biostatistical problem--birds and patch size

#1
I have an interesting statistical problem I'm having trouble solving...here's the story:

I repeatedly sampled birds along 100m-long transects in grassland patches of various sizes. In small patches, I fit a single transect. In larger patches I fit up to 7 connected transects (number of transects proportional to patch size). I'd like to estimate the probability of occurence of individuals of each species as a function of patch size, but:

1. Patches of different sizes have different size samples of transects
2. Transects within a patch may not be independent.

Any ideas?
 
#2
I have an interesting statistical problem I'm having trouble solving...here's the story:

I repeatedly sampled birds along 100m-long transects in grassland patches of various sizes. In small patches, I fit a single transect. In larger patches I fit up to 7 connected transects (number of transects proportional to patch size). I'd like to estimate the probability of occurence of individuals of each species as a function of patch size, but:

1. Patches of different sizes have different size samples of transects
2. Transects within a patch may not be independent.

Any ideas?
Hi Birdman,

Since you sampled multiple transects per patch, and repeated measurements per transect, you've got a mixed model. The assumption is generally that transects within patch are not independent.

I believe you need to use both patch and transect within patch as random factors. But I need to clarify a bunch of things.

I assume patch size is your independent variable of interest. Is patch size continuous or categorical (i.e. small, medium, large).

Is your dependent variable whether or not a bird of a specific species was found on a given transect on a given day? Or the number of birds of a specific species?

At first glance, this looks a bit complicated, and may be beyond email (at least for me to explain). It can be difficult to specify mixed models correctly (and easy to specify them incorrectly :)). I would need to understand a lot of details.

Do you have experience with mixed models? And what statistical software do you plan to use?

Karen
 
#3
Karen,

I have been treating patch size as a continuous variable, but I could change it to a categorical variable for this analysis if there are no other options.

Since each patch was visited 2 times, the dependent variable could be: 1) the probability that an individual of the species was detected, 2) whether or not it was detected (0 or 1) and/or 3) its relative abundance (abundance per transect).

I have some limited experience with mixed models. but am wouldn't call myself capable. Your input is deeply appreciated.

Bruce
 
#4
Hi Bruce,

I think it's okay to keep patch size as continuous. My initial concern (and I haven't figured out yet if it's valid) is that if patch is a random factor, you have to specify it in the model, but the patch size, which is also in the model as an IV, would be confounded (since each patch size has only one patch). If patch size is categorical, there will be multiple patches per size.

Anyway, you have a 3 level model, since each there are multiple transects per patch and two visits per transect. You have two further complications. 1. some patches have only one transect (no variance for that patch) and 2. your DV is not normally distributed. Whether you use a binary or count DV, you're talking either logistic or Poisson regression. Either way, you have to use GEE, not regular mixed models theory. I'm not completely up on this off the top of my head, but there are limitations in GEE. I don't know if it's just software limitations or GEE theory, but I think it's tricky beyond a two level model.

Which software do you use? It might affect your options for how you analyze it. I am most familiar with SAS for mixed models, including GEE, but I believe that Stata has more flexibility in what it can do.

Karen
 
#5
Karen,

Thanks so much for your thoughts. I only have spss right now, but I have experience programming in SAS. I will get ahold of whatever software will work best to get the job done if the technique demands it.

Bruce
 
#6
Hi Bruce,

I don't mean to imply that you should get SAS--it's just what I'm more familiar with. SPSS can do mixed models and GEE. I just haven't done them. But if you can find someone who does, that's probably your best bet.

You don't want to learn SAS at the same time you're learning a relatively compliated statistical technique. :)

Karen