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I´m trying to learn generalized mixed models in SAS and I have now bumbed into a situation that I cannot figure out by myself. So I was thinking that maybe some of you could help me forward.

I´m running a model where I have normally distributed measurements of traits like tarsus etc in birds from different populations. I have few fixed factors (sampling area, sex and year) and their interactions in the model and random term "sampling site clustered within the sampling area" (2 sampling areas with both 2 sampling sites). I´m using SATTERTH as a method for computing the denominator degrees of freedom.

My problem is that for one particular trait I get really low degrees of freedom always when the sampling site is in the model, and for that particular factor. I noticed that playing around with the methods of computing the degrees of freedom, I can get "better" results, but I cannot understand why in this model, one fixed factor eats up my degrees of freedom.

If anyone can and would like to explain to me why this happens and how I should select the method for computing the DDF´s in "dummies" way, it would make my day. I'm happy to provide you with more information, I was not certain how I should present my problem.

Thank you in advance.

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  • $\begingroup$ Are you saying that, in some of your models, you have sampling site as both part of the random term and as a fixed effect? I'm not sure that makes much sense, and might conceivably cause problems.. $\endgroup$ – onestop Jun 8 '12 at 14:05
  • $\begingroup$ The sampling sites are not independent within their research area. Thats why I have clustered sites within the area. (I corrected this to the original question just, i had it wrong there) So im estimating the effect of sampling area as fixed effect and the sampling site within an area as random term. $\endgroup$ – Maisa Jun 8 '12 at 14:37
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The t distribution by Satterwaite is an approximation to the distribution of a t-like statistic when the two variances are unequal and estimated separately. This is the so-called Behren's-Fisher problem. The distribution under the null hypothesis is not a t distribution but it has been found that it can be well approximated by a t with a fractional number for the degrees of freedom parameter. There is a special formula for the degrees of freedom in the approximation. You could look this up but here is a link to Wikipedia: http://en.wikipedia.org/wiki/Behrens%E2%80%93Fisher_problem.

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  • $\begingroup$ Thank you for this Michael! Have you ever encountered a situation where Satterwaite approximation would behave like it does in my case and what could be the reason for this? $\endgroup$ – Maisa Jun 11 '12 at 7:00
  • $\begingroup$ I haven't done much with Satterwaite in linear models with unequal variances. I think if you look at the formula for degrees of freedom it will probably start making sense. $\endgroup$ – Michael Chernick Jun 11 '12 at 10:50
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This could be an interplay of several factors: variances within the ultimate cluster (site X sampling area, as far as I can tell from your post), and/or concentration of the response within relatively few clusters. Satterthwaite approximations tend to be drawn towards the larger variances. In the worst case scenario of having the largest variance associated with the smallest cluster (e.g., due to an outlier in it), if you have say sites with 10, 15, 25 and 50 observations, and the variances happen to be 50, 10, 14 and 9, then you will end up with 11 degrees of freedom overall (I am making the numbers up, of course, but that's how it may play out, in the end).

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