Time Intervals within Robust Design

[Carolinew77]

I have a list of 6 questions related to my data and they are mostly about the robust design within Mark.
This is the first:

How do time intervals when first selecting model type affect the chosen model? – specifically on Robust Design

Robust Design, Closed Caputres, Enter encounter occations (122), Enter easy robust design times (13), Specify number of secondary occations per primary (as table below), SET TIME INTERVALS .

Year Season
Days Interval
1999 S 8
2000 S 7 311
2001 S 7 278
W 5 150
2002 S 3 184
2005 S 8 1101
2006 S 12 360
W 10 101
2007 S 16 192
W 13 89
2008  S 12 152
S 13 140
2009 W 8 149

If time intervals are NOT entered for my data the global model choice is S(.)G"(.)G(.)p=c(t)N (1st non-confounded model with best AIC), best model with only one gamma confounded [and may be improved by added co-variate constraints]: S(.)G"(t)G(t)p=c(t)N
If time inverals ARE entered all models are confounded, with most models confounded ONLY within survival SE. While outputs for the following four models are all the same.
{S(.)G"=G'(t)p=c(t)N}
{S(.)G"(t)G'(t)p=c(t)N}
{S(.)G"(.)G'(.)p=c(t)N}
{S(.)G"=G'(.)p=c(t)N}

What is the influence of the time intervals? Are they necessary?

Regards,
Caroline

[tpuettker]

Hello Caroline,

As long as I understand your data, the time intervals between the primary capture sessions are quite different (ranging between 149 and 1101 days/hours/...). Therefore, if you do not enter time intervals and MARK assumes equal time intervals between primary capture sessions, the "best" model/s are probably not representing your actual data. The time intervals are important for the estimation of open-population parameters (like survival, gamma). The probability of survival of 149 days is probably higher than surviving 1000 days.
Looking at the data, it seems that also the number of secondary occasions differ between primary sessions. Using "easy robust design times" you should get a message, that your combination of primary and secondary capture sessions does not match.In my opinion, you should carefully enter all time intervals as well as not use "easy robust design times", but enter all different numbers of occasions in the primary sessions.

Hope it helps...

thomas

[Carolinew77]

Thomas, thanks for your post.

To clarify my data: the data covers 11 years; the gaps between my 13 primary "seasons" range from 89 - 1101 days, while my secondary periods vary from 3 to 16 days per season (sum to 122 days total).

Yes I definately need to specify specific times under the "easy robust design times" after entering in the number of encouter occations.

So my problem exists as

MARK assumes equal time intervals between primary capture sessions, [so...] the "best" model/s are probably not representing your [my] actual data.
thomas

this is an issue for me as all models computed with time intervals specified appear confounded [some with outlandish estimates for capture and gamma parameters), however most of those models are only confounded for survival.
This is unless I am interpreting the model as confounded when it is, in fact, that the SE is indeed tiny and the model is ok.
The SE's I have been getting (with no other parameter confounded) are as follows:
S 0.9997825
SE 0.2698918E-004 which is... 0.00002698
Lower CI 0.9997226
Upper CI 0.9998295

Would this seem a reasonable estimate for the survival SE?

(The survival estimate itself seems plausible as it is for a population of 'resident' mammals in an area that is entirely 'covered' by the survey day. The animals have a life span of ~<40 years and the study is over 11 years. )

If however the SE estimate is confounded, then what would my next move be? To manipulate the DM to apply biologically appropriate constraints to the corresponding parameters?

Or perhaps look at using the Delta method [MARK appendix B] on two seperate estimations of Survival - one using the data before the large 1101 day gap and one from after. (There was a two year gap in sampling).

Thanks,
Caroline

[Carolinew77]

More information on my data.... and 1st problem solved/question answered.

Time intervals need to be entered at the model selection screen in MARK, otherwise MARK assumes equal time intervals between primary sessions.

When entering time intervals this needs to be on the scale relevent to your question.

I was entering the time intervals in days.... which 0.9998^354 = 0.932/year
I could enter in months which would give me about ... 0.9998^12 = 0.998/year

I have just tried the analysis with years as the time interval and the results:

1:S 0.9857743
SE 0.0047841
LCI 0.9726077
UCI 0.9926599
Which is much nicer.

This was using constant survivial, constant markovian gamma, p=c over time and N.

I will also try applying constraints ( dummy coding for Summers and Winters) on time varying Gamma's and see if that gives me a better global model!

Thanks again!

[cooch]

More information on my data.... and 1st problem solved/question answered.

Time intervals need to be entered at the model selection screen in MARK, otherwise MARK assumes equal time intervals between primary sessions.

...

...most of which is covered in Chapter 4 - sidebar beginning on p. 27. It isn't talked about specifically in Chapter 15 (RD chapter), since the book is structured assuming that all the material in Chapters 1 -> 7 has been read and 'assimilated' before diving into other data types (like the RD). There is also a item in the index to the book specifically pointing to the material in Chapter 4 for 'time intervals'.