% Generated by roxygen2: do not edit by hand % Please edit documentation in R/rope.R \name{rope} \alias{rope} \alias{rope.default} \alias{rope.numeric} \alias{rope.data.frame} \alias{rope.emmGrid} \alias{rope.BFBayesFactor} \alias{rope.MCMCglmm} \alias{rope.stanreg} \alias{rope.brmsfit} \title{Region of Practical Equivalence (ROPE)} \usage{ rope(x, ...) \method{rope}{default}(x, ...) \method{rope}{numeric}(x, range = "default", ci = 0.89, ci_method = "HDI", verbose = TRUE, ...) \method{rope}{data.frame}(x, range = "default", ci = 0.89, ci_method = "HDI", verbose = TRUE, ...) \method{rope}{emmGrid}(x, range = "default", ci = 0.89, ci_method = "HDI", verbose = TRUE, ...) \method{rope}{BFBayesFactor}(x, range = "default", ci = 0.89, ci_method = "HDI", verbose = TRUE, ...) \method{rope}{MCMCglmm}(x, range = "default", ci = 0.89, ci_method = "HDI", verbose = TRUE, ...) \method{rope}{stanreg}( x, range = "default", ci = 0.89, ci_method = "HDI", effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ... ) \method{rope}{brmsfit}( x, range = "default", ci = 0.89, ci_method = "HDI", 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{ci_method}{The type of interval to use to quantify the percentage in ROPE. Can be 'HDI' (default) or 'ETI'. See \code{\link{ci}}.} \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{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.} \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.} } \description{ Compute the proportion of the HDI (default to the 89\% HDI) of a posterior distribution that lies within a region of practical equivalence. } \details{ \subsection{ROPE}{ Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of a single value null hypothesis in a continuous distribution is 0). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are \emph{equivalent to the null} value for practical purposes (\cite{Kruschke 2010, 2011, 2014}). \cr \cr Kruschke (2018) suggests that such null value could be set, by default, to the -0.1 to 0.1 range of a standardized parameter (negligible effect size according to Cohen, 1988). This could be generalized: For instance, for linear models, the ROPE could be set as \code{0 +/- .1 * sd(y)}. This ROPE range can be automatically computed for models using the \link{rope_range} function. \cr \cr Kruschke (2010, 2011, 2014) suggests using the proportion of the 95\% (or 89\%, considered more stable) \link[=hdi]{HDI} that falls within the ROPE as an index for "null-hypothesis" testing (as understood under the Bayesian framework, see \code{\link[=equivalence_test]{equivalence_test()}}). } \subsection{Sensitivity to parameter's scale}{ It is important to consider the unit (i.e., the scale) of the predictors when using an index based on the ROPE, as the correct interpretation of the ROPE as representing a region of practical equivalence to zero is dependent on the scale of the predictors. Indeed, the percentage in ROPE depend on the unit of its parameter. In other words, as the ROPE represents a fixed portion of the response's scale, its proximity with a coefficient depends on the scale of the coefficient itself. } \subsection{Multicollinearity: Non-independent covariates}{ When parameters show strong correlations, i.e. when covariates are not independent, the joint parameter distributions may shift towards or away from the ROPE. Collinearity invalidates ROPE and hypothesis testing based on univariate marginals, as the probabilities are conditional on independence. Most problematic are parameters that only have partial overlap with the ROPE region. In case of collinearity, the (joint) distributions of these parameters may either get an increased or decreased ROPE, which means that inferences based on \code{rope()} are inappropriate (\cite{Kruschke 2014, 340f}). \cr \cr \code{rope()} 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}). } \subsection{Strengths and Limitations}{ \strong{Strengths:} Provides information related to the practical relevance of the effects. \cr \cr \strong{Limitations:} A ROPE range needs to be arbitrarily defined. Sensitive to the scale (the unit) of the predictors. Not sensitive to highly significant effects. } } \note{ There is also a \href{https://easystats.github.io/see/articles/bayestestR.html}{\code{plot()}-method} implemented in the \href{https://easystats.github.io/see/}{\pkg{see}-package}. } \examples{ library(bayestestR) rope(x = rnorm(1000, 0, 0.01), range = c(-0.1, 0.1)) rope(x = rnorm(1000, 0, 1), range = c(-0.1, 0.1)) rope(x = rnorm(1000, 1, 0.01), range = c(-0.1, 0.1)) rope(x = rnorm(1000, 1, 1), ci = c(.90, .95)) \dontrun{ library(rstanarm) model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0) rope(model) rope(model, ci = c(.90, .95)) library(emmeans) rope(emtrends(model, ~1, "wt"), ci = c(.90, .95)) library(brms) model <- brms::brm(mpg ~ wt + cyl, data = mtcars) rope(model) rope(model, ci = c(.90, .95)) library(BayesFactor) bf <- ttestBF(x = rnorm(100, 1, 1)) rope(bf) rope(bf, ci = c(.90, .95)) } } \references{ \itemize{ \item Cohen, J. (1988). Statistical power analysis for the behavioural sciences. \item Kruschke, J. K. (2010). What to believe: Bayesian methods for data analysis. Trends in cognitive sciences, 14(7), 293-300. \doi{10.1016/j.tics.2010.05.001}. \item Kruschke, J. K. (2011). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science, 6(3), 299-312. \doi{10.1177/1745691611406925}. \item Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press. \doi{10.1177/2515245918771304}. \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 Makowski D, Ben-Shachar MS, Chen SHA, Lüdecke D (2019) Indices of Effect Existence and Significance in the Bayesian Framework. Frontiers in Psychology 2019;10:2767. \doi{10.3389/fpsyg.2019.02767} \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} } }