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 $$y ~
Normal(\alpha 1 + X\beta, \sigma^2 I).$$ The joint prior on
\(\alpha,\sigma^2\) is proportional to \(1/\sigma^2\), the prior on
\(\beta\) is $$\beta ~ Normal(0, N g \sigma^2(X'X)^{-1}).$$ 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.