On 05/25/2012 10:18 AM, Gavin Simpson wrote:
On Thu, 2012-05-24 at 15:00 -0700, J Straka wrote:
Hello,
I'm planning on using a regression model to describe seed set of plants (my
response) using some sort of predictor based on temperature. I have a
number of temperature variables calculated from the same set of data
(hourly temperatures for the growing season, converted to variables such as
average temperature, maximum temperature, minimum temperature, degree-days
above zero Celsius, degree days above ten Celsius, etc...), and I want to
decide which one should be included in my model. I know that I would
ideally select one based on "prior knowledge" of the system (e.g. so-called
"planned comparisons" or choosing a temperature threshold that is known to
be important for the development of seeds), but not much is known about
this system.
What is the model for? Understanding so you want to interpret the
coefficients directly as something meaningful or for prediction?
If the latter I would say it doesn't really matter; choose the model
that gives the best out-of-sample predictions (lowest error etc), or
average predictions over a set of best/good models. Simply choosing the
best model via some sort of selection procedure may result in a model
with high variance (change the data a bit and different variables would
be selected). If so, consider a regression method that applies shrinkage
to the coefficients such as the lasso or the elastic net; this will lead
to a small bit of bias in the estimates of the coefficients but should
reduce the variance of the final model because you are considering the
selection of variables as part of the model itself.
If you want to interpret the model coefficients as something real then
you have to be very careful doing any form of selection; the stepwise
procedures and best subsets all can potentially lead to strong bias in
the model coefficients. Be removing a variable from the model in effect
you are saying that the sample estimate of the effect of that variable
on the response is 0, not some small (statistically insignificant)
value.
This is a very tricky thing to get right and I'm not sure I know the
right answer (or even if there is one!?).
An additional complication here is that the variables are going to be
correlated, so a model with all or most in it could be unstable. If a
single temperature variable is enough, then I'd suggest either trying
your best to pick one, or use what everyone else uses (GDD5?), so the
study can be comparable.
Once you have a model, it might be worth checking to see if the other
variables tell a different story. If it's the same story but with
different p-values, you might as well stick to the original analysis.
Bob
--
Bob O'Hara
Biodiversity and Climate Research Centre
Senckenberganlage 25
D-60325 Frankfurt am Main,
Germany
Tel: +49 69 798 40226
Mobile: +49 1515 888 5440
WWW: http://www.bik-f.de/root/index.php?page_id=219
Blog: http://blogs.nature.com/boboh
Journal of Negative Results - EEB: www.jnr-eeb.org
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