[R-sig-Geo] Analysis of three variables considering plot spatial arrangement

[Marta T.]

Dear list members,

Can you please help us?  My colleagues and I are analyzing three response
variables, an averaged count variable, a continuous (normal?) variable and
a proportion, that are determined from sampled plots in seaside habitats.
Within a study site, four observations are generated by averaging four
pairs of plots. These observations are generated in each of three habitats
(total of 12 observations per site). All three habitats are found in all 12
study sites. The 12 sites are nested within four geographic zones, three
sites to a zone. Thus, the sampling is balanced across habitats, sites and
zones (4 obs x 3 habitats x 4 zones x 3 sites = 144 obs total).  The zones
and corresponding sites are distributed along a coastline (E to W), while
plot pairs (within each habitat and site) are located spatially at random
within each habitat, and the plots of a pair are always 14m apart.
Geographic coordinates are available for each observation (averaged plot
pair).

Within a site, each habitat forms a single continuous area, and the four
corresponding observations (from averaged pairs of plots), although
randomly located, are samples from a single contiguous area of habitat.  We
recognize that the four observations within each habitat(site) are not
strictly independent, and that the simplest assumption is that a single 4x4
correlation matrix of the four observations within habitat has identical
(i.e. interchangeable) off-diagonal elements across habitats, sites and
zones.

We would like to construct separate tests for each of the three univariate
responses, to test for a significant effect of habitat. We would like to
find an acceptable univariate analysis framework to account for the
dependencies generated by the geographic, spatial and nested aspects of
this design.  We think that a spatial eigenvector approach might be
appropriate, but we’d appreciate your input before we go down that road. An
outline of an alternative and a citation would be helpful.

Thank you very much in advance.

Marta Torca

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