% Generated by roxygen2: do not edit by hand % Please edit documentation in R/equivalence_test.R \name{equivalence_test} \alias{equivalence_test} \alias{equivalence_test.default} \alias{equivalence_test.numeric} \alias{equivalence_test.data.frame} \alias{equivalence_test.emmGrid} \alias{equivalence_test.BFBayesFactor} \alias{equivalence_test.stanreg} \alias{equivalence_test.brmsfit} \title{Test for Practical Equivalence} \usage{ equivalence_test(x, ...) \method{equivalence_test}{default}(x, ...) \method{equivalence_test}{numeric}(x, range = "default", ci = 0.89, verbose = TRUE, ...) \method{equivalence_test}{data.frame}(x, range = "default", ci = 0.89, verbose = TRUE, ...) \method{equivalence_test}{emmGrid}(x, range = "default", ci = 0.89, verbose = TRUE, ...) \method{equivalence_test}{BFBayesFactor}(x, range = "default", ci = 0.89, verbose = TRUE, ...) \method{equivalence_test}{stanreg}( x, range = "default", ci = 0.89, effects = c("fixed", "random", "all"), component = c("location", "all", "conditional", "smooth_terms", "sigma", "distributional", "auxiliary"), parameters = NULL, verbose = TRUE, ... ) \method{equivalence_test}{brmsfit}( x, range = "default", ci = 0.89, effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ... ) } \arguments{ \item{x}{Vector representing a posterior distribution. Can also be a \code{stanreg} or \code{brmsfit} model.} \item{...}{Currently not used.} \item{range}{ROPE's lower and higher bounds. Should be a vector of length two (e.g., \code{c(-0.1, 0.1)}) or \code{"default"}. If \code{"default"}, the range is set to \code{c(-0.1, 0.1)} if input is a vector, and based on \code{\link[=rope_range]{rope_range()}} if a Bayesian model is provided.} \item{ci}{The Credible Interval (CI) probability, corresponding to the proportion of HDI, to use for the percentage in ROPE.} \item{verbose}{Toggle off warnings.} \item{effects}{Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.} \item{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 \pkg{brms}-models.} \item{parameters}{Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like \code{lp__} or \code{prior_}) are filtered by default, so only parameters that typically appear in the \code{summary()} are returned. Use \code{parameters} to select specific parameters for the output.} } \value{ A data frame with following columns: \itemize{ \item \code{Parameter} The model parameter(s), if \code{x} is a model-object. If \code{x} is a vector, this column is missing. \item \code{CI} The probability of the HDI. \item \code{ROPE_low}, \code{ROPE_high} The limits of the ROPE. These values are identical for all parameters. \item \code{ROPE_Percentage} The proportion of the HDI that lies inside the ROPE. \item \code{ROPE_Equivalence} The "test result", as character. Either "rejected", "accepted" or "undecided". \item \code{HDI_low} , \code{HDI_high} The lower and upper HDI limits for the parameters. } } \description{ Perform a \strong{Test for Practical Equivalence} for Bayesian and frequentist models. } \details{ Documentation is accessible for: \itemize{ \item \href{https://easystats.github.io/bayestestR/reference/equivalence_test.html}{Bayesian models} \item \href{https://easystats.github.io/parameters/reference/equivalence_test.lm.html}{Frequentist models} } For Bayesian models, the \strong{Test for Practical Equivalence} is based on the \emph{"HDI+ROPE decision rule"} (\cite{Kruschke, 2014, 2018}) to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (i.e., a ROPE). In other words, it checks the percentage of the 89\% \link[=hdi]{HDI} that is the null region (the ROPE). If this percentage is sufficiently low, the null hypothesis is rejected. If this percentage is sufficiently high, the null hypothesis is accepted. Using the \link[=rope]{ROPE} and the \link[=hdi]{HDI}, \cite{Kruschke (2018)} suggests using the percentage of the 95\% (or 89\%, considered more stable) HDI that falls within the ROPE as a decision rule. If the HDI is completely outside the ROPE, the "null hypothesis" for this parameter is "rejected". If the ROPE completely covers the HDI, i.e., all most credible values of a parameter are inside the region of practical equivalence, the null hypothesis is accepted. Else, it’s undecided whether to accept or reject the null hypothesis. If the full ROPE is used (i.e., 100\% of the HDI), then the null hypothesis is rejected or accepted if the percentage of the posterior within the ROPE is smaller than to 2.5\% or greater than 97.5\%. Desirable results are low proportions inside the ROPE (the closer to zero the better). \cr \cr Some attention is required for finding suitable values for the ROPE limits (argument \code{range}). See 'Details' in \code{\link[=rope_range]{rope_range()}} for further information. \cr \cr \strong{Multicollinearity: Non-independent covariates} \cr \cr When parameters show strong correlations, i.e. when covariates are not independent, the joint parameter distributions may shift towards or away from the ROPE. In such cases, the test for practical equivalence may have inappropriate results. Collinearity invalidates ROPE and hypothesis testing based on univariate marginals, as the probabilities are conditional on independence. Most problematic are the results of the "undecided" parameters, which may either move further towards "rejection" or away from it (\cite{Kruschke 2014, 340f}). \cr \cr \code{equivalence_test()} performs a simple check for pairwise correlations between parameters, but as there can be collinearity between more than two variables, a first step to check the assumptions of this hypothesis testing is to look at different pair plots. An even more sophisticated check is the projection predictive variable selection (\cite{Piironen and Vehtari 2017}). } \note{ There is a \code{print()}-method with a \code{digits}-argument to control the amount of digits in the output, and there is a \href{https://easystats.github.io/see/articles/bayestestR.html}{\code{plot()}-method} to visualize the results from the equivalence-test (for models only). } \examples{ library(bayestestR) equivalence_test(x = rnorm(1000, 0, 0.01), range = c(-0.1, 0.1)) equivalence_test(x = rnorm(1000, 0, 1), range = c(-0.1, 0.1)) equivalence_test(x = rnorm(1000, 1, 0.01), range = c(-0.1, 0.1)) equivalence_test(x = rnorm(1000, 1, 1), ci = c(.50, .99)) # print more digits test <- equivalence_test(x = rnorm(1000, 1, 1), ci = c(.50, .99)) print(test, digits = 4) \dontrun{ library(rstanarm) model <- rstanarm::stan_glm(mpg ~ wt + cyl, data = mtcars) equivalence_test(model) equivalence_test(model, ci = c(.50, 1)) # plot result test <- equivalence_test(model) plot(test) library(emmeans) equivalence_test(emtrends(model, ~1, "wt")) library(brms) model <- brms::brm(mpg ~ wt + cyl, data = mtcars) equivalence_test(model) equivalence_test(model, ci = c(.50, .99)) library(BayesFactor) bf <- ttestBF(x = rnorm(100, 1, 1)) equivalence_test(bf) equivalence_test(bf, ci = c(.50, .99)) } } \references{ \itemize{ \item Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian estimation. Advances in Methods and Practices in Psychological Science, 1(2), 270-280. \doi{10.1177/2515245918771304} \item Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press \item Piironen, J., & Vehtari, A. (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27(3), 711–735. \doi{10.1007/s11222-016-9649-y} } }