Unexpected beta coefficients for fixed parameters

[tasha]

Hello,

We are running a multistate robust model, with three mass class strata (stratum 1, stratum 2, stratum 3) and four capture occasions. t1 and t2 occur in spring and fall of 2008, and t3 and t4 occur in spring and fall of 2009. We would like to model Psi as (~-1+stratum:tostratum*time - time), but when we did so, we noticed that many of the Beta coefficients had either very high standard errors, or SE = 0. We used transition.pairs to examine the data, and found that some transitions did not occur in all the time periods (see below).

#Time 1
. 1 2 3
1 184 34 18
2 1 302 37
3 0 0 337

#Time 2
. 1 2 3
1 431 4 2
2 27 531 8
3 12 58 436

#Time 3
. 1 2 3
1 1022 97 11
2 54 1181 17
3 15 58 361

#Time4
. 1 2 3
1 702 77 8
2 55 907 12
3 2 25 216

To account for this, we tried to fix transitions that did not occur in specific time periods to 0. We also considered fixing transitions that occurred <2 times to 0.

fromstr=as.character(pdoge.ddl$Psi$stratum); tostr=as.character(pdoge.ddl$Psi$tostratum);
indices.3to1t1=which(fromstr %in% c('3') & tostr %in% c('1') & pdoge.ddl$Psi$Time == 0)
indices.3to2t1=which(fromstr %in% c('3') & tostr %in% c('2') & pdoge.ddl$Psi$Time == 0)
indices.2to1t1=which(fromstr %in% c('2') & tostr %in% c('1') & pdoge.ddl$Psi$Time == 0)
indices.1to3t2=which(fromstr %in% c('1') & tostr %in% c('3') & pdoge.ddl$Psi$Time == 3)
indices.3to1t4=which(fromstr %in% c('3') & tostr %in% c('1') & pdoge.ddl$Psi$Time == 15)

...

Psi.fixedt=list(formula=~-1+stratum:tostratum*time-time,fixed=list(
index=c(indices.3to1t1,indices.3to2t1,indices.2to1t1,indices.1to3t2,indices.3to1t4), value=c(rep(0,length(indices.3to1t1)),rep(0,length(indices.3to2t1)),rep(0,length(indices.2to1t1)),
rep(0,length(indices.1to3t2)),rep(0,length(indices.3to1t4))))) #transitions fixed to 0

Our expectation was that we would not get Beta coefficients for the transitions that are fixed, and that the real parameter estimates would be set to 0. This occurred for the two transitions in Time == 3 and Time ==15, but we have Beta coefficients with SE=0 for each of the fixed transitions in Time==0 even though the corresponding real parameter estimates were set to 0.

In an attempt to understand what was happening, we tried fixing the parameters as above but without a Time component (e.g. indices.3to1=which(fromstr %in% c('3') & tostr %in% c('1')). When we did this, there were no Beta coefficients for the fixed transitions in the output, and the corresponding real parameter estimates were set to 0. This lead us to believe that there is something wrong with how we have coded the time periods.

Does anyone have any suggestions about what might be going on, and how we can correct it?

Thank you!

[jlaake]

See the top post in the RMark subforum about fixing parameters. With the newer approach it is much easier to see that you have them fixed correctly. Also you are making the formula too complicated. You can use -1+stratum:tostratum:time

[tasha]

Thanks for your help, Jeff! I hadn't realized the differences between what I was doing and the newer approach. I think fixed parameters are behaving as expected now.

[tasha]

Hello again, I have a few more questions regarding SE of Beta coefficients for psi.
As described above, I fixed the probability of those transitions which do not occur in certain time periods to 0, so there are no longer betas for those in the output. Good.

Because I still had some problems with beta coefficients and SE after doing this, I then tried fixing transitions which were rare (<4 occurrences) to 0 in addition to those which did not occur at all. I still have an issue with a transition which has 8 occurrences (B = -13.79, SE = 532.04). I am concerned about whether fixing parameters like this is a solution for large SE, and if so, up to what point is it acceptable? Specifically:

1. What is a reasonable beta:SE ratio

2. The real parameter estimates seem to make sense despite the large SE around the beta coefficient. Does this mean the model is actually appropriate?

3. What information can I use to decide whether to fix parameters to deal with large Beta SE

4. If there are only a few transitions with high beta SE can I accept the model based on AICc and acknowledge which transitions have considerable uncertainty around the betas in the results?

5. How do I decided that the model just does not fit my data well despite being the top model based on AICc and choose another model?


Thanks Tasha

[jlaake]

Tasha-

You shouldn't fix betas unless it is a structural 0 (no transitions) or there is some logical reason to do so. As you have seen having a large se on beta doesn't necessarily mean anything is wrong. With a large negative value that transition is likely very close to 0. When the variance is calculated for the real it uses both variances (Se^2) and covariances so the se doesn't always imply a problem. Now if all are very large that would suggest the design is over-parameterized.

--jeff

[tasha]

Thanks Jeff!

after fixing all of the no transitions = 0 it would appear that the design is indeed over-parameterized. I am wondering if there is a way to either group several transitions together into one (e.g. all forward transitions: 1 to 2, 1 to 3, 2 to 3 into a single "up" group) or fix them equal to one another without a value (e.g. attached) in order to reduce the number of parameters in the model? If so could you please point me to a resource.

Thank you

[jlaake]

Tasha-

Email me offlist with the R code you are using and a summary of the model results so I can better understand what you are doing.

[tasha]

Thank you, I will send the script shortly!

[tasha]

Hi Jeff,

I've just sent you an email with subject line "Help with Psi - Tasha" .

Thanks again for your offer of help - much appreciated!

Tasha and Tara