State assignment

[simone77]

Hi,

I have a case study very similar to that described in Conn and Cooch, 2009 as well as in a thread in this forum titled "problem with unequal time intervals". I am using E-Surge (first time) and, at the moment, I have specified:
1 group,
0 individual covariates,
3 states,
4 events (not seen, healthy, diseased, unknown)
1 age class
9 occasions

As told at page 3 of the "E-SURGE Version 1.8 multiEvent SUrvival Generalized Estimation Manual" (downloadable here):

I would expect that in my case the right pattern matrix for the state identification (Event - step two) should be something like this (if I understood well the letters don't matter):

e11 first state (healthy)->not seen, p=0 (because this p is conditional on the p of being captured)
e12 first state (healthy)->seen as healthy, p to be estimated
e13 first state (healthy)->seen as diseased, p=0
e14 first state (healthy)->seen as unknown, redundant p (1-pe12)
the second row is state=diseased, and 3rd row is "dead" (hidden state)

Anyway I have found in both the Conn and Cooch, 2009 paper (Appendix 2) and in the above cited thread, that they specified respectively these pattern matrices for state identification:
1)

2)

There must be a mistake in the way I am doing it but cannot see where.
Thank you for any help you might provide.

Simone

[ganghis]

Hi Simone,
It gets a little tricky when you have multiple "steps" for the observation. In the first step, the rows index the underlying state of the animal (state A, state B, dead). In the second step, the rows index the detection type (not detected, detected in state A, detected in state B) while the columns index the actual observation (not detected, state assigned A, state assigned B, state assigned U). I made a mistake here when I was first fitting these, so you're not alone! To convince myself that this was correct, I multiplied the two matrices (see a linear algebra textbook if you're unsure) on B_1 and B_2... what you want is to get the true state on the rows, and resultant observation on the columns with correct probabilities in the matrix.

Paul

[CHOQUET]

Hello Simone,

your approach may be equivalent to the one used by Paul.

Your step two is correct if column labels in the first step are respectively
'captured as healthy', 'captured as diseased' and 'not captured'.

If I don't make a mistake, Paul used the following labels in the first step
'not captured', 'captured as healthy', 'captured as diseased'.

These columns labels are respectively the row labels of step two.
Thus a permutation of the columns in step 1 imply the same permutation of the rows of step 2.

Sincerely,
Rémi

[simone77]

Hi Paul,

Thank you for your answer, I have already changed that pattern matrix.
Anyway, there are two things I don't understand yet (hope not to be a pain in the neck for anybody).

1)

To convince myself that this was correct, I multiplied the two matrices (see a linear algebra textbook if you're unsure) on B_1 and B_2... what you want is to get the true state on the rows, and resultant observation on the columns with correct probabilities in the matrix.

I realize that the full matrices (initial state, transition, and encounter) are the products of their elementary matrices (each one denoting a step), but I haven't understood your trial (which matrices you multiplied and why). I feel that understanding it would be good point to better realize how this works.

2)
You say that in the second step, the rows index the detection type (not detected, detected in state A, detected in state B) and by the way I trust it, even so I have been reviewing the E-Surge manual and found examples that made me believe that rows index always states ("not detected" would be an event, not a state, isn't it?) and that are not in that order (the first one being the state A and the last one the dead). For example, at page 16-17 (3.2 - A combined formulation of the Arnason-Schwarz model) it is said:

and

Elsewhere in the manual (pg. 18, 19, 21) I have found similar examples.

I know I am missing the point but don't know where...

[simone77]

I was replying Paul post and did not see the other answer.
Thank you Rémi, now I understand where I was missing the point.