bayesfactor_parameters {bayestestR}  R Documentation 
Bayes Factors (BF) for a Single Parameter
Description
This method computes Bayes factors against the null (either a point or an
interval), based on prior and posterior samples of a single parameter. This
Bayes factor indicates the degree by which the mass of the posterior
distribution has shifted further away from or closer to the null value(s)
(relative to the prior distribution), thus indicating if the null value has
become less or more likely given the observed data.
When the null is an interval, the Bayes factor is computed by comparing the
prior and posterior odds of the parameter falling within or outside the null
interval (Morey & Rouder, 2011; Liao et al., 2020); When the null is a point,
a SavageDickey density ratio is computed, which is also an approximation of
a Bayes factor comparing the marginal likelihoods of the model against a
model in which the tested parameter has been restricted to the point null
(Wagenmakers et al., 2010; Heck, 2019).
Note that the logspline
package is used for estimating densities and
probabilities, and must be installed for the function to work.
bayesfactor_pointnull()
and bayesfactor_rope()
are wrappers
around bayesfactor_parameters
with different defaults for the null to
be tested against (a point and a range, respectively). Aliases of the main
functions are prefixed with bf_*
, like bf_parameters()
or
bf_pointnull()
.
For more info, in particular on specifying correct priors for factors
with more than 2 levels, see
the Bayes factors vignette.
Usage
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
bayesfactor_pointnull(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
bayesfactor_rope(
posterior,
prior = NULL,
direction = "twosided",
null = rope_range(posterior, verbose = FALSE),
verbose = TRUE,
...
)
bf_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
bf_pointnull(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
bf_rope(
posterior,
prior = NULL,
direction = "twosided",
null = rope_range(posterior, verbose = FALSE),
verbose = TRUE,
...
)
## S3 method for class 'numeric'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
## S3 method for class 'stanreg'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("conditional", "location", "smooth_terms", "sigma", "zi",
"zero_inflated", "all"),
parameters = NULL,
...
)
## S3 method for class 'brmsfit'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("conditional", "location", "smooth_terms", "sigma", "zi",
"zero_inflated", "all"),
parameters = NULL,
...
)
## S3 method for class 'blavaan'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
## S3 method for class 'data.frame'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "twosided",
null = 0,
verbose = TRUE,
...
)
Arguments
posterior 
A numerical vector, 
prior 
An object representing a prior distribution (see 'Details'). 
direction 
Test type (see 'Details'). One of 
null 
Value of the null, either a scalar (for pointnull) or a range (for a intervalnull). 
verbose 
Toggle off warnings. 
... 
Arguments passed to and from other methods. (Can be used to pass
arguments to internal 
effects 
Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated. 
component 
Should results for all parameters, parameters for the conditional model or the zeroinflated part of the model be returned? May be abbreviated. Only applies to brmsmodels. 
parameters 
Regular expression pattern that describes the parameters
that should be returned. Metaparameters (like 
Details
This method is used to compute Bayes factors based on prior and posterior distributions.
Onesided & Dividing Tests (setting an order restriction)
One sided tests (controlled by direction
) are conducted by restricting
the prior and posterior of the nonnull values (the "alternative") to one
side of the null only (Morey & Wagenmakers, 2014). For example, if we
have a prior hypothesis that the parameter should be positive, the
alternative will be restricted to the region to the right of the null (point
or interval). For example, for a Bayes factor comparing the "null" of 00.1
to the alternative >0.1
, we would set
bayesfactor_parameters(null = c(0, 0.1), direction = ">")
.
It is also possible to compute a Bayes factor for dividing
hypotheses  that is, for a null and alternative that are complementary,
opposing onesided hypotheses (Morey & Wagenmakers, 2014). For
example, for a Bayes factor comparing the "null" of <0
to the alternative
>0
, we would set bayesfactor_parameters(null = c(Inf, 0))
.
Value
A data frame containing the (log) Bayes factor representing evidence
against the null (Use as.numeric()
to extract the nonlog Bayes
factors; see examples).
Setting the correct prior
For the computation of Bayes factors, the model priors must be proper priors
(at the very least they should be not flat, and it is preferable that
they be informative); As the priors for the alternative get wider, the
likelihood of the null value(s) increases, to the extreme that for completely
flat priors the null is infinitely more favorable than the alternative (this
is called the JeffreysLindleyBartlett paradox). Thus, you should
only ever try (or want) to compute a Bayes factor when you have an informed
prior.
(Note that by default, brms::brm()
uses flat priors for fixedeffects;
See example below.)
It is important to provide the correct prior
for meaningful results.
When
posterior
is a numerical vector,prior
should also be a numerical vector.When
posterior
is adata.frame
,prior
should also be adata.frame
, with matching column order.When
posterior
is astanreg
,brmsfit
or other supported Bayesian model:
prior
can be set toNULL
, in which case prior samples are drawn internally. 
prior
can also be a model equivalent toposterior
but with samples from the priors only. Seeunupdate()
. 
Note: When
posterior
is abrmsfit_multiple
model,prior
must be provided.

When
posterior
is anemmGrid
/emm_list
object:
prior
should also be anemmGrid
/emm_list
object equivalent toposterior
but created with a model of priors samples only. Seeunupdate()
. 
prior
can also be the original (posterior) model. If so, the function will try to update theemmGrid
/emm_list
to use theunupdate()
d priormodel. (This cannot be done forbrmsfit
models.) 
Note: When the
emmGrid
has undergone any transformations ("log"
,"response"
, etc.), orregrid
ing, thenprior
must be anemmGrid
object, as stated above.

Interpreting Bayes Factors
A Bayes factor greater than 1 can be interpreted as evidence against the null, at which one convention is that a Bayes factor greater than 3 can be considered as "substantial" evidence against the null (and vice versa, a Bayes factor smaller than 1/3 indicates substantial evidence in favor of the nullmodel) (Wetzels et al. 2011).
Note
There is also a
plot()
method
implemented in the
seepackage.
Author(s)
Mattan S. BenShachar
References
Wagenmakers, E. J., Lodewyckx, T., Kuriyal, H., and Grasman, R. (2010). Bayesian hypothesis testing for psychologists: A tutorial on the SavageDickey method. Cognitive psychology, 60(3), 158189.
Heck, D. W. (2019). A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters. British Journal of Mathematical and Statistical Psychology, 72(2), 316333.
Morey, R. D., & Wagenmakers, E. J. (2014). Simple relation between Bayesian orderrestricted and pointnull hypothesis tests. Statistics & Probability Letters, 92, 121124.
Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological methods, 16(4), 406.
Liao, J. G., Midya, V., & Berg, A. (2020). Connecting and contrasting the Bayes factor and a modified ROPE procedure for testing interval null hypotheses. The American Statistician, 119.
Wetzels, R., Matzke, D., Lee, M. D., Rouder, J. N., Iverson, G. J., and Wagenmakers, E.J. (2011). Statistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 t Tests. Perspectives on Psychological Science, 6(3), 291–298. doi:10.1177/1745691611406923
Examples
library(bayestestR)
prior < distribution_normal(1000, mean = 0, sd = 1)
posterior < distribution_normal(1000, mean = .5, sd = .3)
(BF_pars < bayesfactor_parameters(posterior, prior, verbose = FALSE))
as.numeric(BF_pars)
# rstanarm models
# 
contrasts(sleep$group) < contr.equalprior_pairs # see vingette
stan_model < suppressWarnings(stan_lmer(
extra ~ group + (1  ID),
data = sleep,
refresh = 0
))
bayesfactor_parameters(stan_model, verbose = FALSE)
bayesfactor_parameters(stan_model, null = rope_range(stan_model))
# emmGrid objects
# 
group_diff < pairs(emmeans(stan_model, ~group, data = sleep))
bayesfactor_parameters(group_diff, prior = stan_model, verbose = FALSE)
# Or
# group_diff_prior < pairs(emmeans(unupdate(stan_model), ~group))
# bayesfactor_parameters(group_diff, prior = group_diff_prior, verbose = FALSE)
# brms models
# 
## Not run:
contrasts(sleep$group) < contr.equalprior_pairs # see vingette
my_custom_priors <
set_prior("student_t(3, 0, 1)", class = "b") +
set_prior("student_t(3, 0, 1)", class = "sd", group = "ID")
brms_model < suppressWarnings(brm(extra ~ group + (1  ID),
data = sleep,
prior = my_custom_priors,
refresh = 0
))
bayesfactor_parameters(brms_model, verbose = FALSE)
## End(Not run)