I am trying to fit CJS multistate models on a c-r turtle dataset, but a bit confused about model specification regarding transition probabilities (Psi).

Could you please elucidate me about what the specifications below are actually modelling? (not sure whether the first two make sense)

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`Psi=list(formula=-1+stratum)`

Psi=list(formula=~-1+tostratum)

Psi=list(formula=-1+stratum:tostratum)

I'm posting my answer below which may be useful for others:

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`Psi=list(formula=-1+stratum)`

The -1 here is not necessary. It simply removes the intercept and replaces with S values where S is the number of strata. ~stratum specifies that movement is the same across tostratum from each stratum but can differ for stratum. All that matters is where you are at but not where you are going.

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`Psi=list(formula=~-1+tostratum)`

The -1 here is also not necessary. It simply removes the intercept and replaces with S values where S is the number of strata. ~tostratum specifies that movement is the same across stratum from each tostratum value but can differ for tostratum. All that matters is where you are going and not where you are at.

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`Psi=list(formula=-1+stratum:tostratum)`

Here the -1 is necessary. This formula allows different values depending on where you are at and where you are going and typically makes the most sense.

There is an important difference between the way marked and RMark work with regard to mlogit parameters like Psi. An mlogit parameter is one in which the sum of the probabilities is 1. For Psi, if I'm in stratum A and can go to B or C or remain in A, the probabilities A to A, A to B and A to C must sum to 1 because that is all of the possibilities. In RMark/MARK the design data would only contain 2 records which are determined based on what you select as subtract.stratum. If subtract.stratum was set as A for the A stratum, the design data for Psi would only contain records for A to B and A to C. The value for A to A would be computed by subtraction.

In marked, all 3 records are in the design data and the default of staying in A (A to A) has a value of fix=1 which makes it computed by subtraction. I did this for 2 reasons. Firstly, that way you get a real parameter estimate for the subtracted stratum which you don't get in RMark/MARK. Secondly, you can change the value to be subtracted at will and it is not fixed across the entire model fit, but you do have to be careful when specifying the model when you do that because the formula specifies the parameters for those that are not fixed.