Multistate Presence constrain psi1+psi2 <= 1

[lucrezia]

Hello,

I'm running a single-season multi-state (1=non breeding, 2=breeding females) model in Presence but don't know how to set the constraint psi1+psi2 <=1. I tried with the Fix parameters option but obviously did something wrong. I'd be grateful to have an advise.

Thank you,
lucrezia

[jhines]

lucrezia,

Why would you want to constrain psi1+psi2<1? psi1 is the probability that a site is occupied, and psi2 is the probability that breeding occurs at a site, given that it is occupied. So, if both psi1 and psi2 were 1.0, then all sites would be occupied and breeding would be happening at all sites (and psi1+psi2=2.0).

Cheers,

Jim

[lucrezia]

Jim,

thank you very much for the really quick reply!

I thought about setting this constraint due to the example in the exercise 16 (Multiple state occupancy models) in

Donovan, T. M. and J. Hines. 2007. Exercises in
occupancy modeling and estimation.
<http://www.uvm.edu/envnr/vtcfwru/spreadsheets/occupancy.htm>

which seemed fairly similar to my case and got me a bit confused. Now I understand your answer but don't fully understand the reason of the constraint in the example in exercise 16..

Thank you for your time,
lucrezia

[jhines]

lucrezia,

There are two ways of parameterizing the multi-state occupancy model. The way it's done in the online exercise,

psi1 = prob(site occupied and no breeding), and
psi2 = prob(site occupied and breeding occurs at site),
1-psi1-psi2 = prob(site not occupied)

The way it's done in PRESENCE,

PSI1 = prob(site occupied by species), and
PSI2 = prob(breeding occurs, given site is occupied).
1-PSI1 = prob(site not occupied)

The exercise parameterization was the original thinking for the model, but after coding into PRESENCE, I noticed numerical optimization problems. These were due to the fact that there was nothing to constrain the optimization process such that psi1+psi2 <= 1. So, I came up with the other parameterization, which allows both psi1 and psi2 to be any value between zero and one. This poses no problems for the optimization routine, and parameter estimates can be converted to the first definitions of psi1 and psi2 by these equations:

psi1 = PSI1*(1-PSI2)
psi2 = PSI1*PSI2

So, you don't need the constraint in PRESENCE, but do need it in the spreadsheet exercise. Soon (hopefully), I will have both parameterizations in PRESENCE (using an mlogit transformation to constrain psi1+psi2 < 1).

Jim