Problem with boundary estimate

[tamarlok]

I am doing an analysis to estimate site fidelity. My species shows strong site fidelity, with most values between 0.9 and 1.0.
One of the values is estimated at 0.997, with SE=0.05 and 95% CI 0.00-1.00. After running the model, E-Surge says that all parameters could be estimated. Moreover, looking at my data, I am quite convinced that this value is actually very close to 1. But I find it difficult to understand how a SE of 0.05 leads to a huge 95% CI of 0.00-1.00 for a boundary estimate (0.997), whereas for an estimate of 0.93 with SE=0.05 (in the same analysis), the 95% CI = 0.72-0.99.
I ran this model several times using multiple random inital values; although the outcomes seemed to have exactly the same deviance (at least up to 4 digits behind the comma) and the estimated values were very similar up to the 4th digit after the comma as well, the standard errors - and therefore also the 95% CI - around all estimates (including the boundary one) were somewhat different. In case of the boundary estimate of 0.997, one run gave SE=0.056, whereas another gave SE=0.050.
How should I cope with this huge confidence interval around a boundary estimate? What does it tell me? Is the uncertainty around boundary estimates really that much bigger than around more intermediate estimates (give similar SE's), or is this caused by E-Surge (as well as MARK) having problems in coping with boundary estimates? Is there any solution to this?

I hope anybody can help on this!

Kind regards, Tamar

[CHOQUET]

Hello Tamar,
CI on the boundary or very close to a boundary with the delta method ( the method used in E-SURGE)
are quite difficult to obtain because 1) on the boundary the wald method is not valid
2) very close to a boundary, the estimate of some part of the Hessian is sometimes very bad.

Additionaly, for transition Psi(i,j) with more than 2 possibilities (i,j>2), the problem is even harder
because the CI of Psi(ii) depends also of the values of Psi(ij), i not equal to j (because of the multinomial logit).
So if the estimate of Psi(ij) is on the boundary or very close to the boundary, valid estimates for the CI for Psi(ii)
are not availables.

On our case, 0.997 is quite close to 1 but not very close. I suspect that additionaly there is some
transition Psi(ij, i not equal to j) very close to 0.
Sincerely,
Rémi