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st: migration analysis


From   Seth J Myers <sjmyers@syr.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: migration analysis
Date   Thu, 17 Dec 2009 18:51:07 +0000

 Hi,

I would like to analyze the following while steering clear of Bayesian approaches, if possible.  I have records of the migration of individual salamanders (30 or more salamanders per site) to several breeding sites (small temporary pools) in different US states.  There is typically a population of animals that live underground near a breeding site most of the year and a subset of these migrate to the nearby pool to breed once in early spring.  The stimulus to breeding migration is typically temperatures above freezing and some rainfall, so that they do not freeze or dry out while traveling.  However, the triggers to migration have not been well quantified.  At the several sites, traps were erected to catch every salamander attempting to enter a particular site.  The traps were checked daily.  Trapping began well before any animals would begin to move and ended well after the breeding season ended, so no animals escaped notice.  For each salamander captured while migrating, t!
 he sex of the animal is known, its mass and length, the min/max/average temperature on the day it was captured, and the amount of rainfall on that day, and (obviously) the day of capture is known.  The sites differ in longitude and latitude, surrounding vegetation type, elevation, and topographic aspect (among other differences).  So to visualize, for each location, I could plot the number of males and females captured each day, their body characteristics, and the meteorological conditions of the day.

My knee jerk first idea was logistic regression then I considered survival (time to event) analysis, but neither seem like quite the correct method.  A simple, arbitrary data set would be as follows.  Assume that temperature is constant across the five days (the entire duration of the breeding migration period) and rain (the only variable to consider in this example) increases from 1 to 5 units by 1 unit each day and that a total of 20 animals migrate.  Please forgive the simple example.

day 1 = 3 animals move in
day 2 = 4 " "
day 3 = 5 " "
day 4 = 6 " "
day 5 = 2 " "

For each day, the proportion migrating that can (have not yet done so would be the following).

day 1 = 3/20 = 0.15
day 2 = 4/17 = 0.24
day 3 = 5/13 = 0.38
day 4 = 6/8   = 0.75
day 5 = 2/2   = 1.00


If I were just modeling this population with day and rain amount as the predictors, it is unclear how I could use logistic regression because individuals are removed each day from the sample.  If I modeled this as proportions, I'm unsure how to reflect that the sample size is diminishing and so the proportions toward the end should be weighted less.  Survival analysis seems tricky here because the start of the period of migration differs by breeding site, and I believe the underlying hazard rate (which I'm interested in describing) is removed in common techniques.  Perhaps a panel data analysis is in order.  Anyways, if you can think of a similar situation or have advice on techniques to look into, I would appreciate any suggestions.

Seth

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