R: Use R^2 statistic to compute Bayes factor for regression...

linearReg.R2stat {BayesFactor} | R Documentation

## Use R^2 statistic to compute Bayes factor for regression designs

### Description

Using the classical R^2 test statistic for (linear) regression designs, this function computes the corresponding Bayes factor test.

### Usage

    linearReg.R2stat(N, p, R2, rscale = "medium", simple = FALSE)

### Arguments

`N` | number of observations
`p` | number of predictors in model, excluding intercept
`R2` | proportion of variance accounted for by the predictors, excluding intercept
`rscale` | numeric prior scale
`simple` | if `TRUE`, return only the Bayes factor

### 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 `lmBF`, but you do have the test statistic.

For details about the model, see the help for `regressionBF`, and the references therein.

The Bayes factor is computed via Gaussian quadrature.

### Value

If `simple` is `TRUE`, returns the Bayes factor (against the intercept-only null). If `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.

### Author(s)

Richard D. Morey (richarddmorey@gmail.com) and Jeffrey N. Rouder (rouderj@missouri.edu)

### 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.

Perception and Cognition Lab (University of Missouri): Bayes factor calculators. http://pcl.missouri.edu/bayesfactor

### See Also

`integrate`, `lm`; see `lmBF` for the intended interface to this function, using the full data set.

### 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']])

[Package BayesFactor version 0.9.12-4.2 Index]