Hello again,
I am building a multi-state multi-season model using the Psi, R, p, delta parameterization. In an earlier stage of my modeling procedure, I have found support for a logarithmic time trend in CR that is additive with state and with land ownership type ("Type," an indicator variable). I am very interested in testing whether this logarithmic time trend is the same or different between the two different land ownership types. I have set up the design matrix like this:
a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15
...
CR0(1) 0 0 0 0 0 0 0 0 0 1 0 0 0.69 Type Int1
CR1(1) 0 0 0 0 0 0 0 0 0 1 1 0 0.69 Type Int1
CR2(1) 0 0 0 0 0 0 0 0 0 1 0 1 0.69 Type Int1
CR0(2) 0 0 0 0 0 0 0 0 0 1 0 0 1.1 Type Int2
CR1(2) 0 0 0 0 0 0 0 0 0 1 1 0 1.1 Type Int2
CR2(2) 0 0 0 0 0 0 0 0 0 1 0 1 1.1 Type Int2
CR0(3) 0 0 0 0 0 0 0 0 0 1 0 0 1.39 Type Int3
CR1(3) 0 0 0 0 0 0 0 0 0 1 1 0 1.39 Type Int3
CR2(3) 0 0 0 0 0 0 0 0 0 1 0 1 1.39 Type Int3
CR0(4) 0 0 0 0 0 0 0 0 0 1 0 0 1.61 Type Int4
CR1(4) 0 0 0 0 0 0 0 0 0 1 1 0 1.61 Type Int4
CR2(4) 0 0 0 0 0 0 0 0 0 1 0 1 1.61 Type Int4
...
Where the last column (Int1, Int2, etc.) is the product of the log time trend and the indicator variable Type for each transition. When I run this model, it is exactly 2 deltaAIC from the additive model that doesn't include the interaction term, leading me to believe that either there is absolutely no support for the interaction model over the additive OR that I am setting up the interaction wrong and being penalized 2 AIC for running exactly the same model with an extra nonsense variable. I'd be super happy for any feedback!
Thanks!
KB