## Beginner Question: Model averaging estimates of abundance

Forum for discussion of general questions related to study design and/or analysis of existing data - software neutral.

### Beginner Question: Model averaging estimates of abundance

Hello,

I apologise in advance if this question is very basic, I am new to modelling. I have read several forum threads and manuals but am still struggling in understanding if/how I should approach model averaging for my abundance estimates. I have been working with program Distance to estimate the abundance of local bird populations. In a few cases, a few the models have had very similar AIC values and I wanted to consider the model averaged estimates. From what I understand about the Distance program, it currently can only perform model averaging for key function+series expansion models but not for models incorporating co-variates. Many of our models do incorporate environmental co-variates and so I am left a bit unsure how to approach this problem. Is it appropriate to take the weighted average of the abundance estimates directly? As in, if "w" is the Akaike weight of the model and "abun" is the abundance estimate produced by that model: (w1*abun1)+(w2*abun2)...+(wn*abunn), for example. Would you then approach the CV and 95% CI in the same fashion?

Ashleigh
AWest

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Joined: Mon Feb 04, 2019 5:06 pm

### Re: Beginner Question: Model averaging estimates of abundanc

AWest wrote:Hello,

I apologise in advance if this question is very basic, I am new to modelling. I have read several forum threads and manuals but am still struggling in understanding if/how I should approach model averaging for my abundance estimates. I have been working with program Distance to estimate the abundance of local bird populations. In a few cases, a few the models have had very similar AIC values and I wanted to consider the model averaged estimates. From what I understand about the Distance program, it currently can only perform model averaging for key function+series expansion models but not for models incorporating co-variates. Many of our models do incorporate environmental co-variates and so I am left a bit unsure how to approach this problem. Is it appropriate to take the weighted average of the abundance estimates directly? As in, if "w" is the Akaike weight of the model and "abun" is the abundance estimate produced by that model: (w1*abun1)+(w2*abun2)...+(wn*abunn), for example. Would you then approach the CV and 95% CI in the same fashion?

Ashleigh

Your basic intuition is correct, but constructing averaged CI for abundance estimates is a bit different than for 'other parameters', like say survival. The reason has to do with the fact that abundance is on the interval [0, something bigger than 0], and not noramally distributed (as contrasted with say survival, which is on the interval [0,1], and generally can be handled using normal sorts of CI assumptions, albeit on the logit scale).

Here is what I suggest you do -- read a bit in the MARK book (http://www.phidot.org/software/mark/docs/book/), where this is all laid out in some detail. You're not working with MARK, but in fact, that won't matter at all. The principles are the same.

Here is the sequence of 'reading homework':

Section 4.5, in Chapter 4 -- covers the basic theory about how you model average and (more to the point) construct CI's for parms on the [0,1] interval. The best starting point...

Section 14.10 in Chapter 14, but you can skip through much of it until you come to the subsection 14.10.1, which deals specifically with constructing CI's for model averaged abundance estimates. It carries you through the step-by-step calculations.
cooch

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Joined: Thu May 15, 2003 4:11 pm
Location: Cornell University