Stage specific nest survival

[Rebecca]

Hi,
I'm currently using the Nest survival model in MARK. I know from already analysing my data using a stage-specific model in SAS (Stanley 2000) that nest 'stage' (incubation or nestling) is an important factor in modelling nest success. Since I cannot use continuous covariates in this method I want to run the analysis in MARK. Am I correct in finding no way in having a plain stage model (k=2k) rather than "age+stage" (k=3) with the recommended system (from the help file on design matrix functions), as the stage column (which uses the "greater than" function) depends on having the age column.

thank you

[cooch]

Hi,
I'm currently using the Nest survival model in MARK. I know from already analysing my data using a stage-specific model in SAS (Stanley 2000) that nest 'stage' (incubation or nestling) is an important factor in modelling nest success. Since I cannot use continuous covariates in this method I want to run the analysis in MARK. Am I correct in finding no way in having a plain stage model (k=2k) rather than "age+stage" (k=3) with the recommended system (from the help file on design matrix functions), as the stage column (which uses the "greater than" function) depends on having the age column.

thank you

Not sure what you mean, exactly. Having a mixed factorial/linear covariate model in MARK is straightforward. If this is what you want, I'd suggest reading the nest survival chapter (14), and (more specific to design matrices), the linear models chapter (chapter 7). Your reference to the help file suggests that perhaps you didn't.

[gwhite]

Rebecca:
The Stanley method assumes you don't know the exact day at which a nest would transition from one stage to the next. The method in MARK assumes you do know that day, i.e., that you are able to age nests and specify the day that the nest would hatch. Thus, you have to supply more information to the method used in MARK. Assuming that you used the Stanly method because you don't know the exact day of transition, then you probably should not be using MARK. However, if you do know these days of transition, then you can use the design matrix functions and an age covariate to model different daily survival rates for each stage.
Gary

[Anton Antonov]

Hi Gary and all the guys you’re working with!

I’m quite new at using MARK and completely new to this forum. Perhaps you’ve heard this thousands of times but I feel the need to say it again: Congratulations and admirations for the monumental work you’ve done!!!

Now to the point. I join Rebecca with the problem of modeling stage (egg vs. nestling) in nest survival analysis. I have read the relevant chapters (7, 12 and 14) as well as the help info on design matrix functions, where you actually provide an example how to model stage for a passerine, i.e. the same kind of problem I’m concerned with. Let’s focus on this example. Very nice, but as Rebecca points out, there is the problem of having to have 2 columns instead of 1 column in the design matrix. It is because in order to use the appropriate function (ge in the example you provide), which returns stage (0 or 1) depending on whether the current nest age is greater than or equal to a specified age of transition (15 days in your example), we need to have an age column. The problem could be solved if there had been a possibility to apply the ge function in the following compound manner (as in Excel for instance): ge(add(AgeDay1, n), 15), where the function only depends on the individual covariate (age of the nest at the first day in the nesting season) we have specified in the INP file. Unfortunately, when I write this expression, an error occurs (it says something with the floating points :o). It would be so nice if a greater flexibility could be achieved with the application of design matrix functions. So, following the example in the MARK help file, we eventually end up with having the model B0+B1xAge+B2xStage, instead the model B0+B1xStage, which we want!
One possible solution to circumvent this limitation I can think of is the inclusion of individual covariates representing each day of the total time span of the data which indicate for each day whether a nest is at the egg stage (to say coded as 1) or at the nestling stage (coded as 2) or its individual history has not begun or ended (coded 0). I’d like to ask you: 1) Is this approach correct? 2) Is the coding (0, 1, 2) appropriate?
Assuming that I’ve been correct, there’s one more subtlety. If a nest is successful, coding its stage this way for each day is straightforward. But what if it was destroyed to say somewhere within a period of 5 days? According to the Mayfield method, we’d assume the failure occurred midway. Thus the days after the failure but still ‘captured’ in this interval remain ‘questionable’ (at least to me :-))) in terms of stage coding. Should I code ALL the days of this interval with the appropriate stage the nest was before destruction (with 1 if the nest was destroyed during incubation and was not due to hatch in the interval) or put 1s for the first two days only, and 0s for the remaining three days?!
I’d like to apologize if I’m asking stupid questions, but I’m pretty sure that many others are bothered by exactly the same problems but are not asking! :roll:

Thank you in advance!

[gwhite]

Anton:
Responses below.

GCW> You're right that you can't have multiple functions in the design matrix, such as your example "ge(add(AgeDay1, n), 15)". You have to code the covariates directly in the input file. I've been thinking of a way to do multiple functions, but haven't been able to test it out yet.

"One possible solution to circumvent this limitation I can think of is the inclusion of individual covariates representing each day of the total time span of the data which indicate for each day whether a nest is at the egg stage (to say coded as 1) or at the nestling stage (coded as 2) or its individual history has not begun or ended (coded 0). I’d like to ask you: 1) Is this approach correct? 2) Is the coding (0, 1, 2) appropriate?"

GCW> Your idea is correct, but I wouldn't code the nest stage as a single ordinal covariate. Rather, I would use 2 covariates to code the 3 stages. Code the egg stage as 0 0, the nestling stage as 1 0, and the third stage as 0 1. However, I'm not clear on what this third stage is all about. Anyway, the point is to code the stages with 0,1 dummy variables, with 1 less dummy variable than there are stages, just like how you code 0 and 1 values in the design matrix for other discrete categories.


"But what if it was destroyed to say somewhere within a period of 5 days? According to the Mayfield method, we’d assume the failure occurred midway. Thus the days after the failure but still ‘captured’ in this interval remain ‘questionable’ (at least to me :-))) in terms of stage coding. Should I code ALL the days of this interval with the appropriate stage the nest was before destruction (with 1 if the nest was destroyed during incubation and was not due to hatch in the interval) or put 1s for the first two days only, and 0s for the remaining three days?! "

GCW>Assume for my answer to this question that you have only 2 stages, egg and nestling. Further, assume you have a 0,1 covariate coded in the encounter histories file that is called 'nestling', and is 0 for the egg stage and 1 for the nestling stage. To keep it simple, assume 10 days of egg stage and 10 days of nestling stage, so you would have individual covariates values for each day of the study. For a nest that was checked at age 8 and again at age 13, and was destroyed during this interval, the likelihood would be 1 - S(8)S(9)S(10)S(11)S(12). S(8), S(9), and S(10) would all have zero values for the nestling covariate. S(11) and S(12) would have the additive effect of the nestling covariate because these daily survival rates would have a 1 for the nestling covariate. Thus, you never have to assume that the failure occurred during the midpoint of the interval, like the Mayfield estimator does. Doug Johnson first demonstrated this likelihood back in 1978 or so, and Jon Bart refined it further in 1982.

Gary

[Anton Antonov]

Thank you very much Gary for your fast and detailed reply!!!

Now things just work perfectly (both in my head and in the dataset ))and I'm very happy.

[Anton Antonov]

Dear Gary and all who may be concerned,

Suppose we have a 70-day nesting period over which nest data are collected and a passerine with 15 days egg period and 11 days nestling period. My intent was to see if there are stage-specific differences in DSR. First, I analyzed stage specific DSR with the Mayfield estimator and tested the difference between stages by the method developed by Johnson (1979). A highly significant difference appeared, DSR being much higher at the nestling stage. Obviously, by applying a corresponding model in MARK (B0 + B1Stage) I expect to find similar results if everything is OK.
As we discussed it previously, I have to add individual covariates for stage of each nest for each day of the 70-day nesting period (named stageDay1….stageDay70). In my example, as I have asked in a previous posting, I’ve coded age as Gary advised me with “0”s for egg stage and “1”s for nestling period for each of the 70 days. I applied 2 approaches to code the days before a nest’s individual history entered the 70-day period (PRE-days) and the days after it was no more active in the 70-day period (POST-days):

Coding 1) PRE-days filled with “0”s and POST-days filled with “1s” (if there were any nestling days before the nest became inactive due to either fledging or failure).

Coding 2) PRE-days filled with “-1”s and POST-days filled with “-1”s. In the chapter of Nest survival of the MARK book Dr. J. Rotella explains that a nest does not enter the likelihood until the value of a covariate is “0”. This second coding seems to me better and more natural.

Please, comment on how each of these two types of coding would affect estimates. Which one is theoretically better? I noted that both types of codings yielded similar estimates of stage specific DSR but the second one resulted in DSR values closer to the estimates derived from the Mayfield estimator.

Second, NO MATTER THE CODING ABOVE, we end up with 69 estimates for survival for a 70-day period (day 1=the first observation day with any nest content of the earliest nest), so we have to leave out one of the potential 70 stage covariates, when we fill the design matrix. The question is which one – the first one or the last one? I have tried both ways with my dataset and ended up with very much different results when I filled the design matrix this way:

B1 B2
1 stageDay2 1:S
1 stageDay3 2:S
1 stageDay4 3:S
.
.
.
1 stageDay70 69:S

AND this way:


B1 B2
1 stageDay1 1:S
1 stageDay2 2:S
1 stageDay3 3:S
.
.
.
1 stageDay69 69:S

With the first design matrix estimates of DSR for each stage were very nice, i.e. very close to the ones derived from the Mayfield estimator and a highly significant effect of stage on DSR as should be. With the second design matrix, I got a nonsense (survival decreased with age and no significant effect of stage, CI included 0).

The first coding is intuitive to me as day 1 of the 70-day nesting season is the starting point so we do not have survival parameter at this day, yet why the results are so dramatically different?

Thanks,
Anton

[gwhite]

Anton:
You should get exactly the same beta estimates from either coding -- because the individual covariate values before or after the nest exists never enter the likelihood.
One way that you might have errored is that you used the MARK option to standardize the covariates -- DON'T do that. You want the coding to be just 0 and 1, not the standardized values. If you standardize, the the different covariates will each standardize differently, and as a result, you end up with each covariate having a different impact on the beta estimate.
You will see differences in the real estimates from the different coding conventions if you don't specify user values. In other words, if you use the mean or the first record to compute the real estimates, the -1 values will affect the real estimates. Thus, I would not advise using the -1 coding, even though it makes it easier to see where the nest existed.
You should code the input file both ways and prove to yourself that you get the same likelihood value and the same beta estimates, but different real estimates, and then make sure you understand why.
Gary