parameter count covariates and additive model

[mthompson86]

Hi,
I am fitting a multi-state model where the general model is phi(site*sex*t)p(trap effort*t)psi(site*t). there are 4 occasions. there are 2 sites as states. sex is a covariate. trap effort is real covariate (#traps). I would like to find out if there is a difference in survival between sites and if both sexes have the same response. i would also like to find out if there are differences in prob of transition between the sites.
i have done my best to try to figure out how to count the number of parameters but i am at a loss. i have read everything there is to read in a gentle introduction about estimating parameters and i am still extremely confused, especially when it comes to additive models.

so, there are a total of 24 total parameters in the general model. however, there is time dependence in phi and p. so for each group (site) there is a confounded term leaving 24-2=22 parameters we can estimate?

as for additive models

phi(site*t)p(eff+t)psi(site*t)
phi(site+t)p(eff*t)psi(site*t)

I am having a hard time grasping how to count the parameters in these models. please help or direct me to some sort of supplemental literature that can help.

**Thank you!**

michelle

[tpuettker]

Hello Michelle,

In my opinion there is something wrong with your count of the number of parameters in the general model. I think that the described structure the model would lead to 30 parameters (24 of which are identifiable):

12 for survival parameters:
6 for each site:
Logit S = intercept + beta1(sex) + beta2(t1) + beta2(t2) + beta3(sex*t1) + beta 4 (sex*t2)

12 for capture probabilities:
6 for each site:
Logit p = intercept + beta1(effort) + beta2 (t1) + beta3 (t2) + beta4(effort*t1) + beta5 (effort*t2)

6 for transition probabilities:
3 for each „direction“:
Logit Psi = intercept + beta1(t1) + beta2(t2)

I´m not totally sure about the number of confounded parameters though, but I think the last survival estimate for each sex and each site is confounded with the capture probability at the last occasion for each site. Hence there are 6 confounded parameters: S3 site1 males, S3 site1 females, p3 site1, S3 site2 males, S3 site2 females, p3 site2.

In relation to the additive models:
phi(site*t)p(eff+t)psi(site*t): taking out the two interaction terms for capture probability at each site leads to 20 parameters

phi(site+t)p(eff*t)psi(site*t): taking out the two interaction terms in survival for each site leads to 20 parameters


Can anybody confirm (or correct) this parameter count?


thomas

[mthompson86]

thank you for your help, its starting to make more sense to me

michelle