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.
I don't know if anyone has responded privately, but the analysis should
just be an ordinal regression, e.g.
Guisan, A. and Harrell, F.E. (2000) Ordinal Response Regression Models
in Ecology. Journal of Vegetation Science, 11: 617-626.
For R (and S-PLUS) users, there is the polr() function in the MASS
package that will do this.
Incidentally, regression might not be too bad: it sounds as if the data
are approximately interval data. A bit of model checking to see if the
assumptions of normality and (probably more importantly) linearity are
reasonable might be all that is needed.
Bob
--
Bob O'Hara
Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
