equiv.boot: Regression-based TOST using bootstrap

In equivalence: Provides Tests and Graphics for Assessing Tests of Equivalence

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.

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.

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.

Author(s)

Andrew Robinson [e-mail]

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.

See Also

lm, boot, tost

Examples

# Approximately reproduces the first row from Table 2 of Robinson et al. (2005)

data(pref.4PG)
equiv.boot(pref.4PG$volinc4PG, pref.4PG$stemvolinc)

equivalence documentation built on May 1, 2019, 9:15 p.m.