Generalized linear mixed model help with binary data

[jkj4]

Hello,

I am needing help with setting up a generalized linear mixed model for a research project that involves binary, non-normal, non-gaussian data.  Here is the experimental layout:

4 ranches were used in the project where two treatments were applied to cattle in a minimum of one pasture per ranch.  More specifically trt 1 was fed to all cattle in pasture 1 for Ranch A and trt 2 was fed to all cattle in pasture 2 for Ranch A.  Ranches B and C had the same model.  Ranch D had 3 pastures (7,8,9) on trt 1 and 3 pastures (10 ,11, 12) on treatment 2.  There was a minimum of 20 cows in each pasture.  I was originally thinking this was a completely randomized block design with ranch as a block, but was wondering if there might be a better experimental design.

The first variable I am looking to evaluate include pregnancy rate.  I currently have each animal identified by ranch, pasture, and treatment, with their pregnancy status of open (coded as 0) or pregnant (coded as 1).  Please help me determine if pasture becomes the experimental unit or if animal within pasture is the experimental unit for this treatment layout.  Also, please help with the SAS code.

[sld · Accepted solution]

Regarding your design question: I also would say that this is a randomized block design (RBD), and I would incorporate the multiple pastures within a treatment at Ranch D as a form of subsampling. As a RBD, blocks (i.e., ranchs) define the statistical inference space and are the factor that replicates treatment. Cows are nested within a given pasture and are not independent in their response to implementation of a particular treatment to that pasture. Similarly, pastures are nested with Ranch D and are not necessarily independent in their response to implementation of a particular treatment.

Some people (who are less likely to be statisticians, I would surmise) might say otherwise, that cows nested within a ranch are independent in their response to treatment. (Ranch is still a block.) That argument is context-specific: how the were cows fed (jointly? individually?), how are cows impregnated (natural by a bull in the pasture? AI?), pasture management protocols, pasture forage heterogeneity, etc. These are questions to discuss with your peers; the SAS Community does not have the expertise or the information.

Regarding your request for code: Once you've sorted out the roles of various random effects factors (e.g., ranch, pasture, cow) in your study and if you have code problems, please show us code that you've tried. Some one may be able to help then.