Regression with few observations per factor level

Thank you for this helpful thought. So if I get it correctly it is hopeless to try testing an interaction, but we neverless may assess if a covariate has an impact, providing it is the same in all treatments.

Message du 20/10/14 ? 16h46
De : "Elgin Perry"
A : v_coudrain at voila.fr
Copie ? :
Objet : Regression with few observations per factor level

If it is reasonable to assume that the slope of the covariate is the same for all treatments and you have numerous treatments then you can do this by specifying one slope parameter for all treatments as you gave in your example (e.g. lm(var ~ trt + cov)).  By combining slope information over treatments, you can obtain a reasonably precise estimate.   With so few observations per treatment, you will not be able to estimate separate slopes for each treatment with any degree of precision (e.g. lm(var ~ trt + trt:cov))

Elgin S. Perry, Ph.D.
Statistics Consultant
377 Resolutions Rd.
Colonial Beach, Va.  22443
ph. 410.610.1473


Date: Mon, 20 Oct 2014 10:53:41 +0200 (CEST)
From: "V. Coudrain" < v_coudrain at voila.fr >
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] Regression with few observations per factor level
Message-ID: < 2127199056.738451413795221981.JavaMail.www at wwinf7128 >
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Hi, I would like to test the impact of a treatment of some variable using regression (e.g. lm(var ~ trt + cov)).?
However I only have four observations per factor level. Is it still possible to apply a regression with such a small
sample size. I think that i should be difficult to correctly estimate variance.Do you think that I rather should compute
a non-parametric test such as Kruskal-Wallis? However I need to include covariables in my models and I am not sure if
basic non-parametric tests are suitable for this. Thanks for any suggestion.