Indiv. heterogeneity with mixtures - unrealistic estimates

[howeer]

When using full closed capture with heterogeneity models and sparse data sets, models including heterogeneity often ranked as or among the top models, but parameter estimates were unrealistic: the estimates of pi were low and imprecise, and p estimates for one of the mixtures was very (unrealistically) low, leading to unrealistically high (and imprecise) estimates of N. So, I am stuck with a situation where the best-supported models yield parameter estimates that are obviously incorrect, and am unsure how to proceed.

Is there a way to restrict the range of possible capture probabilities in each mixture, or limit the difference in capture probabilities between mixutres (as in program capwire), to avoid getting unrealistic p and N estimates from those models?

[ganghis]

Hi Eric,

Not really sure exactly what Capwire does here, but there is no way to constain the pi's and p's in MARK that I know of short of setting them to fixed constants or specifying prior distributions in a Bayesian analysis. However, I would think twice about using the mixture formulation with sparse data sets (btw, how sparse is sparse in your case?). While mixtures might perform well in certain circumstances, they don't have good power for detecting heterogeneity when the number of capture occasions are low (<6 for example). Also, as you found, there can also be some numerical instabilities.

Is there an individual covariate you could use that might explain some of the heterogeneity? If so, Huggins models might work well... if not, and you do expect a fair amount of heterogeneity, you might be better off using one of the nonparametric estimators (Chao, jackknife, etc.) available in CAPTURE.

Unfortunately, numerical instability comes up fairly frequently in abundance analyses when dealing with sparse data sets. My usual approach is to delete all models where this is suspected, but you'll want to report that you did this if you do delete any models. You might also argue that this was why you went to a nonparametric model.

Cheers, Paul Conn

[howeer]

Thanks Paul!
I had only 4 encounter occassions, and quite a few animals captured only once, so I guess my data are pretty sparse. The data comes from barbed-wire hair snags for black bears, so there is no additional information on the animals to use as individual covariates.... so, I appreciate your comments and advice about potential inappropriateness of the mixture models in this case - For my preliminary report, I presented complete model selection results, explained the problem with the high-ranking mixture models, and presented abundance estimates from models that had less AIC support than models with heterogeneity, and/or from nonparametric heterogeneity estimators in CAPTURE.

One more thing... does high AIC support for those models with unrealistic estimates (i.e. with numerical instability) really indicate that there's individual heterogeneity in the data, or are model selection criteria for those models as unreliable as the estimates?
eric

[Paul Lukacs]

Eric:

In the absense of lots of data, individual heterogeneity, low capture probability and misidentification all appear as an overabundance of encounter histories with only a single observation. One or more of those are likely in your data. Model selection criteria don't have much information to use in that situation.

Capwire essentially trades estimating the mixture parameter for an assumption that you know the group to which an individual belongs. Thus, the increased precision is merely an artificact of a stronger assumption.

Paul Lukacs