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Tip revision: e1fa15d202de277bb07e58bb3013557724072b2b authored by Dominique Makowski on 22 September 2019, 15:30 UTC
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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bayesfactor_restricted.R
\title{Bayes Factors (BF) for Order Restricted Models}
bayesfactor_restricted(posterior, hypothesis, prior = NULL,
  verbose = TRUE, ...)

\method{bayesfactor_restricted}{stanreg}(posterior, hypothesis,
  prior = NULL, verbose = TRUE, effects = c("fixed", "random",
  "all"), ...)

\method{bayesfactor_restricted}{brmsfit}(posterior, hypothesis,
  prior = NULL, verbose = TRUE, effects = c("fixed", "random",
  "all"), ...)

\method{bayesfactor_restricted}{emmGrid}(posterior, hypothesis,
  prior = NULL, verbose = TRUE, ...)
\item{posterior}{A \code{stanreg} / \code{brmsfit} object, \code{emmGrid} or a data frame - representing a posterior distribution(s) from (see Details).}

\item{hypothesis}{A character vector specifying the restrictions as logical conditions (see examples below).}

\item{prior}{An object representing a prior distribution (see Details).}

\item{verbose}{Toggle off warnings.}

\item{...}{Currently not used.}

\item{effects}{Should results for fixed effects, random effects or both be returned?
Only applies to mixed models. May be abbreviated.}
A data frame containing the Bayes factor representing evidence \emph{against} the un-restricted model.
This method computes Bayes factors for comparing a model with an order restrictions on its parameters
with the fully unrestricted model. \emph{Note that this method should only be used for confirmatory analyses}.
\cr \cr
\strong{For info on specifying correct priors for factors with more than 2 levels, see \href{}{the Bayes factors vignette}.}
\cr \cr
For more info, see \href{}{the Bayes factors vignette}.
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
(\cite{Morey & Wagenmakers, 2013}).

(Though it is possible to use \code{bayesfactor_restricted} to test interval restrictions,
it is more suitable for testing order restrictions (see examples)).

When \code{posterior} is a model (\code{stanreg}, \code{brmsfit}), posterior and prior samples are
extracted for each parameter, and Savage-Dickey Bayes factors are computed for each parameter.

\strong{NOTE:} For \code{brmsfit} models, the model must have been fitted with \emph{custom (non-default)} priors. See example below.

\subsection{Setting the correct \code{prior}}{
It is important to provide the correct \code{prior} for meaningful results.
  \item When \code{posterior} is a \code{data.frame}, \code{prior} should also be a \code{data.frame}, with matching column order.
  \item When \code{posterior} is a \code{stanreg} or \code{brmsfit} model: \itemize{
    \item \code{prior} can be set to \code{NULL}, in which case prior samples are drawn internally.
    \item \code{prior} can also be a model equvilant to \code{posterior} but with samples from the priors \emph{only}.
  \item When \code{posterior} is an \code{emmGrid} object: \itemize{
    \item \code{prior} should be the \code{stanreg} or \code{brmsfit} model used to create the \code{emmGrid} objects.
    \item \code{prior} can also be an \code{emmGrid} object equvilant to \code{posterior} but created with a model of priors samples \emph{only}.
\subsection{Interpreting Bayes Factors}{
A Bayes factor greater than 1 can be interpereted 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-hypothesis)
(\cite{Wetzels et al. 2011}).
prior <- data.frame(
  X = rnorm(100),
  X1 = rnorm(100),
  X3 = rnorm(100)

posterior <- data.frame(
  X = rnorm(100, .4),
  X1 = rnorm(100, -.2),
  X3 = rnorm(100)

hyps <- c(
  "X > X1 & X1 > X3",
  "X > X1"

bayesfactor_restricted(posterior, hypothesis = hyps, prior = prior)
# rstanarm models
# ---------------
fit_stan <- stan_glm(mpg ~ wt + cyl + am,
  data = mtcars
hyps <- c(
  "am > 0 & cyl < 0",
  "cyl < 0",
  "wt - cyl > 0"
bayesfactor_restricted(fit_stan, hypothesis = hyps)

# emmGrid objects
# ---------------

# replicating
disgust_data <- read.table(url(""), header = TRUE)

contrasts(disgust_data$condition) <- contr.bayes # 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) Bayes Factor
# >  lemon < control & control < sulfur     0.17         0.75         4.49
# > ---
# > Bayes factors for the restricted movel vs. the un-restricted model.

\item Morey, R. D., & Wagenmakers, E. J. (2014). Simple relation between Bayesian order-restricted and point-null hypothesis tests. Statistics & Probability Letters, 92, 121-124.
\item Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological methods, 16(4), 406.
\item Morey, R. D. (Jan, 2015). Multiple Comparisons with BayesFactor, Part 2 – order restrictions. Retrived from
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