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.