[R] Block factor as random or fixed effect?

[Robert A LaBudde]

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
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