Testing equality of within-groups and between-groups distances regression
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 class 'regdistbetween' print(x,...)
dmx |
dissimilarity matrix or object of class
|
dmy |
dissimilarity matrix or object of class
|
grouping |
something that can be coerced into a factor,
defining the grouping of
objects represented by the dissimilarities |
groups |
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 |
x |
object of class |
... |
optional arguments for print method. |
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).
list of class "regdistbetween" with components
pval |
p-value. |
coeffdiff |
difference between regression fits (all distances
minus within-group distances only) at |
condition |
condition numbers of regressions, see |
lmfit |
list. Output objects of |
jr |
output object of |
xcenter |
mean of within-groups distances of explanatory variable, used for centering. |
xcenterbetween |
mean of between-groups distances of explanatory
variable (after centering by |
tstat |
t-statistic. |
tdf |
degrees of freedom of t-statistic. |
jackest |
jackknife-estimator of difference between regression
fitted values at |
jackse |
jackknife-standard error for
|
jackpseudo |
vector of jacknife pseudovalues on which the test is based. |
testname |
title to be printed out when using
|
groups |
see above. |
Hausdorf, B. and Hennig, C. (2019) Species delimitation and geography. Submitted.
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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