Multi-season design matrix question

[pricsj7]

Hi All –
I’m currently running single-species, multiple season occupancy models to assess the effect of disturbance (i.e., urban development) on amphibian occupancy and vital rates. Monitoring was done over a period of 5 years at 30 sites. Two surveys were conducted at each site during each year. Sites are classified as either control (never experienced disturbance) or impact (disturbance occurred after year 1). Essentially, I follow a before/after control/impact study design, and thus I’m particularly interested in the interaction between treatment (control vs. impact) and time.

I’m having trouble grasping the design matrix for this type of analysis. I coded treatment as a binary site covariate. I assume I can get at the effect of time by using a full identity matrix. How do I code the interaction term? The Mark book recommends using the design below:

psi1 Location 0 0 0 0
psi2 0 Location 0 0 0
psi3 0 0 Location 0 0
psi4 0 0 0 Location 0
psi5 0 0 0 0 Location
.
…But results from the above matrix don’t make sense and in my discussions with others and through searching this forum it appears that there are other ways to code this interaction term. Any advice would be appreciated.
Thanks
Steve

[darryl]

Hi Steve,
Is that your full design matrix? If so then you're implicitly assuming that whenever Location=0, the psi = 0.5, exactly. A full time*location interaction design matrix would have 10 columns, first a series of 1's on the diagonal, then Location on the diagonal.
Cheers
Darryl