Perform a Test for Practical Equivalence for Bayesian and frequentist models.
equivalence_test(x, ...)# S3 method for default
equivalence_test(x, ...)
# S3 method for data.frame
equivalence_test(
x,
range = "default",
ci = 0.95,
rvar_col = NULL,
verbose = TRUE,
...
)
# S3 method for stanreg
equivalence_test(
x,
range = "default",
ci = 0.95,
effects = c("fixed", "random", "all"),
component = c("location", "all", "conditional", "smooth_terms", "sigma",
"distributional", "auxiliary"),
parameters = NULL,
verbose = TRUE,
...
)
# S3 method for brmsfit
equivalence_test(
x,
range = "default",
ci = 0.95,
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
verbose = TRUE,
...
)
A data frame with following columns:
Parameter The model parameter(s), if x is a model-object. If x is a vector, this column is missing.
CI The probability of the HDI.
ROPE_low, ROPE_high The limits of the ROPE. These values are identical for all parameters.
ROPE_Percentage The proportion of the HDI that lies inside the ROPE.
ROPE_Equivalence The "test result", as character. Either "rejected", "accepted" or "undecided".
HDI_low , HDI_high The lower and upper HDI limits for the parameters.
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.
A single character - the name of an rvar column in the data
frame to be processed. See example in p_direction().
Toggle off warnings.
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.
Documentation is accessible for:
For Bayesian models, the Test for Practical Equivalence is based on the
"HDI+ROPE decision rule" (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% 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 ROPE and the HDI, 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).
Some attention is required for finding suitable values for the ROPE limits
(argument range). See 'Details' in rope_range() for further
information.
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. 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 (Kruschke 2014, 340f).
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 (Piironen and Vehtari 2017).
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")
Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press
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")