Description Usage Arguments Details Value Author(s) References See Also Examples

This function simultaneously computes Bayes factors for groups of models in regression designs

1 2 3 | ```
regressionBF(formula, data, whichModels = "all",
progress = options()$BFprogress, rscaleCont = "medium",
noSample = FALSE)
``` |

`formula` |
a formula containing all covariates to include in the analysis (see Examples) |

`data` |
a data frame containing data for all factors in the formula |

`whichModels` |
which set of models to compare; see Details |

`progress` |
if |

`rscaleCont` |
prior scale on all standardized slopes |

`noSample` |
if |

`regressionBF`

computes Bayes factors to test the
hypothesis that slopes are 0 against the alternative that
all slopes are nonzero.

The vector of observations *y* is assumed to be
distributed as

*y ~ Normal(α 1 + Xβ,
σ^2 I).*

The joint prior on *α,σ^2* is
proportional to *1/σ^2*, the prior on
*β* is

*β ~ Normal(0, N g
σ^2(X'X)^{-1}).*

where *g ~
InverseGamma(1/2,r/2)*. See Liang et al. (2008) section 3
for details.

Possible values for `whichModels`

are 'all', 'top',
and 'bottom', where 'all' computes Bayes factors for all
models, 'top' computes the Bayes factors for models that
have one covariate missing from the full model, and
'bottom' computes the Bayes factors for all models
containing a single covariate. Caution should be used
when interpreting the results; when the results of 'top'
testing is interpreted as a test of each covariate, the
test is conditional on all other covariates being in the
model (and likewise 'bottom' testing is conditional on no
other covariates being in the model).

An option is included to prevent analyzing too many
models at once: `options('BFMaxModels')`

, which
defaults to 50,000, is the maximum number of models that
'regressionBF' will analyze at once. This can be
increased by increasing the option value.

For the `rscaleCont`

argument, several named values
are recongized: "medium", "wide", and "ultrawide", which
correspond *r* scales of *sqrt(2)/4*,
1/2, and *sqrt(2)/2*, respectively. These
values were chosen to yield consistent Bayes factors with
`anovaBF`

.

An object of class `BFBayesFactor`

, containing the
computed model comparisons

Richard D. Morey ([email protected])

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). Bayesian testing in regression. Multivariate Behavioral Research.

Zellner, A. and Siow, A., (1980) Posterior Odds Ratios for Selected Regression Hypotheses. In Bayesian Statistics: Proceedings of the First Interanational Meeting held in Valencia (Spain). Bernardo, J. M., Lindley, D. V., and Smith A. F. M. (eds), pp. 585-603. University of Valencia.

`lmBF`

, for testing specific models, and
`anovaBF`

for the function similar to
`regressionBF`

for ANOVA models.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## See help(attitude) for details about the data set
data(attitude)
## Classical regression
summary(fm1 <- lm(rating ~ ., data = attitude))
## Compute Bayes factors for all regression models
output = regressionBF(rating ~ ., data = attitude, progress=FALSE)
head(output)
## Best model is 'complaints' only
## Compute all Bayes factors against the full model, and
## look again at best models
head(output / output[63])
``` |

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