log likelihood in scatman

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log likelihood in scatman

Postby R.S. » Fri Jul 16, 2010 8:16 am

Hi there,

I am working on diet analyses from scats and my situation is somewhat similar to the Karanth and Sunquist paper on prey selectivity in tigers, leopards and dholes (1995) in that I have scat frequencies as measure of resource use and intend to calculate the expected proportion of field collectable scats per prey species under the null hypothesis of no selectivity for comparison. I saw that SCATMAN does all the necessary selection statistics on these data, but have some questions:

1. Is there a reason why SCATMAN uses the Chi² statistic instead of the log-likelihood statistic advocated by Manly (2002)? My data fulfill two of the characteristics Manly names as causing different results between Chi² an the log-likelihood (small expected frequencies - 1 of 4 below five - and considerbale differences between observed and expected frequencies), so I wonder whether that could pose a problem.

2. Is there an available R code for the procedures implemented in SCATMAN (I always find that helpful to fully understand what's happening)?

3. As I have a small sample size (33 scats) with an uneven distribution of frequencies across four prey categories, three of my observed and one of my expected frequencies are below 5. Can anyone tell me whether in this case the bootstrapping implemented in SCATMAN is a reasonable approach to evaluate results, or whether it would make sense and be possible to re-do the analyses with a Fisher's exact test?

Thanks so much to all of you already; I hope I don't repeat what has already been asked, but I couldn't find a single SCATMAN related entry in this forum.

cheers,

Rahel
R.S.
 
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Re: log likelihood in scatman

Postby jhines » Fri Jul 16, 2010 1:47 pm

Rahel,

I asked Dr. Bill Link to look at your question and he had the following reply:

I had a look at the questions. It's been a long time since SCATMAN was born, and I think I'd do the analyses quite differently these days, especially given Rahel's small sample sizes. We need to write program SCATBAYESIAN, especially if there are many folks still using SCATMAN.

Regarding question about chi^2 versus G^2: these are asymptotically equivalent; I know of no reason to favor one over the other for small sample sizes (and doubt there is any). I'm not sure about the bootstrapping in SCATMAN -- I believe it was a parametric bootstrap -- and if so, it is a reasonable albeit imperfect approximation, just like most frequentist procedures. It shouldn't make any difference whether one uses chi^2 or G^2.


I don't know of any R-code to mimick what SCATMAN does. It probably wouldn't be difficult to convert the code, but after seeing Dr. Link's comments, it probably wouldn't be worth the time investment.

Jim
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Re: log likelihood in scatman

Postby R.S. » Fri Jul 16, 2010 1:52 pm

Thanks a lot for your quick reply, Jim, and my thanks to Bill Link, too. I see what I can figure out in terms of analysis of the data.
Cheers,
Rahel
R.S.
 
Posts: 10
Joined: Fri Dec 11, 2009 6:47 am

Re: log likelihood in scatman

Postby R.S. » Wed Jul 21, 2010 9:46 am

Hi Jim and Bill,

in an attempt to consider your previous post, I tried to analyse the data in WinBUGS. Don't worry, this is not a BUGS related question, I know that's not the right place, but I'd just really appreciate a comment on my approach:

I had my observed scat counts come from a multinomial ditribution with parameter vector p[] and n=33 (my sample size).
I used a Dirichlet prior with alpha = c(1,1,1,1) on p, as I had seen before for a two-category example.

For each MCMC iteration I drew lambda (=number of scats per individual consumed) from a normal distribution with a SD of 0.4*(mean(lambda)) and prey abundance from a normal distribution with mean and SD obtained from my field data, multiplied these values and calculated expected proportions, pex[] (i.e. scaled values of prey categories to sum to 1). Finally, I calculated the difference in oberved and expected proportions as p-pex and looked at the posterior of these differences.

As I said, I am rather new at this, so I feel like I am overlooking something. Also, what bothers me is that I had to round my observed scat frequencies to integers (I have non-integer frequencies because some scats contain more than 1 prey species).

I'd really thank you for any comment,

cheers,

Rahel
R.S.
 
Posts: 10
Joined: Fri Dec 11, 2009 6:47 am


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