View source: R/bayesfactor_parameters.R
bayesfactor_parameters | 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 = FALSE),
...,
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 = FALSE),
...,
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,
effects = c("fixed", "random", "all"),
component = c("conditional", "location", "smooth_terms", "sigma", "zi",
"zero_inflated", "all"),
parameters = NULL,
...,
verbose = TRUE
)
## S3 method for class 'brmsfit'
bayesfactor_parameters(
posterior,
prior = NULL,
direction = "two-sided",
null = 0,
effects = c("fixed", "random", "all"),
component = c("conditional", "location", "smooth_terms", "sigma", "zi",
"zero_inflated", "all"),
parameters = NULL,
...,
verbose = TRUE
)
## 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,
rvar_col = NULL,
...,
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). |
... |
Arguments passed to and from other methods. (Can be used to pass
arguments to internal |
verbose |
Toggle off warnings. |
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 |
rvar_col |
A single character - the name of an |
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,
to match the posterior
-type input:
A numeric vector - prior
should also be a numeric vector, representing the prior-estimate.
A data frame - prior
should also be a data frame, representing the prior-estimates, in matching column order.
If rvar_col
is specified, prior
should be the name of an rvar
column that represents the prior-estimates.
Supported Bayesian model (stanreg
, brmsfit
, etc.)
prior
should be a model an equivalent model with MCMC samples from the priors only. See unupdate()
.
If prior
is set to NULL
, unupdate()
is called internally (not supported for brmsfit_multiple
model).
Output from a {marginaleffects}
function - prior
should also be an equivalent output from a {marginaleffects}
function based on a prior-model
(See unupdate()
).
Output from an {emmeans}
function
prior
should also be an equivalent output from an {emmeans}
function based on a prior-model (See unupdate()
).
prior
can also be the original (posterior) model, in which case the function
will try to "unupdate" the estimates (not supported if the estimates have undergone
any transformations – "log"
, "response"
, etc. – or any regrid
ing).
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/1745691611406923")}
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)
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