3rd-Order Interaction

[TGrant7]

I'm doing an occupancy analysis with several plot covariates and 3 groups.

I want to double-check that my design matrix is correct for a third-order interaction (also called a 3-way interaction?) between the groups and 2 covariates:

Beta B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13
p 1 0 0 0 0 0 0 0 0 0 0 0 0
psi 0 1 1 0 Cov1 Cov2 product(Cov1,Cov2) Cov1 0 Cov2 0 product(Cov1,Cov2) 0
psi 0 1 0 1 Cov1 Cov2 product(Cov1,Cov2) 0 Cov1 0 Cov2 0 product(Cov1,Cov2)
psi 0 1 0 0 Cov1 Cov2 product(Cov1,Cov2) 0 0 0 0 0 0

I can' figure out how better to represent the design matrix in this post. I inserted spaces to space everything out into discret columns, but the preview shows only one space between everything. I added my email address to my profile and I'd be happy to email a spreadsheet of the dm. I included all lower-order interactions, which I understand is accepted practice.

Of course, the data may not be able to support this model.

For those interested, it's a study of a federally listed butterfly subspecies that only lives on one mountaintop, which is a bad place to be during climate change. Groups are different meadows and covariates are aspect and distance from edge of the meadow. There is reason to believe that there is an interaction between all these.

Thanks for your help.