Goodness of fit for multi-state model in U-CARE

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

Goodness of fit for multi-state model in U-CARE

Postby mariadzul » Tue Jan 07, 2014 4:08 pm

Hello,

I am currently running a multi-state model using RMark (a package in R that calls upon Program MARK) and using U-CARE to assess goodness of fit. I am studying how survival and movement of humpback chub vary spatially along the Little Colorado River, which is a tributary to the Colorado River. The ‘states’ in the model correspond to sites along the Little Colorado River. There are three sites: Boulders (the most downstream), Coyote (mid-stream), and Salt (the upstream site). I had a few questions concerning using U-CARE to assess goodness of fit and estimate c-hat:

Q1: I can’t seem to figure out how to account for unequal time intervals in U-CARE. I’m not sure whether it’s important to account for unequal time intervals for any of the chi-square GOF tests.

Q2: My initial results (that don’t account for unequal time intervals) show that Test 3G is close to significant (p=0.06), indicating there might be transience in the population. When I look at the individual tests, this result seems to be driven by Boulders site, which has p-values< 0.05 for both 3G.R and 3G.M. Boulders site is adjacent to the Colorado River, and it is therefore not surprising that fish sampled at this site have a higher probability of emigration from the study area. Furthermore, estimates of apparent survival are lower at Boulders site compared to the other two sites. Here are my options as I see it:

1) Keep the current parameterization of the model (that does not include an effect for transience), and say that the differences in apparent survival among sites might be influenced by increased emigration at Boulders site.

2) Restructure the model to account for transience at Boulders only.

3) Restructure the model to account for transience at all sites.

I don’t really know if 2) or 3) are options because this model only has two “cohorts.” In other words, we only marked fish in the first two sampling occasions, with the remaining four occasions used for recapture information only. Thus, occasion 2 is the only time when both newly marked and previously marked individuals are both present in the population. Since there is no way to estimate ‘p’ for newly marked fish during occasion 2 (this model is fully parameterized for capture probability), I can’t really think of a good way to compare capture probabilities for newly marked and recaptured fish during occasion 2.

Thanks,
Maria
mariadzul
 
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Re: Goodness of fit for multi-state model in U-CARE

Postby Guillaume Souchay » Mon Jan 13, 2014 7:35 am

Hi Maria,

Q1: I can’t seem to figure out how to account for unequal time intervals in U-CARE. I’m not sure whether it’s important to account for unequal time intervals for any of the chi-square GOF tests.

Maybe Remi could confirm it but I don't think that unequal interval time is really important for GoF tests.

Q2: My initial results (that don’t account for unequal time intervals) show that Test 3G is close to significant (p=0.06), indicating there might be transience in the population. When I look at the individual tests, this result seems to be driven by Boulders site, which has p-values< 0.05 for both 3G.R and 3G.M. Boulders site is adjacent to the Colorado River, and it is therefore not surprising that fish sampled at this site have a higher probability of emigration from the study area. Furthermore, estimates of apparent survival are lower at Boulders site compared to the other two sites. Here are my options as I see it:

1) Keep the current parameterization of the model (that does not include an effect for transience), and say that the differences in apparent survival among sites might be influenced by increased emigration at Boulders site.

2) Restructure the model to account for transience at Boulders only.

3) Restructure the model to account for transience at all sites.

Transient issue involved the survival parameter only. To account for this effect, you can either add an age-effect in survival for your 3 sites or only for Boulders sites. Another way to deal with transient is to add a state "alive and emigrate" and individuals in that state can't not be detected and can't come back to one of the 3 sites. This state is thus an unobservable state, see more details in Henaux et al 2007 J Avian Biology 38:44-57or Lebreton et al 2009 Advances in Ecol Research 41:87-173.

Since there is no way to estimate ‘p’ for newly marked fish during occasion 2 (this model is fully parameterized for capture probability), I can’t really think of a good way to compare capture probabilities for newly marked and recaptured fish during occasion 2.

I may miss something in your question. If you want to compare capture probabilities of just marked vs old marked individuals, you should add an age effect, but I don't get the relation between this and the transient effect.

Hope this could help.

Cheers,
Guillaume
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