equiv.boot: Regression-based TOST using bootstrap
Description
This function wraps the regression-based TOST equivalence test inside a
bootstrap, extracts and reports the useful quantities, and reports the
outcome of the test. The function was written for validating models,
and requires paired data points. To
use it for this purpose, pass the model predictions as the predictor
variable, and the observations (which the predictions are intended to
match) as the response variable.
Usage
equiv.boot(x, y, alpha = 0.05, b0.ii = 0.25, b1.ii = 0.25, reps = 100, b0.ii.absolute = FALSE)
Arguments
x
the predictor variable (commonly predictions)
y
the response variable (commonly observations)
alpha
the size of the test
b0.ii
the half-length of the region of similarity for the
intercept, expressed as a proportion of the estimate or in the same
units as the estimate (see b0.ii.absolute).
b1.ii
the half-length of the region of similarity for the
slope, expressed as a proportion of the estimate.
reps
the number of bootstrap replicates required
b0.ii.absolute
option to express b0.ii in the same units as
the estimate of the intercept.
Value
A list of length 10, comprising
- n
- The effective (non-missing) sample size
- ci.b0
- The intercept TOST confidence interval
- rs.b0
- The intercept region of similarity
- q.b0
- The proportions of simulations below, within, and above, the intercept region of similarity
- Test.b0
- The outcome of the test of the null hypothesis of
dissimilarity for the intercept (Reject/Not Reject)
- ci.b1
- The slope TOST confidence interval
- rs.b1
- The slope region of similarity
- q.b1
- The proportions of simulations below, within, and above, the slope region of similarity
- Test.b1
- The outcome of the test of the null hypothesis of
dissimilarity for the slope (Reject/Not Reject)
- eff.alpha
- The corrected alpha for each of the two independent tests.
Acknowledgements
Feedback from Mohammad Al-Ahmadi has been
very useful for this function.Details
In each case, if the two one-sided confidence
interval is inside the region of similarity then the null hypothesis of
dissimilarity is rejected.
References
Robinson, A.P., R.A. Duursma, and J.D. Marshall. 2005. A
regression-based equivalence test for model validation: shifting the
burden of proof. Tree Physiology 25, 903-913. Examples
Run this code
# Approximately reproduces the first row from Table 2 of Robinson et al. (2005)
data(pref.4PG)
equiv.boot(pref.4PG$volinc4PG, pref.4PG$stemvolinc)
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