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My experimental design is as follows: Three sites (Treatments) that were not replicated (Healthy Control [HC], Untreated [U], and Treated [T]). Six independent measurements (Samples) of a response variable (RV) were taken randomly at each site. The exercise was repeated at two different times (before and after treatment). Thus my dataset looks something like this:

  • SampleID = unique identifier
  • Site: Factor with three levels
  • Time: Factor with two levels Site
  • RV: Count data

I would like to know if treating the site had an effect on RV. Due to the lack of replicability and correlation between the measurements, I consider running a GLMM. This is where I need some help. I don't know how to build the correct model to test the site effect accounting for the lack of replicability.

m1 = RV ~ Time + Site + (Time|SampleID))

Will this model provide a fixed-effects estimate for site that tells you whether site had an effect on RV values?

 m2 = RV ~ Time + Site + Time*Site +(Time|SampleID)

Will this model provide a fixed-effects estimate for the interaction between change over time and site that tells me whether the rate of change with respect to RV is significantly different between sites? Is this possible to test at all with my data?

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