Multi-state Multi-Season Occupancy DM

[kyle.artym]

Hi there,

I'm getting a little spun around by the Occupancy matrix for a 4Season, 3State (0,1,2) model. I am modeling relative abundance, to be distiguished by catch per unit effort. I want changes in occupancy between season to be held equal for their respective states (i.e.Cpsi0,Cpsi1,Cpsi2), so that I can see which covariates have the greatest impact on detection/nondetection. So the dm I wrote in was the following:

Matrix 1: rows=21, cols=9
-,a1,a2,a3,a4,a5,a6,a7,a8,
psi0 1 0 0 0 0 0 0 0
Cpsi0(1) 0 1 0 0 0 0 0 0
Cpsi1(1) 0 0 1 0 0 0 0 0
Cpsi2(1) 0 0 0 1 0 0 0 0
Cpsi0(2) 0 1 0 0 0 0 0 0
Cpsi1(2) 0 0 1 0 0 0 0 0
Cpsi2(2) 0 0 0 1 0 0 0 0
Cpsi0(3) 0 1 0 0 0 0 0 0
Cpsi1(3) 0 0 1 0 0 0 0 0
Cpsi2(3) 0 0 0 1 0 0 0 0
R0 0 0 0 0 1 0 0 0
CR0(1) 0 0 0 0 0 1 0 0
CR1(1) 0 0 0 0 0 0 1 0
CR2(1) 0 0 0 0 0 0 0 1
CR0(2) 0 0 0 0 0 1 0 0
CR1(2) 0 0 0 0 0 0 1 0
CR2(2) 0 0 0 0 0 0 0 1
CR0(3) 0 0 0 0 0 1 0 0
CR1(3) 0 0 0 0 0 0 1 0
CR2(3) 0 0 0 0 0 0 0 1

There are a few inflated estimates and SE values for Cpsi0, Cpsi2, and CR0 but the jump down in AIC from the null model is >100. Once I add covariates, however, the model no longer reaches convergence.

An alternative dm I tried was the following one where at least I am not holding the Cpsi and R values constant, but I am not sure the matrix is asking the right questions:

Matrix 1: rows=21, cols=9
-,a1,a2,a3,a4,a5,a6,a7,a8,
psi0 1 0 0 0 0 0 0 0
Cpsi0(1) 0 1 0 0 0 0 0 0
Cpsi1(1) 0 1 0 0 0 0 0 0
Cpsi2(1) 0 1 0 0 0 0 0 0
Cpsi0(2) 0 0 1 0 0 0 0 0
Cpsi1(2) 0 0 1 0 0 0 0 0
Cpsi2(2) 0 0 1 0 0 0 0 0
Cpsi0(3) 0 0 0 1 0 0 0 0
Cpsi1(3) 0 0 0 1 0 0 0 0
Cpsi2(3) 0 0 0 1 0 0 0 0
R0 0 0 0 0 1 0 0 0
CR0(1) 0 0 0 0 0 1 0 0
CR1(1) 0 0 0 0 0 1 0 0
CR2(1) 0 0 0 0 0 1 0 0
CR0(2) 0 0 0 0 0 0 1 0
CR1(2) 0 0 0 0 0 0 1 0
CR2(2) 0 0 0 0 0 0 1 0
CR0(3) 0 0 0 0 0 0 0 1
CR1(3) 0 0 0 0 0 0 0 1
CR2(3) 0 0 0 0 0 0 0 1

Here the AIC only drops about 15 relative to the null model, but I can add several covariates and we see strong shifts in AIC.

Thank you for your help!

[kyle.artym]

I have 67 sampling units, with 8 surveys per unit split 2,2,2,2 across 4 seasons

[jhines]

Hi,
Since you say that you’re modeling relative abundance using the multi-state model, I assume your states are: 0=unoccupied, 1=occupied, and 2=hi-abund. When you say that you want changes in occupancy between seasons to be held equal for their respective states, do you mean that you want the probability of each occupancy state to be constant over seasons for each state? Or do you want the probability of each occupancy state to vary over seasons, but irrespective of previous occupancy state?

The first design matrix appears to set occupancy state to be constant after the first season (occupancy state in the first season is determined by psi0 and R) –
Cpsi0(1)=Cpsi0(2)=Cpsi0(3) means that the probability of an unoccupied site becoming occupied is the same for seasons 2,3 and 4.
R0(1)=R0(2)=R0(3) means that the probability of occupancy/hi-abund, given occupancy for previously unoccupied sites is the same for seasons 2,3 and 4.
Cpsi1(1)=Cpsi1(2)=Cpsi1(3) means that the probability of an occupied site remaining occupied is the same for seasons 2,3 and 4.
Cpsi2(1)=Cpsi2(2)=Cpsi2(3) means that the probability of an occupied/hi-abund site remaining occupied is the same for seasons 2,3 and 4.

The 2nd design matrix constrains the probability of occupancy to be the same, irrespective of the occupancy status in the preceeding season –
Cpsi0(1)=Cpsi1(1)=Cpsi2(1) means that the probability of occupancy in season 2 is the same for unoccupied sites in year 1, occupied sites in year 1, and occupied/hi-abund sites in year 1.