Dear friend Demilade Israel Ibiwoye

In order to model your data using a GLMM, you would need to determine the response variable, the fixed effects, and the random effects. In your case, the response variable is likely the oocyst per gram (OPG) count, and the fixed effects could include things like treatment, time, and their interaction. The random effect would be the pen (or set pen) in which the birds were kept.

Since your data is non-random, you would need to account for any potential confounding variables or biases that could affect your results. For example, if the birds were not randomly assigned to the pens, there could be differences in the birds or the environment that could affect the OPG count. You could control for this by including additional fixed effects in your model, such as the age or breed of the birds, or environmental factors like temperature or humidity.

To specify the non-randomness of your data, you could include a binary variable in your model indicating whether the birds were in the same pen or a different pen each time you collected data. This variable would be a fixed effect, and it would help control for any potential biases that could arise from differences between pens. Additionally, you would specify the random effect of pen in your model to account for any variability between pens that is not explained by the fixed effects.

Overall, the structure of your GLMM could look something like this:

OPG ~ treatment + time + treatment*time + same_pen + (1|pen)

Here, OPG is the response variable, treatment, time, and their interaction are fixed effects, same_pen is a binary variable indicating whether the birds were in the same pen or a different pen each time, and (1|pen) is the random effect of pen.

It's worth noting that the specific structure of your GLMM may vary depending on the details of your experiment and the nature of your data. It's always a good idea to consult with a statistician or data analyst to ensure that your model is appropriate for your data and research question.

Thanks so much for the great response.