## Help interpreting Psi in multi-state analysis

questions concerning analysis/theory using program MARK

### Help interpreting Psi in multi-state analysis

Hi all,

I'm working on a multi-state with live recapture analysis but am having some trouble interpreting the transition values (Psi) from the real estimates. There are 4 states (river pools A, B, C, & D). The best model only looked at differences in transitions between states and did not include a time variable. I am trying to determine the monthly and annual transition probabilities between river pools, but am not sure how to take the real estimates I obtained, and calculate those values. Below are a portion of the estimates for Psi as an example.

Code: Select all
` Real Function Parameters of {S(.) p(s*t) Psi(s)_V2}                                                               95% Confidence Interval  Parameter                  Estimate       Standard Error      Lower           Upper --------------------------  --------------  --------------  --------------  --------------      50:Psi A to B            0.0054571       0.0031360       0.0017649       0.0167438                               51:Psi A to B            0.1030576       0.0218812       0.0673790       0.1544992                               52:Psi A to B            0.1277947E-007  0.4036407E-005  0.1773397E-276  1.0000000                               53:Psi A to B            0.0188353       0.0032476       0.0134208       0.0263760                               54:Psi A to B            0.1233908       0.0093985       0.1061192       0.1430238                               55:Psi A to B            0.3173135E-008  0.1077794E-005 -0.2109303E-005  0.2115649E-005                          56:Psi A to B            0.0028548       0.0016157       0.9403275E-003  0.0086333                               57:Psi A to B            0.0796322       0.0080515       0.0652122       0.0969102                               58:Psi A to B            0.7159411E-003  0.5080549E-003  0.1780848E-003  0.0028736                               59:Psi A to B            0.2301455E-007  0.8670414E-005  0.2269160E-311  1.0000000                               60:Psi A to B            0.1513007E-008  0.1701518E-005 -0.3333462E-005  0.3336488E-005                          61:Psi A to B            0.0101993       0.0057397       0.0033697       0.0304479                           `

Thanks for any help!
Last edited by NGillespie10 on Wed Feb 14, 2018 11:56 am, edited 4 times in total.
NGillespie10

Posts: 2
Joined: Tue Feb 13, 2018 1:53 pm

### Re: Help interpreting Psi in multi-state analysis

This is actually a really involved question, which is probably why you haven't received a reply. The easy answer is "it isn't easy."

I think your best approach is to consult Miller and Andersen 2008 (Biometrics 64:1196-1206) who establish relationships between infinitesimal hazard rates for transition intensities and the probabilities you are estimating from MARK, which are defined relative to a particular interval between capture periods
(actually, the interval between midpoints of capture periods would probably be better). If you are willing to assume that transition rates are homogeneous (constant across time, I think you've stated this might be okay), you would want to solve for the A matrix that produces the P matrix from MARK (using Miller and Andersen's notation here), and then use your new desired time interval with the A matrix to produce a new P matrix. You could probably solve for the elements of A using an optimization routine, but the calculations involve matrix exponentials and/or eigenvalues, etc. so getting any sort of precision via the delta method would be a disaster. It would probably be easier to fit your multistate model using the elements of A as the parameters of your model (i.e. estimate the transition hazards directly instead of estimating probabilities). Of course, all this assumes that you're able to do fairly sophisticated coding.

Cheers, Paul
ganghis

Posts: 83
Joined: Tue Aug 10, 2004 2:05 pm

### Re: Help interpreting Psi in multi-state analysis

Hi Paul,

Thanks for the response! I'm going to read up on Miller and Anderson like you suggested and see if what you suggest is something I'm capable of.

Again, thank you for the help!

Neil
NGillespie10

Posts: 2
Joined: Tue Feb 13, 2018 1:53 pm

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