Compute the proportion of the HDI (default to the 89% HDI) of a posterior
distribution that lies within a region of practical equivalence.
rope(x, ...)# S3 method for numeric
rope(x, range = "default", ci = 0.95, ci_method = "ETI", verbose = TRUE, ...)
# S3 method for data.frame
rope(
x,
range = "default",
ci = 0.95,
ci_method = "ETI",
rvar_col = NULL,
verbose = TRUE,
...
)
# S3 method for 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 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,
...
)
Vector representing a posterior distribution. Can also be a
stanreg or brmsfit model.
Currently not used.
ROPE's lower and higher bounds. Should be "default" or
depending on the number of outcome variables a vector or a list. For models
with one response, range can be:
a vector of length two (e.g., c(-0.1, 0.1)),
a list of numeric vector of the same length as numbers of parameters (see 'Examples').
a list of named numeric vectors, where names correspond to parameter
names. In this case, all parameters that have no matching name in range
will be set to "default".
In multivariate models, 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 "default" and input is a vector, the range is set to
c(-0.1, 0.1). If "default" and input is a Bayesian model,
rope_range() is used.
The Credible Interval (CI) probability, corresponding to the proportion of HDI, to use for the percentage in ROPE.
The type of interval to use to quantify the percentage in
ROPE. Can be 'HDI' (default) or 'ETI'. See ci().
Toggle off warnings.
A single character - the name of an rvar column in the data
frame to be processed. See example in p_direction().
Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.
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 brms-models.
Regular expression pattern that describes the parameters
that should be returned. Meta-parameters (like lp__ or prior_) are
filtered by default, so only parameters that typically appear in the
summary() are returned. Use parameters to select specific parameters
for the output.
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 "null-hypothesis" testing (as understood under the
Bayesian framework, see equivalence_test()).
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.
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: 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.
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), 293-300. tools:::Rd_expr_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), 299-312. tools:::Rd_expr_doi("10.1177/1745691611406925").
Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press. tools:::Rd_expr_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), 270-280. tools:::Rd_expr_doi("10.1177/2515245918771304").
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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1007/s11222-016-9649-y")