regdistbetween {prabclus}

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])

## S3 method for class 'regdistbetween'
print(x,...)

Arguments

dmx

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).

dmy

dissimilarity matrix or object of class dist. Response dissimilarities.

grouping

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).

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 grouping.

x

object of class "regdistbetween".

...

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 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).

Value

list of class "regdistbetween" with components

pval

p-value.

coeffdiff

difference between regression fits (all distances minus within-group distances only) at xcenterbetween, see below.

condition

condition numbers of regressions, see kappa.

lmfit

list. Output objects of lm within the two groups.

jr

output object of jackknife for difference between regression fitted values at xcenterbetween.

xcenter

mean of within-groups distances of explanatory variable, used for centering.

xcenterbetween

mean of between-groups distances of explanatory variable (after centering by xcenter); at this point regression fitted values are computed.

tstat

t-statistic.

tdf

degrees of freedom of t-statistic.

jackest

jackknife-estimator of difference between regression fitted values at xcenterbetween.

jackse

jackknife-standard error for jackest.

jackpseudo

vector of jacknife pseudovalues on which the test is based.

testname

title to be printed out when using print.regdistbetween.

groups

see above.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en

References

Hausdorf, B. and Hennig, C. (2019) Species delimitation and geography. Submitted.

See Also

regeqdist, 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)