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Hi.  I have a question about how to specify an nested/mixed ancova model using GLM.

The study involves 2x2 crossed treatments (Factor A crossed with Factor B, both with 2 levels) and each treatment combination is applied to 4 cages, all containing an equal number of insects. Hence, there are 16 cages in all.  The response of interest, plus a covariate are measured for each insect separately.

I believe that the experimental unit is cage rather than insect, so one option would be to calculate the mean for each cage and analyse as a simple factorial anova with a covariate.  However, this means that the covariate adjustment is applied to the whole cage rather than to each observation and I feel I would be losing some potentially useful information.

The alternative (I think) is to analyse the individual data, specifying the model in such a way that cage is treated as a random effect, and nested within the 2x2 fixed effects model.  This would allow the covariate to be applied at the level of the individual insect.  First of all, does this sound like a reasonable approach?  If so, please could you help me to work out how to specify the model.  I am familiar with SAS GLM model syntax.

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Just to get the ball rolling, here is my best guess:

 

  Covar + A|B + Cage(A*B)

 

This results in the following terms in the anova table:

 

  Covar

  A

  B

  A*B

  Cage(A*B)

 

I'm currently using type III sums of squares.

 

Does this look right?

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