rope {bayestestR}  R Documentation 
Region of Practical Equivalence (ROPE)
Description
Compute the proportion of the HDI (default to the 89%
HDI) of a posterior
distribution that lies within a region of practical equivalence.
Usage
rope(x, ...)
## S3 method for class 'numeric'
rope(x, range = "default", ci = 0.95, ci_method = "ETI", verbose = TRUE, ...)
## S3 method for class 'stanreg'
rope(
x,
range = "default",
ci = 0.95,
ci_method = "ETI",
effects = c("fixed", "random", "all"),
component = c("location", "all", "conditional", "smooth_terms", "sigma",
"distributional", "auxiliary"),
parameters = NULL,
verbose = TRUE,
...
)
## S3 method for class 'brmsfit'
rope(
x,
range = "default",
ci = 0.95,
ci_method = "ETI",
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
verbose = TRUE,
...
)
Arguments
x 
Vector representing a posterior distribution. Can also be a

... 
Currently not used. 
range 
ROPE's lower and higher bounds. Should be 
ci 
The Credible Interval (CI) probability, corresponding to the proportion of HDI, to use for the percentage in ROPE. 
ci_method 
The type of interval to use to quantify the percentage in
ROPE. Can be 'HDI' (default) or 'ETI'. See 
verbose 
Toggle off warnings. 
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 zeroinflated part of the model be returned? May be abbreviated. Only applies to brmsmodels. 
parameters 
Regular expression pattern that describes the parameters
that should be returned. Metaparameters (like 
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 equivalent to the null value for practical purposes (Kruschke 2010, 2011, 2014).
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 0 +/ .1 * sd(y)
.
This ROPE range can be automatically computed for models using the
rope_range function.
Kruschke (2010, 2011, 2014) suggests using the proportion of the 95%
(or 89%
, considered more stable) HDI that falls within the
ROPE as an index for "nullhypothesis" testing (as understood under the
Bayesian framework, see equivalence_test()
).
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.
Multicollinearity  Nonindependent 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 rope()
are inappropriate
(Kruschke 2014, 340f).
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 (Piironen and Vehtari 2017).
Strengths and Limitations
Strengths: Provides information related to the practical relevance of the effects.
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 plot()
method implemented in the seepackage.
References
Cohen, J. (1988). Statistical power analysis for the behavioural sciences.
Kruschke, J. K. (2010). What to believe: Bayesian methods for data analysis. Trends in cognitive sciences, 14(7), 293300. doi:10.1016/j.tics.2010.05.001.
Kruschke, J. K. (2011). Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science, 6(3), 299312. doi:10.1177/1745691611406925.
Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press. doi:10.1177/2515245918771304.
Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian estimation. Advances in Methods and Practices in Psychological Science, 1(2), 270280. doi:10.1177/2515245918771304.
Makowski D, BenShachar 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
Piironen, J., & Vehtari, A. (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27(3), 711–735. doi:10.1007/s112220169649y
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(0.90, 0.95))
library(rstanarm)
model < suppressWarnings(
stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
)
rope(model)
rope(model, ci = c(0.90, 0.95))
library(emmeans)
rope(emtrends(model, ~1, "wt"), ci = c(0.90, 0.95))
library(brms)
model < brm(mpg ~ wt + cyl, data = mtcars)
rope(model)
rope(model, ci = c(0.90, 0.95))
library(brms)
model < brm(
bf(mvbind(mpg, disp) ~ wt + cyl) + set_rescor(rescor = TRUE),
data = mtcars
)
rope(model)
rope(model, ci = c(0.90, 0.95))
library(BayesFactor)
bf < ttestBF(x = rnorm(100, 1, 1))
rope(bf)
rope(bf, ci = c(0.90, 0.95))