Jackknife-based test for equality of two regressions between distances. Given two groups of objects, this tests whether the regression involving all distances is compatible with the regression involving within-group distances only.
regdistbetween(dmx,dmy,grouping,groups=levels(as.factor(grouping))[1:2])# S3 method for regdistbetween
print(x,...)
list of class "regdistbetween" with components
p-value.
difference between regression fits (all distances
minus within-group distances only) at xcenterbetween, see below.
condition numbers of regressions, see kappa.
list. Output objects of lm within the two groups.
output object of jackknife for difference
between regression fitted values at xcenterbetween.
mean of within-groups distances of explanatory variable, used for centering.
mean of between-groups distances of explanatory
variable (after centering by xcenter); at this point
regression fitted values are computed.
t-statistic.
degrees of freedom of t-statistic.
jackknife-estimator of difference between regression
fitted values at xcenterbetween.
jackknife-standard error for
jackest.
vector of jacknife pseudovalues on which the test is based.
title to be printed out when using
print.regdistbetween.
see above.
dissimilarity matrix or object of class
dist. Explanatory dissimilarities (often these will be proper
distances, but more general dissimilarities that do not
necessarily fulfill the triangle inequality can be used, same for dmy).
dissimilarity matrix or object of class
dist. Response dissimilarities.
something that can be coerced into a factor,
defining the grouping of
objects represented by the dissimilarities dmx and dmy
(i.e., if grouping has length n, dmx and dmy
must be dissimilarities between n objects).
Vector of two levels. The two groups defining the
regressions to be compared in the test. These can be
factor levels, integer numbers, or strings, depending on the entries
of grouping.
object of class "regdistbetween".
optional arguments for print method.
Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en
The null hypothesis that the regressions based on all distances and based on within-group distances only are equal is tested using jackknife pseudovalues. This assumes that a single regression is appropriate at least for the within-group distances alone. The test statistic is the difference between fitted values with x (explanatory variable) fixed at the center of the between-group distances. The test is run one-sided, i.e., the null hypothesis is only rejected if the between-group distances are larger than expected under the null hypothesis, see below.
The test cannot be run in case that within-group regressions or jackknifed within-group regressions are ill-conditioned.
This was implemented having in mind an application in which the
explanatory distances represent geographical distances, the response
distances are genetic distances, and groups represent species or
species-candidates. In this application, for testing whether the
regression patterns are compatble with the two groups behaving like a
single species, one would first use regeqdist to test whether a
joint regression for the within-group distances of both groups makes
sense. If this is not rejected, regdistbetween is run to see
whether the between-group distances are compatible with the
within-group distances. This is only rejected if the between-group
distances are larger than expected under equality of regressions,
because if they are smaller, this is not an indication against the
groups belonging together genetically.
If a joint regression on
within-group distances is rejected by regeqdist,
regdistbetweenone can be
used to test whether the between-group distances are at least
compatible with the within-group distances of one of the groups, which
can still be the case within a single species, see Hausdorf and Hennig (2019).
Hausdorf, B. and Hennig, C. (2019) Species delimitation and geography. Submitted.
regeqdist, regdistbetweenone
options(digits=4)
data(veronica)
ver.geo <- coord2dist(coordmatrix=veronica.coord[173:207,],file.format="decimal2")
vei <- prabinit(prabmatrix=veronica[173:207,],distance="jaccard")
loggeo <- log(ver.geo+quantile(as.vector(as.dist(ver.geo)),0.25))
species <-c(rep(1,13),rep(2,22))
rtest2 <-
regdistbetween(dmx=loggeo,dmy=vei$distmat,grouping=species,groups=c(1,2))
print(rtest2)
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