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 School of Biological and Chemical Sciences Queen Mary, University of London 'Phone +44 (0)20 7882 7720 Skype Rob Knell Research: http://webspace.qmul.ac.uk/rknell/
Block factor as random or fixed effect?
3 messages · Rob Knell, Robert A LaBudde, Ben Bolker
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 "Vere scire est per causas scire"
Robert A LaBudde wrote:
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.
It depends what you're doing. If everything is normally distributed, (nearly) balanced, orthogonal, etc., and you can successfully use classical method-of-moments approaches to ANOVA, then you have the choice whether to treat the 3 blocks as random or fixed (although you will have a really bad estimate of the block variance). If all of the above are not true, then you are almost guaranteed not to be able to estimate the variance properly -- symptoms will range from an estimated block variance of 0, to various warnings and errors. (The rule of thumb quoted above applies.) See also Andrew Gelman, "Analysis of variance: why it is more important than ever" for ammunition, if you need it ...
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