John,
Basically you are doing a ranked regression analysis. I believe you can
find a paper on that from several years ago. It works, but you just
cannot make inferences based on the regression line. That is, you can't
find a phenology rate due to the regression, but you can still talk
about direction and effect. One goal of regression is to decide cause
and effect of some predicted trend. You may do that with rank
regression - that is, reject the null hypothesis of independence between
your independent and dependent variables.
Cheers,
Jim
John Skillman wrote:
Ecologgers...
We have regularly censused populations of several different plant species
throughout the growing season and categorized the observed individuals into
one of 7 different phenological stages (e.g., stage 1 = initial greening,
stage 4 = peak flowering, stage 6 = seed drop, etc.). These numeral IDs for
the different stages are ordinal data that, by coincidence, tend to scale
linearly with day of the growing season. Although using ordinal data is not
permitted (and makes no sense) in regression analyses, we've done it anyway!
By running regressions we are able to get slopes (change in phenological
stage vs. day of year) which, in essence, quantifies the seasonal rates of
development for the different species. Taking it one step further, Analyses
of Covariance confirm that some species progress through these phenological
stages at rates that are significantly different from that of other species.
So if this tells me what I want to know, what is the problem? The problem,
of course, is that this approach treats these phenological stage IDs (1-7)
as quantitative values when, in fact, they are nothing more than category
labels.
Can anyone suggest an alternative way to use these data to quantify seasonal
development rates and test for differences among species?
BTW, we censused different individuals within each population haphazardly
(~10 individuals per population per census date) and did NOT follow the same
individuals over the season.
John Skillman
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James J. Roper
Smithsonian Tropical Research Institute
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