R: Bayesian Model Averaging for linear regression models.
bicreg
R Documentation
Bayesian Model Averaging for linear regression models.
Description
Bayesian Model Averaging accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to approximate posterior model probability.
logical. FALSE returns all models whose posterior model probability is within a factor of 1/OR of that of the best model. TRUE returns a more parsimonious set of models, where any model with a more likely submodel is eliminated.
OR
a number specifying the maximum ratio for excluding models in Occam's window
maxCol
a number specifying the maximum number of columns in the design matrix (including the intercept) to be kept.
drop.factor.levels
logical. Indicates whether factor levels can be individually dropped in the stepwise procedure to reduce the number of columns in the design matrix, or if a factor can be dropped only in its entirety.
nbest
a value specifying the number of models of each size
returned to bic.glm by the leaps algorithm. The default is 150
(replacing the original default of 10).
Details
Bayesian Model Averaging accounts for the model uncertainty inherent in the variable selection problem by averaging over the best models in the model class according to the approximate posterior model probabilities.
Value
bicreg returns an object of class bicreg
The function 'summary' is used to print a summary of the results. The function 'plot' is used to plot posterior distributions for the coefficients.
An object of class bicreg is a list containing at least the following components:
postprob
the posterior probabilities of the models selected
namesx
the names of the variables
label
labels identifying the models selected
r2
R2 values for the models
bic
values of BIC for the models
size
the number of independent variables in each of the models
which
a logical matrix with one row per model and one column per variable indicating whether that variable is in the model
probne0
the posterior probability that each variable is non-zero (in percent)
postmean
the posterior mean of each coefficient (from model averaging)
postsd
the posterior standard deviation of each coefficient (from model averaging)
condpostmean
the posterior mean of each coefficient conditional on the variable being included in the model
condpostsd
the posterior standard deviation of each coefficient conditional on the variable being included in the model
ols
matrix with one row per model and one column per variable giving the OLS estimate of each coefficient for each model
se
matrix with one row per model and one column per variable giving the standard error of each coefficient for each model
reduced
a logical indicating whether any variables were dropped before model averaging
dropped
a vector containing the names of those variables dropped before model averaging
residvar
residual variance for each model
call
the matched call that created the bicreg object
Author(s)
Original Splus code developed by Adrian Raftery (raftery@AT@stat.washington.edu) and revised by Chris T. Volinsky. Translation to R by Ian Painter.
References
Raftery, Adrian E. (1995). Bayesian model selection in social research (with Discussion). Sociological Methodology 1995 (Peter V. Marsden, ed.), pp. 111-196, Cambridge, Mass.: Blackwells.
See Also
summary.bicreg, print.bicreg, plot.bicreg
Examples
library(MASS)
data(UScrime)
x<- UScrime[,-16]
y<- log(UScrime[,16])
x[,-2]<- log(x[,-2])
lma<- bicreg(x, y, strict = FALSE, OR = 20)
summary(lma)
plot(lma)
imageplot.bma(lma)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(BMA)
Loading required package: survival
Loading required package: leaps
Loading required package: robustbase
Attaching package: 'robustbase'
The following object is masked from 'package:survival':
heart
Loading required package: inline
Loading required package: rrcov
Scalable Robust Estimators with High Breakdown Point (version 1.3-11)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/BMA/bicreg.Rd_%03d_medium.png", width=480, height=480)
> ### Name: bicreg
> ### Title: Bayesian Model Averaging for linear regression models.
> ### Aliases: bicreg
> ### Keywords: regression models
>
> ### ** Examples
>
> library(MASS)
> data(UScrime)
> x<- UScrime[,-16]
> y<- log(UScrime[,16])
> x[,-2]<- log(x[,-2])
> lma<- bicreg(x, y, strict = FALSE, OR = 20)
> summary(lma)
Call:
bicreg(x = x, y = y, strict = FALSE, OR = 20)
115 models were selected
Best 5 models (cumulative posterior probability = 0.2039 ):
p!=0 EV SD model 1 model 2 model 3
Intercept 100.0 -23.45301 5.58897 -22.63715 -24.38362 -25.94554
M 97.3 1.38103 0.53531 1.47803 1.51437 1.60455
So 11.7 0.01398 0.05640 . . .
Ed 100.0 2.12101 0.52527 2.22117 2.38935 1.99973
Po1 72.2 0.64849 0.46544 0.85244 0.91047 0.73577
Po2 32.0 0.24735 0.43829 . . .
LF 6.0 0.01834 0.16242 . . .
M.F 7.0 -0.06285 0.46566 . . .
Pop 30.1 -0.01862 0.03626 . . .
NW 88.0 0.08894 0.05089 0.10888 0.08456 0.11191
U1 15.1 -0.03282 0.14586 . . .
U2 80.7 0.26761 0.19882 0.28874 0.32169 0.27422
GDP 31.9 0.18726 0.34986 . . 0.54105
Ineq 100.0 1.38180 0.33460 1.23775 1.23088 1.41942
Prob 99.2 -0.24962 0.09999 -0.31040 -0.19062 -0.29989
Time 43.7 -0.12463 0.17627 -0.28659 . -0.29682
nVar 8 7 9
r2 0.842 0.826 0.851
BIC -55.91243 -55.36499 -54.69225
post prob 0.062 0.047 0.034
model 4 model 5
Intercept -22.80644 -24.50477
M 1.26830 1.46061
So . .
Ed 2.17788 2.39875
Po1 0.98597 .
Po2 . 0.90689
LF . .
M.F . .
Pop -0.05685 .
NW 0.09745 0.08534
U1 . .
U2 0.28054 0.32977
GDP . .
Ineq 1.32157 1.29370
Prob -0.21636 -0.20614
Time . .
nVar 8 7
r2 0.838 0.823
BIC -54.60434 -54.40788
post prob 0.032 0.029
> plot(lma)
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> imageplot.bma(lma)
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> dev.off()
null device
1
>