Regression with few observations per factor level

Yes, the analysis with a small sample size would be valid (under the assumption that the model - both fixed and random effects are correctly specified) but at some point there must be a practical assessment as to the desired precision and the costs of the consequences of either inadequate estimates or wrong acceptance or rejection of hypotheses.  If it were just about the numbers from a sample and resulting P-values, we would only need statisticians and no subject-matter experts (which is clearly not the case).

And while I'm soapboxing, situations with low variability require fewer samples than situations with high variability.  One can't make assessments of the adequacy of an analysis solely on the sample size.

Jim

Jim Baldwin
Station Statistician
Pacific Southwest Research Station
USDA Forest Service

-----Original Message-----
From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of V. Coudrain
Sent: Monday, October 20, 2014 8:54 AM
To: ElginPerry
Cc: r-sig-ecology at r-project.org
Subject: Re: [R-sig-eco] 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.
___________________________________________________________
Mode, hifi, maison,? J'ach?te malin. Je compare les prix avec



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With such a small data set, why not simulate some data sets with
reasonable effect sizes and see how an analysis performs?  Krzysztof

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 >
Content-Type: text/plain; charset="UTF-8"


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.

___________________________________________________________
Mode, hifi, maison,? J'ach?te malin. Je compare les prix avec
     [[alternative HTML version deleted]]



___________________________________________________________
Mode, hifi, maison,? J'ach?te malin. Je compare les prix avec
        [[alternative HTML version deleted]]

_______________________________________________
R-sig-ecology mailing list
R-sig-ecology at r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology