multiple regression

Nathan,

Species richness is categorical, so if your richness values are
usually low (say < 20), you should consider the use of Poisson GLM, or
log-transform your response (and log is the canonical link function
for Poisson GLM). This usually improves the model fit. And this might
apply to abundance as well.

If you use lm(), you can inspect the residual variance of the models
after excluding one of the covariates. The increase in residual
variance compared to the full model will tell which variance component
is higher (explains more of your data). Or you may as well inspect the
anova() table of the fitted model (both for lm or glm).

Best,

Peter

P?ter S?lymos
Alberta Biodiversity Monitoring Institute
Department of Biological Sciences
CW 405, Biological Sciences Bldg
University of Alberta
Edmonton, Alberta, T6G 2E9, Canada
Phone: 780.492.8534
Fax: 780.492.7635



On Sat, Feb 6, 2010 at 9:17 AM, Nathan Lemoine <lemoine.nathan at gmail.com> wrote:

Hi everyone,

I'm trying to fit a multiple regression model and have run into some
questions regarding the appropriate procedure to use. I am trying to compare
fish assemblages (species richness, total abundance, etc.) to metrics of
habitat quality. I swam transects are recorded all fish observed, then I
measured the structural complexity and live coral cover over each transect.
I am interested in weighting which of these two metrics has the largest
influence on structuring fish assemblages.

My strategy was to use a multiple linear regression. Since the data were in
two different measurement units, I scaled the variables to a mean of 0 and
std. dev. of 1. This should allow me to compare the sizes of the beta
coefficients to determine the relative (but not absolute) importance of each
habitat variable on the fish assemblage, correct?

My model was lm(Species Richness~Complexity+Coral Cover). I had run a full
model and found no evidence of interactions, so I ran it without the
interaction present.

It turns out coral cover was not significant in any regression. I have been
told that the test I used was incorrect and that the appropriate procedure
is a stepwise regression, which would, undoubtedly, provide me with
Complexity as a significant variable and remove Coral Cover. This seems to
me to be the exact same interpretation as the above model. So, since I'm
very new to all of this, I am wondering how to tell whether one model is
'incorrect' or 'inappropriate' given that they yield almost identical
results? What are the advantages of a stepwise regression over a standard
multiple regression like I have run?