, A., Hoeting, J., Volinsky, C., Painter, I. & Yeung, K. Y. (2010), BMA: Bayesian Model Averaging. R package version 3.13.

URL: http://CRAN.R-project.org/package=BMA Sala-i-Martin, X. (1997), ‘I just ran two million regressions’, The American Economic Review 87(2), 178–183.

Sala-i-Martin, X., Doppelhofer, G. & Miller, R. (2004), ‘Determinants of long-term growth: A Bayesian averaging of classical estimates (BACE) approach’, American Economic Review 94(4), 813–835.

Strawderman, W. (1971), ‘Proper Bayes minimax estimators of the multivariate normal mean’, The Annals of Mathematical Statistics 42(1), 385–388.

Venables, W. N. & Ripley, B. D. (2002), Modern Applied Statistics with S, fourth edn, Springer, New York. ISBN 0-387-95457-0.

URL: http://www.stats.ox.ac.uk/pub/MASS4 Zellner, A. & Siow, A. (1980), ‘Posterior odds ratios for selected regression hypotheses’, Trabajos de Estad´ ıstica y de Investigaci´n Operativa 31(1), 585–603.

o

18 SHAHRAM M. AMINI AND CHRISTOPHER F. PARMETER

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We used the following codes to generate the results shown in the tables.

# Loading datasets and required libraries ######################################### set.seed(2011) library(MASS) data(UScrime); attach(UScrime) UScrime1 - (cbind(log(UScrime[,c(16,1,3:15)]), So)) noise- matrix(rnorm(35*nrow(UScrime)), ncol=35) colnames(noise)- paste(’noise’, 1:35, sep=’’) UScrime.log - cbind(UScrime1,noise) X - UScrime1[,-1]; Y - UScrime1[,1] x - UScrime.log[,-1]; y - UScrime.log[,1] # Full enumaration of model space (Tables 4 and 5) ################################################## # BMS Package:

library(BMS) bms_enu - bms(UScrime1, mcmc="enumerate", g="UIP", mprior="uniform", user.int=FALSE) coef(bms_enu) detach("package:BMS") # BMA Package:

library(BMA) bma_enu - iBMA.bicreg(X, Y, thresProbne0 = 5, verbose = TRUE, maxNvar = 30) summary(bma_enu) detach("package:BMA")

–  –  –

coef(bas_enu) detach("package:BAS") # Using model space search mechanisms (Tables 6 and 7) ###################################################### # BMS Package:

library(BMS) bms.time - system.time(bms_sam - bms(UScrime.log, burn=2000, iter = 100000, mcmc="bd", g="UIP", mprior="uniform", nmodel=2000, user.int=FALSE)) cat("Elapsed Time=", bms.time[3], "Seconds") # Figure 1 plot(bms_sam[1:200]) # Figure 2 bms_sam2 - bms(UScrime.log, burn=2000, iter = 100000, mcmc="bd", g="UIP", mprior="fixed", nmodel=2000, user.int=FALSE) plot(bms_sam2[1:200]) # Figure 3(a) density.bma(bms_sam, reg = "GDP", addons="esEpl") detach("package:BMS") # BMA Package:

library(BMA) bma.time - system.time(bma_sam - iBMA.bicreg(x, y, thresProbne0 = 5, verbose = TRUE, maxNvar = 30, nIter = 100000)) cat("Elapsed Time=", bma.time[3], "Seconds") #Figure 3(b) bma_fig - bicreg(x, y) plot(bma_fig, include=5, include.intercept=FALSE) detach("package:BMA") # BAS Package:

library(BAS) bas.time - system.time(bas_sam - bas.lm(y~., data=UScrime.log, n.models=2^15, prior="ZS-null", modelprior=uniform(), initprobs="Uniform",

20 SHAHRAM M. AMINI AND CHRISTOPHER F. PARMETER

method="AMCMC", Burnin.iterations=2000, MCMC.iterations=100000)) cat("Elapsed Time=", bas.time[3],"Seconds") # Figure 3(c) plot(coefficients(bas_sam), subset=12, ask=TRUE) # Figures 4(a), 4(b), and 4(c) plot(bas_sam, add.smooth=TRUE, panel="add.smooth") detach("package:BAS") # Evaluating time performance of the packages (Table 8) ####################################################### UScrime.time - as.data.frame(matrix(rnorm(6050000),nclo=121)) # BMS Package:

library(BMS) bms.mat - matrix(0,4,4) m - 1; n - 1 for(i in c(15,30,60,120)){ for(j in c(50,500,5000,50000)){ bms.run.time - system.time(bms.run - bms(UScrime.time[1:j,1:(i+1)], burn=2000, iter = 100000, mcmc="bd", g="UIP", mprior="uniform", nmodel=2000, user.int=FALSE)) bms.mat[m,n] - bms.run.time[3] m - m+1 } m - 1 n - n+1 } detach("package:BMS")

–  –  –

for(i in c(15,30,60,120)){ for(j in c(50,500,5000,50000)){ bma.run.time - system.time(bma.run - iBMA.bicreg(x[1:j,1:i], y[1:j,], thresProbne0 = 5, verbose = TRUE, maxNvar = 30, nIter = 100000)) bma.mat[m,n] - bma.run.time[3] m - m+1 } m - 1 n - n+1 } detach("package:BMA") # BAS Package:

library(BAS) bas.mat - matrix(0,4,4) m - 1; n - 1 for(i in c(15,30,60,120)){ for(j in c(50,500,5000,50000)){ bas.run.time - system.time(bas.run - bas.lm(V1~., data=UScrime.time[1:j,1:(i+1)], n.models=2^15, prior="ZS-null", modelprior=uniform(), initprobs="Uniform", method="AMCMC", Burnin.iterations=2000, MCMC.iterations=100000)) bas.mat[m,n] - bas.run.time[3] m - m+1 } m - 1 n - n+1 } detach("package:BAS") # Evaluating the replicability of three packages (Table 9) ########################################################## mydata - read.dta("fls21.dta", convert.dates=TRUE, convert.factors=TRUE, missing.type=TRUE, convert.underscore=TRUE,

22 SHAHRAM M. AMINI AND CHRISTOPHER F. PARMETER

arn.missing.labels=TRUE) bmadata - mydata[,-2] y - bmadata[,1] ; x - bmadata[,-1] attach(bmadata) library(BMS) bms.time - system.time(fls.bms - bms(bmadata, burn=10000, iter=500000, g="UIP", mprior="uniform", nmodel=3000, mcmc="bd", ser.int=FALSE)) coef(fls.bms) detach("package:BMS") library(BAS) bas.time - system.time(fls.bas - bas.lm(gr56092~., data=bmadata, n.models=2^15, prior="ZS-null", modelprior=uniform(), initprobs="Uniform", method="AMCMC", Burnin.iterations=10000, MCMC.iterations=500000)) coef(fls.bas) detach("package:BAS") library(BMA) bma.time - system.time(fls.bma- iBMA.bicreg(x, y, thresProbne0 = 5, verbose = TRUE, maxNvar = 30, nIter = 500000)) summary(fls.bma) detach("package:BMA")

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0.4 0.4 0.15 0.10 0.2 0.2 0.05 0.00 0.0 0.0 −1 0 1 2 0.0 0.5 1.0 1.5 −2 0 2 4

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6.0 6.5 7.0 7.5 0 10 20 30 40

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0.6 0.4 0.2 0.0

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Table 8. A comparison of BMS, BAS, and BMA run times.

Tabular values are total run time in seconds for the BMS, BAS and BMA packages respectively.

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