Sample Size and Number of Model Parameters

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Hello,

First, so glad to see this forum!

There have been a few discussions here regarding effective sample size (ESS) and the number of parameters that can be reasonably estimated in models. I have always used the most conservative sample size designation - the number of sites - when considering the number of covariates I use in models (yes, well-considered and biologically relevant covariates), but I am interested in alternative ways of thinking about ESS within the occupancy modeling framework. Among these, Darryl has mentioned number of detections and number of surveys at ‘occupied sites’. Therefore, for a modest dataset (e.g., 50 sampling units and 5 surveys), the difference in ESS can be quite large. From most to least conservative:

50 = number of sites (and there was at least one detection at 60% of the sites)
72 = number of detections
150 = number of surveys at occupied sites
250 = number of surveys

I am interested because the addition of the detectability component, p, uses > 1 parameters. Even if you choose a relatively small number of habitat covariates to evaluate Ψ, say 4 with no interaction terms, k could easily be >8 depending on the number of factors you need to model p in addition to Ψ.

Say, you wish to use a ‘rule of thumb’ approach to limiting the number of parameters in models based on the effective sample size. I was wondering what, if any, new developments/discussions there has been on this topic, and the rationale for using each of these approaches. As an aside, I always have used AICc when n/K < 40 which in my case is always!