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\name{regdistbetween}
\alias{regdistbetween}
\alias{print.regdistbetween}
%- Also NEED an `\alias' for EACH other topic documented here.
\title{Testing equality of within-groups and between-groups distances regression}
\description{
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.
}
\usage{
regdistbetween(dmx,dmy,grouping,groups=levels(as.factor(grouping))[1:2])
\method{print}{regdistbetween}(x,...)
}
%- maybe also `usage' for other objects documented here.
\arguments{
\item{dmx}{dissimilarity matrix or object of class
\code{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 \code{dmy}).}
\item{dmy}{dissimilarity matrix or object of class
\code{dist}. Response dissimilarities.}
\item{grouping}{something that can be coerced into a factor,
defining the grouping of
objects represented by the dissimilarities \code{dmx} and \code{dmy}
(i.e., if \code{grouping} has length n, \code{dmx} and \code{dmy}
must be dissimilarities between \code{n} objects).}
\item{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 \code{grouping}.}
\item{x}{object of class \code{"regdistbetween"}.}
\item{...}{optional arguments for print method.}
}
\details{
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 \code{regeqdist} to test whether a
joint regression for the within-group distances of both groups makes
sense. If this is not rejected, \code{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 \code{regeqdist},
\code{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).
}
\value{
list of class \code{"regdistbetween"} with components
\item{pval}{p-value.}
\item{coeffdiff}{difference between regression fits (all distances
minus within-group distances only) at \code{xcenterbetween}, see below.}
\item{condition}{condition numbers of regressions, see \code{\link{kappa}}.}
\item{lmfit}{list. Output objects of \code{\link{lm}} within the two groups.}
\item{jr}{output object of \code{\link[bootstrap]{jackknife}} for difference
between regression fitted values at \code{xcenterbetween}.}
\item{xcenter}{mean of within-groups distances of explanatory
variable, used for centering.}
\item{xcenterbetween}{mean of between-groups distances of explanatory
variable (after centering by \code{xcenter}); at this point
regression fitted values are computed.}
\item{tstat}{t-statistic.}
\item{tdf}{degrees of freedom of t-statistic.}
\item{jackest}{jackknife-estimator of difference between regression
fitted values at \code{xcenterbetween}.}
\item{jackse}{jackknife-standard error for
\code{jackest}.}
\item{jackpseudo}{vector of jacknife pseudovalues on which the test is
based.}
\item{testname}{title to be printed out when using
\code{print.regdistbetween}.}
\item{groups}{see above.}
}
\references{
Hausdorf, B. and Hennig, C. (2019) Species delimitation and
geography. Submitted.
}
\author{Christian Hennig
\email{christian.hennig@unibo.it}
\url{https://www.unibo.it/sitoweb/christian.hennig/en}}
\seealso{
\code{\link{regeqdist}}, \code{\link{regdistbetweenone}}
}
\examples{
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)
}
\keyword{htest}% __ONLY ONE__ keyword per line
\keyword{regression}% __ONLY ONE__ keyword per line
\keyword{spatial}% __ONLY ONE__ keyword per line
|
