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Tip revision: 68a979e69aa2a1e57017730e1397470d5614d216 authored by Dominique Makowski on 02 September 2021, 23:10:30 UTC
version 0.11.0
Tip revision: 68a979e
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/rope.R
\title{Region of Practical Equivalence (ROPE)}
rope(x, ...)

\method{rope}{default}(x, ...)

\method{rope}{numeric}(x, range = "default", ci = 0.95, ci_method = "HDI", verbose = TRUE, ...)

\method{rope}{data.frame}(x, range = "default", ci = 0.95, ci_method = "HDI", verbose = TRUE, ...)

\method{rope}{emmGrid}(x, range = "default", ci = 0.95, ci_method = "HDI", verbose = TRUE, ...)

\method{rope}{BFBayesFactor}(x, range = "default", ci = 0.95, ci_method = "HDI", verbose = TRUE, ...)

\method{rope}{MCMCglmm}(x, range = "default", ci = 0.95, ci_method = "HDI", verbose = TRUE, ...)

  range = "default",
  ci = 0.95,
  ci_method = "HDI",
  effects = c("fixed", "random", "all"),
  component = c("location", "all", "conditional", "smooth_terms", "sigma",
    "distributional", "auxiliary"),
  parameters = NULL,
  verbose = TRUE,

  range = "default",
  ci = 0.95,
  ci_method = "HDI",
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL,
  verbose = TRUE,
\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 \code{"default"} or
depending on the number of outcome variables a vector or a list. In models with one response,
\code{range} should be a vector of length two (e.g., \code{c(-0.1, 0.1)}). In
multivariate models, \code{range} should be a list with a numeric vectors for
each response variable. Vector names should correspond to the name of the response
variables. If \code{"default"} and input is a vector, the range is set to \code{c(-0.1, 0.1)}. If \code{"default"} and input is a Bayesian model,
\code{\link[=rope_range]{rope_range()}} is used.}

\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]{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{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.}
Compute the proportion of the HDI (default to the \verb{89\%} HDI) of a posterior distribution that lies within a region of practical equivalence.
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 \verb{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 \verb{95\%}
(or \verb{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.
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}.

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))
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
rope(model, ci = c(.90, .95))

rope(emtrends(model, ~1, "wt"), ci = c(.90, .95))

model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
rope(model, ci = c(.90, .95))

model <- brms::brm(brms::mvbind(mpg, disp) ~ wt + cyl, data = mtcars)
rope(model, ci = c(.90, .95))

bf <- ttestBF(x = rnorm(100, 1, 1))
rope(bf, ci = c(.90, .95))
\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}
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