Number of parmeters in nest survival analysis

[Lutfor_Rahman]

Dear Forum members,

I was doing nest survival analysis using MARK and develop two models nest survival constant and nest survival varies over time. I have 40 data points (40 nests were observed 127 days during the season). I am having number of parameter 1 for constant survival model S(.) (which is fine); but I am getting number of parameters 95 for time varying survival model S(t). could any one please explain why that number coming automatically though i don't set number of parameter and how to calculate number of parameters in a model.

best regards
Lutfor

[gstauffer]

Are you expecting 126 parameters? If you are trying to estimate time-varying daily survival without placing some constraint on time (e.g., a linear trend), then I suspect that your data are too sparse and that MARK is not counting all the parameters specified in the PIM or the DM.

[Lutfor_Rahman]

Thank you for your response. I am not sure how to calculate number of parameters but I would expect 126 (Number of days nest monitoring done in a season-1). I arbitrarily chose 1 April as start of season (Day 1 of season) and last nest monitoring done on 127 days after 1 April though my study species have 80 days nesting period. I am sure that 80 nesting period is not related with my number of parameters. I was trying to develop time varying model without putting any constraint on time varying model. However, could you please shed a little light what is the difference between nest survival varies with time S(t) and constant nest survival with linear trend as co-variate, S(.)+linear trend. Number of parameters should be 2 in later model. Am I right?

Thanks again
Lutfor

[gstauffer]

The number of parameters should be the number of columns in your design matrix.
So, if you try to estimate unconstrained time variation (S(t)), you'll likely have either an identity matrix or a DM with reference coding. Either way, your DM will have 126 columns and MARK will have to estimate a parameter for each column. Many of these might not be estimable because of data sparseness, and consequently, when MARK tries to count the number of parameters it will come up with something less than 126 - it counts only the ones it thinks are estimable. See the addendum in chapter 4 of the MARK book for an explanation of how MARK counts parameters.
If you estimate a logit-linear trend model (S(T)), you are correct - you will have an intercept and one additional beta parameter to estimate the slope of the relationship between time and the logit of survival. This might be a reasonable model if you expect some systematic change in survival over time, e.g., increasing vegetation hides nest from predators (survival gradually increases), or predators learn over time to find nests (survival decreases), etc.