bayesfactor_parameters {bayestestR} | R Documentation |
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 Savage-Dickey 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.
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
bayesfactor_pointnull(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
bayesfactor_rope(
posterior,
prior = NULL,
direction = "two-sided",
null = rope_range(posterior),
verbose = TRUE,
...
)
bf_parameters(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
bf_pointnull(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
bf_rope(
posterior,
prior = NULL,
direction = "two-sided",
null = rope_range(posterior),
verbose = TRUE,
...
)
## S3 method for class 'numeric'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
## S3 method for class 'stanreg'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "two-sided",
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 = "two-sided",
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 = "two-sided",
null = 0,
verbose = TRUE,
...
)
## S3 method for class 'data.frame'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
verbose = TRUE,
...
)
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 point-null) or a range (for a interval-null). |
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 zero-inflated part of the model be returned? May be abbreviated. Only applies to brms-models. |
parameters |
Regular expression pattern that describes the parameters
that should be returned. Meta-parameters (like |
This method is used to compute Bayes factors based on prior and posterior distributions.
One sided tests (controlled by direction
) are conducted by restricting
the prior and posterior of the non-null 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 0-0.1
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 one-sided 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))
.
A data frame containing the (log) Bayes factor representing evidence
against the null (Use as.numeric()
to extract the non-log Bayes
factors; see examples).
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 Jeffreys-Lindley-Bartlett 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 fixed-effects;
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 a data.frame
, prior
should also be a data.frame
, with matching column order.
When posterior
is a stanreg
, brmsfit
or other supported Bayesian model:
prior
can be set to NULL
, in which case prior samples are drawn internally.
prior
can also be a model equivalent to posterior
but with samples from the priors only. See unupdate()
.
Note: When posterior
is a brmsfit_multiple
model, prior
must be provided.
When posterior
is an emmGrid
/ emm_list
object:
prior
should also be an emmGrid
/ emm_list
object equivalent to posterior
but created with a model of priors samples only. See unupdate()
.
prior
can also be the original (posterior) model. If so, the function will try to update the emmGrid
/ emm_list
to use the unupdate()
d prior-model. (This cannot be done for brmsfit
models.)
Note: When the emmGrid
has undergone any transformations ("log"
, "response"
, etc.), or regrid
ing, then prior
must be an emmGrid
object, as stated above.
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 null-model) (Wetzels et al. 2011).
There is also a
plot()
-method
implemented in the
see-package.
Mattan S. Ben-Shachar
Wagenmakers, E. J., Lodewyckx, T., Kuriyal, H., and Grasman, R. (2010). Bayesian hypothesis testing for psychologists: A tutorial on the Savage-Dickey method. Cognitive psychology, 60(3), 158-189.
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), 316-333.
Morey, R. D., & Wagenmakers, E. J. (2014). Simple relation between Bayesian order-restricted and point-null hypothesis tests. Statistics & Probability Letters, 92, 121-124.
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, 1-19.
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
library(bayestestR)
if (require("logspline")) {
prior <- distribution_normal(1000, mean = 0, sd = 1)
posterior <- distribution_normal(1000, mean = .5, sd = .3)
(BF_pars <- bayesfactor_parameters(posterior, prior))
as.numeric(BF_pars)
}
## Not run:
# rstanarm models
# ---------------
if (require("rstanarm") && require("emmeans") && require("logspline")) {
contrasts(sleep$group) <- contr.equalprior_pairs # see vingette
stan_model <- stan_lmer(extra ~ group + (1 | ID), data = sleep)
bayesfactor_parameters(stan_model)
bayesfactor_parameters(stan_model, null = rope_range(stan_model))
# emmGrid objects
# ---------------
group_diff <- pairs(emmeans(stan_model, ~group))
bayesfactor_parameters(group_diff, prior = stan_model)
# Or
group_diff_prior <- pairs(emmeans(unupdate(stan_model), ~group))
bayesfactor_parameters(group_diff, prior = group_diff_prior)
}
# brms models
# -----------
if (require("brms")) {
contrasts(sleep$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 <- brm(extra ~ group + (1 | ID),
data = sleep,
prior = my_custom_priors
)
bayesfactor_parameters(brms_model)
}
## End(Not run)