[R] Block factor as random or fixed effect?

Robert A LaBudde
Wed, 13 May 2009 22:21:41 -0000

At 05:49 PM 5/13/2009, Rob Knell wrote:
>People
>
>I apologise for asking a general stats question, but I'm at a bit of a
>loss as to what to do following some hostile referees' comments. If I
>have a fully randomised blocked design, with only three blocks, should
>I treat block as a random or fixed effect? I have read comments about
>not treating block as a random effect if the number of blocks is less
>than 6 or 7: is this right?
>
>Any advice much appreciated
>
>Rob Knell

If you treat the variable as fixed effects, then inference will only
apply to those particular choices of blocks. If you treat the
variable as a random effect, you are probably going to estimate a
variance for a population distribution plus a mean effect, so
inference can be made to the population of all possible blocks.

The rule you've probably seen quoted could be paraphrased to say: "If
you're trying to estimate a random effect (i.e., variance), you will
need at least 6 subjects, or you won't get any precision on the
estimate. For fewer than 6 subjects, you might as well give up on
modeling a random effect, and just settle for doing the fixed effects
model."

That being said, if you really need inferences on the population of
blocks, model the random effect and bite the bullet on the imprecision.

Also, remember the assumption that the blocks are chosen randomly
(from a normal distribution). If they're not, stick with the fixed
effects model.

===============================================================Robert A.
LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

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