average of detection probabilities

[Eurycea]

I'm trying to summarize detection probabilities that were estimated from a robust design model, and were full time varying (p varied within and between primary periods). For example, it's of interest to know what the average detection probability is for this type of survey.

Is it ok to calculate the arithmetic mean of all the individual p estimates for this?
How do I calculate the SE? Delta method? something else?

Model averaging is not necessary (weight is 1).

I thought about using a simpler p(.) model for this summary, but it doesn't seem right.

[gwhite]

Nathan:
One way to compute the overall mean is to use the 1, -1 coding trick that is documented in the Gentle Introduction (I think).

Gary

[Eurycea]

Gary,

I think I understand what -1, 1 coding trick you are referring to (e.g. ch 15.8) but I don't understand what you mean about using it to compute an overall mean, or even how the design matrix plays into it. Could you elaborate?

Thanks,

Nathan

[cooch]

Nathan:
One way to compute the overall mean is to use the 1, -1 coding trick that is documented in the Gentle Introduction (I think).

Gary

Indeed it is -- chapter 6, sidebar beginning on p. 84. A couple of different approaches are described: the (1,-1) coding trick Gary refers to, and another approach based on a variance components approach.

[cooch]

Gary,

I think I understand what -1, 1 coding trick you are referring to (e.g. ch 15.

There is no use of the (1,-1) trick on p. 8 (or in section of chapter 15. There is use of something analogous wrt building what is known as an 'even flow' model in a robust design, but thats it.

What Gary is referring to (as per my recent reply) is covered in chapter 6 (sidebar on p. 84).

[gwhite]

Nathan:
The first beta in the following design matrix corresponds to the mean on the beta scale of the set of beta parameters.

1 1 0 0 0
1 0 1 0 0
1 0 0 1 0
1 0 0 0 0
1 -1 -1 -1 -1

For a longer discussion, see http://www.cnr.colostate.edu/~gwhite/ma ... vanced.PDF

Gary

[Eurycea]

Awesome, thanks Gary and Evan. Yeah I guess I was looking in the totally wrong spot. The explanation in the book is really helpful. I feel silly for not finding it the first times I looked.

Nathan

[cooch]

Nathan:
The first beta in the following design matrix corresponds to the mean on the beta scale of the set of beta parameters.

1 1 0 0 0
1 0 1 0 0
1 0 0 1 0
1 0 0 0 0
1 -1 -1 -1 -1

For a longer discussion, see http://www.cnr.colostate.edu/~gwhite/ma ... vanced.PDF

Gary

Or (once more, with feeling) in more detail, the relevant sections of Chapter 6 from the 'Gentle Introduction' (basically, Chapter 6 takes the 'Hungary paper' as a starting point, and fleshes it out a fair bit. In fact, the -sidebar- beginning on p. 84 covers 3 different approaches to estimating a mean, and the appropriate SE of the mean).

However, it is worth noting that these methods (as described) still focus on using a single model to generate an estimate of the mean. There is another approach based on model averaging (wherein you generate interval-specific estimate, which you use to calculate the mean -- the SE you have to get using somewhat more involved methods). This isn't covered in the book (yet).

[Eurycea]

Luckily, for me, my single best (used loosely) models are all by themselves with respect to the QAICc, if we aren't counting the models with convergence issues (see several posts down).

Thanks again for your prompt and detailed replies- saves me many headaches. I had tried searching the forums, the book, and WoK...all were fruitless with my keywords of choice. This forum is a great resource.

[cooch]

Luckily, for me, my single best (used loosely) models are all by themselves with respect to the QAICc, if we aren't counting the models with convergence issues (see several posts down).

No - you're missing the point somewhat. You're fitting a new model to estimate the mean -- it might be a different model from the one you've currently identified as 'best'.

Thanks again for your prompt and detailed replies- saves me many headaches. I had tried searching the forums, the book, and WoK...all were fruitless with my keywords of choice. This forum is a great resource.

Good.

However, if you

1. download the book as an entire file (single big PDF file
2. search for 'parameter mean' within the PDF file,

then

3. you'd have found the appropriate sidebar in about 10 seconds (second hit in the file, in fact).

Also, with a bit of 'good luck' (in your forum searches) you'd have discovered that there has been some mention of this on the forum. For example,

viewtopic.php?f=1&t=1193&p=3273&hilit=variance+components#p3273

What I generally recommend is that folks download the 'entire book' (single file) and get used to searching it. In fact, Adobe (and some third-parties) make a number o f tools to allow you to create your own searchable indexes for PDF file(s). There is an index of sorts that we generated for the book, but it isn't as complete as I would like (generating a real index is time-consuming -- you need to wrestle with lots of decisions about what gets indexed, and how...).