View source: R/equivalence_test.R
equivalence_test.lm  R Documentation 
Compute the (conditional) equivalence test for frequentist models.
## S3 method for class 'lm'
equivalence_test(
x,
range = "default",
ci = 0.95,
rule = "classic",
verbose = TRUE,
...
)
## S3 method for class 'merMod'
equivalence_test(
x,
range = "default",
ci = 0.95,
rule = "classic",
effects = c("fixed", "random"),
verbose = TRUE,
...
)
## S3 method for class 'ggeffects'
equivalence_test(
x,
range = "default",
rule = "classic",
test = "pairwise",
verbose = TRUE,
...
)
x 
A statistical model. 
range 
The range of practical equivalence of an effect. May be

ci 
Confidence Interval (CI) level. Default to 
rule 
Character, indicating the rules when testing for practical
equivalence. Can be 
verbose 
Toggle warnings and messages. 
... 
Arguments passed to or from other methods. 
effects 
Should parameters for fixed effects ( 
test 
Hypothesis test for computing contrasts or pairwise comparisons.
See 
In classical null hypothesis significance testing (NHST) within a frequentist
framework, it is not possible to accept the null hypothesis, H0  unlike
in Bayesian statistics, where such probability statements are possible.
"... one can only reject the null hypothesis if the test
statistics falls into the critical region(s), or fail to reject this
hypothesis. In the latter case, all we can say is that no significant effect
was observed, but one cannot conclude that the null hypothesis is true."
(Pernet 2017). One way to address this issues without Bayesian methods
is Equivalence Testing, as implemented in equivalence_test()
.
While you either can reject the null hypothesis or claim an inconclusive result
in NHST, the equivalence test  according to Pernet  adds a third category,
"accept". Roughly speaking, the idea behind equivalence testing in a
frequentist framework is to check whether an estimate and its uncertainty
(i.e. confidence interval) falls within a region of "practical equivalence".
Depending on the rule for this test (see below), statistical significance
does not necessarily indicate whether the null hypothesis can be rejected or
not, i.e. the classical interpretation of the pvalue may differ from the
results returned from the equivalence test.
"bayes"  Bayesian rule (Kruschke 2018)
This rule follows the "HDI+ROPE decision rule" (Kruschke, 2014, 2018) used
for the Bayesian counterpart()
. This
means, if the confidence intervals are completely outside the ROPE, the
"null hypothesis" for this parameter is "rejected". If the ROPE
completely covers the CI, the null hypothesis is accepted. Else, it's
undecided whether to accept or reject the null hypothesis. Desirable
results are low proportions inside the ROPE (the closer to zero the
better).
"classic"  The TOST rule (Lakens 2017)
This rule follows the "TOST rule", i.e. a two onesided test procedure
(Lakens 2017). Following this rule, practical equivalence of an effect
(i.e. H0) is rejected, when the coefficient is statistically significant
and the narrow confidence intervals (i.e. 12*alpha
) include or
exceed the ROPE boundaries. Practical equivalence is assumed
(i.e. H0 "accepted") when the narrow confidence intervals are completely
inside the ROPE, no matter if the effect is statistically significant
or not. Else, the decision whether to accept or reject practical
equivalence is undecided.
"cet"  Conditional Equivalence Testing (Campbell/Gustafson 2018)
The Conditional Equivalence Testing as described by Campbell and Gustafson 2018. According to this rule, practical equivalence is rejected when the coefficient is statistically significant. When the effect is not significant and the narrow confidence intervals are completely inside the ROPE, we accept (i.e. assume) practical equivalence, else it is undecided.
For rule = "classic"
, "narrow" confidence intervals are used for
equivalence testing. "Narrow" means, the the intervals is not 1  alpha,
but 1  2 * alpha. Thus, if ci = .95
, alpha is assumed to be 0.05
and internally a cilevel of 0.90 is used. rule = "cet"
uses
both regular and narrow confidence intervals, while rule = "bayes"
only uses the regular intervals.
The equivalence pvalue is the area of the (cumulative) confidence distribution that is outside of the region of equivalence. It can be interpreted as pvalue for rejecting the alternative hypothesis and accepting the "null hypothesis" (i.e. assuming practical equivalence). That is, a high pvalue means we reject the assumption of practical equivalence and accept the alternative hypothesis.
Second generation pvalues (SGPV) were proposed as a statistic that represents the proportion of datasupported hypotheses that are also null hypotheses (Blume et al. 2018, Lakens and Delacre 2020). It represents the proportion of the confidence interval range that is inside the ROPE.
Some attention is required for finding suitable values for the ROPE limits
(argument range
). See 'Details' in bayestestR::rope_range()
for further information.
A data frame.
There is also a plot()
method
implemented in the seepackage.
Blume, J. D., D'Agostino McGowan, L., Dupont, W. D., & Greevy, R. A. (2018). Secondgeneration pvalues: Improved rigor, reproducibility, & transparency in statistical analyses. PLOS ONE, 13(3), e0188299. https://doi.org/10.1371/journal.pone.0188299
Campbell, H., & Gustafson, P. (2018). Conditional equivalence testing: An alternative remedy for publication bias. PLOS ONE, 13(4), e0195145. doi: 10.1371/journal.pone.0195145
Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press
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
Lakens, D. (2017). Equivalence Tests: A Practical Primer for t Tests, Correlations, and MetaAnalyses. Social Psychological and Personality Science, 8(4), 355–362. doi: 10.1177/1948550617697177
Lakens, D., & Delacre, M. (2020). Equivalence Testing and the Second Generation PValue. MetaPsychology, 4. https://doi.org/10.15626/MP.2018.933
Pernet, C. (2017). Null hypothesis significance testing: A guide to commonly misunderstood concepts and recommendations for good practice. F1000Research, 4, 621. doi: 10.12688/f1000research.6963.5
For more details, see bayestestR::equivalence_test()
.
Further readings can be found in the references.
data(qol_cancer)
model < lm(QoL ~ time + age + education, data = qol_cancer)
# default rule
equivalence_test(model)
# conditional equivalence test
equivalence_test(model, rule = "cet")
# plot method
if (require("see", quietly = TRUE)) {
result < equivalence_test(model)
plot(result)
}
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