1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
|
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/linearReg_R2stat.R
\name{linearReg.R2stat}
\alias{linearReg.R2stat}
\title{Use R^2 statistic to compute Bayes factor for regression designs}
\usage{
linearReg.R2stat(N, p, R2, rscale = "medium", simple = FALSE)
}
\arguments{
\item{N}{number of observations}
\item{p}{number of predictors in model, excluding intercept}
\item{R2}{proportion of variance accounted for by the predictors, excluding
intercept}
\item{rscale}{numeric prior scale}
\item{simple}{if \code{TRUE}, return only the Bayes factor}
}
\value{
If \code{simple} is \code{TRUE}, returns the Bayes factor (against the
intercept-only null). If \code{FALSE}, the function returns a
vector of length 3 containing the computed log(e) Bayes factor,
along with a proportional error estimate on the Bayes factor and the method used to compute it.
}
\description{
Using the classical R^2 test statistic for (linear) regression designs, this
function computes the corresponding Bayes factor test.
}
\details{
This function can be used to compute the Bayes factor corresponding to a
multiple regression, using the classical R^2 (coefficient of determination)
statistic. It can be used when you don't have access to the full data set
for analysis by \code{\link{lmBF}}, but you do have the test statistic.
For details about the model, see the help for \code{\link{regressionBF}},
and the references therein.
The Bayes factor is computed via Gaussian quadrature.
}
\examples{
## Use attitude data set
data(attitude)
## Scatterplot
lm1 = lm(rating~complaints,data=attitude)
plot(attitude$complaints,attitude$rating)
abline(lm1)
## Traditional analysis
## p value is highly significant
summary(lm1)
## Bayes factor
## The Bayes factor is over 400,000;
## the data strongly favor hypothesis that
## the slope is not 0.
result = linearReg.R2stat(30,1,0.6813)
exp(result[['bf']])
}
\references{
Liang, F. and Paulo, R. and Molina, G. and Clyde, M. A. and
Berger, J. O. (2008). Mixtures of g-priors for Bayesian Variable
Selection. Journal of the American Statistical Association, 103, pp.
410-423
Rouder, J. N. and Morey, R. D. (in press, Multivariate Behavioral Research). Bayesian testing in
regression.
}
\seealso{
\code{\link{integrate}}, \code{\link{lm}}; see
\code{\link{lmBF}} for the intended interface to this function, using
the full data set.
}
\author{
Richard D. Morey (\email{richarddmorey@gmail.com}) and Jeffrey N.
Rouder (\email{rouderj@missouri.edu})
}
\keyword{htest}
|
