equiv.boot.lm {equivalence}R Documentation

Fits an OLS regression and returns equivalence information.

Description

This is called by equiv.boot(). This function fits an OLS regression to the observations denoted by index, assess whether the intercept and slope are within their respective regions of similarity, and returns the outcome as well as the estimates.

Usage

equiv.boot.lm(compare, index, rel.int.int = 0.25, rel.int.slope = 0.25)

Arguments

compare a pair of equal length vectors, response first, predictor second.
index index integers supplied by boot.
rel.int.int the relative size of the region of similarity for the intercept.
rel.int.slope the relative size of the region of similarity for the slope.

Details

The outcome is assessed via the bootstrap statistics, which are a four-row table. We focus on the first two, corresponding to the intercept region of similarity and the slope region of similarity. The original column shows whether or not the fitted line is within the interval (0 or 1). The bias column shows the difference between the first column and the bootstrap-estimated proportion. Obtain the bootstrapped statistics using apply (see the examples).

The estimates of slope and intercept are kept for interest, e.g. to check the distribution, obtain estimates of standard errors, etc.

Value

The output is a four-component vector, comprising:

Boolean is the estimated intercept below the region of similarity?
Boolean is the estimated intercept within the region of similarity?
Boolean is the estimated intercept above the region of similarity?
Boolean is the estimated slope below the region of similarity?
Boolean is the estimated slope within the region of similarity?
Boolean is the estimated slope above the region of similarity?
Double estimated intercept
Double estimated slope

Author(s)

Andrew Robinson A.Robinson@ms.unimelb.edu.au

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, equiv.boot

Examples

data(pref.4PG)
FourPG.plot.boot <- boot(cbind(pref.4PG$stemvolinc, pref.4PG$volinc4PG),
                         equiv.boot.lm,
                         R=100,
                         rel.int.int=0.25, rel.int.slope=0.25)
FourPG.plot.boot
apply(FourPG.plot.boot$t, 2, mean)[1:6]

data(pref.LAI)
lai.plot.boot <- boot(cbind(pref.LAI$lai.pa, pref.LAI$lai.bl),
                      equiv.boot.lm,
                      R=100,
                      rel.int.int=0.25, rel.int.slope=0.25)
lai.plot.boot
apply(lai.plot.boot$t, 2, mean)[1:6]

data(ufc)
ufc.plot.boot <- boot(cbind(ufc$Height.m, ufc$Height.m.p),
                      equiv.boot.lm,
                      R=100,
                      rel.int.int=0.25, rel.int.slope=0.25)
ufc.plot.boot
apply(ufc.plot.boot$t, 2, mean)[1:6]


[Package equivalence version 0.3.4 Index]