bayesfactor_restricted {bayestestR} | R Documentation |
This method computes Bayes factors for comparing a model with an order restrictions on its parameters
with the fully unrestricted model. Note that this method should only be used for confirmatory analyses.
The bf_*
function is an alias of the main function.
For more info, in particular on specifying correct priors for factors with more than 2 levels, see the Bayes factors vignette.
bayesfactor_restricted(
posterior,
hypothesis,
prior = NULL,
verbose = TRUE,
...
)
bf_restricted(posterior, hypothesis, prior = NULL, verbose = TRUE, ...)
## S3 method for class 'stanreg'
bayesfactor_restricted(
posterior,
hypothesis,
prior = NULL,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
...
)
## S3 method for class 'brmsfit'
bayesfactor_restricted(
posterior,
hypothesis,
prior = NULL,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
...
)
## S3 method for class 'blavaan'
bayesfactor_restricted(
posterior,
hypothesis,
prior = NULL,
verbose = TRUE,
...
)
## S3 method for class 'emmGrid'
bayesfactor_restricted(
posterior,
hypothesis,
prior = NULL,
verbose = TRUE,
...
)
posterior |
A |
hypothesis |
A character vector specifying the restrictions as logical conditions (see examples below). |
prior |
An object representing a prior distribution (see Details). |
verbose |
Toggle off warnings. |
... |
Currently not used. |
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. |
This method is used to compute Bayes factors for order-restricted models vs un-restricted
models by setting an order restriction on the prior and posterior distributions
(Morey & Wagenmakers, 2013).
(Though it is possible to use bayesfactor_restricted()
to test interval restrictions,
it is more suitable for testing order restrictions; see examples).
A data frame containing the (log) Bayes factor representing evidence
against the un-restricted model (Use as.numeric()
to extract the
non-log Bayes factors; see examples). (A bool_results
attribute contains
the results for each sample, indicating if they are included or not in the
hypothesized restriction.)
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).
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.
Morey, R. D. (Jan, 2015). Multiple Comparisons with BayesFactor, Part 2 – order restrictions. Retrieved from https://richarddmorey.org/category/order-restrictions/.
set.seed(444)
library(bayestestR)
prior <- data.frame(
A = rnorm(1000),
B = rnorm(1000),
C = rnorm(1000)
)
posterior <- data.frame(
A = rnorm(1000, .4, 0.7),
B = rnorm(1000, -.2, 0.4),
C = rnorm(1000, 0, 0.5)
)
hyps <- c(
"A > B & B > C",
"A > B & A > C",
"C > A"
)
if (getRversion() > "3.5.0") {
(b <- bayesfactor_restricted(posterior, hypothesis = hyps, prior = prior))
as.numeric(b)
if (require("see") && require("patchwork")) {
i <- attr(b, "bool_results")[["posterior"]]
see::plots(
plot(estimate_density(posterior)),
# distribution **conditional** on the restrictions
plot(estimate_density(posterior[i[[hyps[1]]], ])) + ggplot2::ggtitle(hyps[1]),
plot(estimate_density(posterior[i[[hyps[2]]], ])) + ggplot2::ggtitle(hyps[2]),
plot(estimate_density(posterior[i[[hyps[3]]], ])) + ggplot2::ggtitle(hyps[3]),
guides = "collect"
)
}
}
## Not run:
# rstanarm models
# ---------------
if (require("rstanarm") && require("emmeans")) {
fit_stan <- stan_glm(mpg ~ wt + cyl + am,
data = mtcars, refresh = 0
)
hyps <- c(
"am > 0 & cyl < 0",
"cyl < 0",
"wt - cyl > 0"
)
bayesfactor_restricted(fit_stan, hypothesis = hyps)
# emmGrid objects
# ---------------
# replicating http://bayesfactor.blogspot.com/2015/01/multiple-comparisons-with-bayesfactor-2.html
disgust_data <- read.table(url("http://www.learnbayes.org/disgust_example.txt"), header = TRUE)
contrasts(disgust_data$condition) <- contr.equalprior_pairs # see vignette
fit_model <- stan_glm(score ~ condition, data = disgust_data, family = gaussian())
em_condition <- emmeans(fit_model, ~condition)
hyps <- c("lemon < control & control < sulfur")
bayesfactor_restricted(em_condition, prior = fit_model, hypothesis = hyps)
# > # Bayes Factor (Order-Restriction)
# >
# > Hypothesis P(Prior) P(Posterior) BF
# > lemon < control & control < sulfur 0.17 0.75 4.49
# > ---
# > Bayes factors for the restricted model vs. the un-restricted model.
}
## End(Not run)