# Probability of event modeling help needed

1. Nov 4, 2009

### wvguy8258

Hi,

I have a data set where temperature and precipitation were monitored for a series of days at 5 ephemeral freshwater wetlands on various years (i.e. each wetlands was in a different spot (state even) and was monitored for a slightly different time period in any one year/wetland). Over this time period, the number of amphibians that entered each wetland for breeding was also recorded for each day. The size and sex of each animal was recorded as well. The monitoring of each wetland began significantly (1 month) prior to when it is reasonable to think that any amphibians had entered the wetland, so it is assumed that no animals were missed (they do not move for the breeding migration until the soil has at least thawed). So, I know the total number of amphibians that used the wetland that year (they breed only once), when they traveled to it, and the conditions on that day and prior. For each wetland, I also know its latitude/longitude, surrounding forest cover, and elevation.

I would like to do the following: for an amphibian that is known to breed in a certain year that is of particular sex and size, given site characteristics and weather of a certain day (and also prior days such as using a lagged variable or a cumulative one (degree days concept)), what is the probability that this day in question is the day of breeding migration to the wetland. Logistic regression seems the obvious choice right off. But since each animal only breeds once, once they do this, they are not eligible again. Is there a defensible way to formulate a logistic regression model so that as animals breed they are removed from consideration in the likelihood formulation used to estimate parameters? I've considered using survival/time-to-event analysis but the time of 'birth' in each year is not obvious while time of 'death' would be the day of migration. I suppose some type of technique for censored data could be employed. Any thoughts? Further, time is not so important, at least according to most theory. If several warm rainy days happen, animals will likely migrate, whether this happens in january or not until march. Any help is appreciated. A little more information, the amphibian in question typically migrates to the same wetland for breeding each year (where it was hatched) and individuals often skip breeding seasons (e.g. they could not consume enough to yolk eggs).

Seth

PS looking at the way survival analysis models are formulated, it seems they may be quite similar to a logistic regression model where individuals are removed from consideration once the event occurs

Last edited: Nov 4, 2009
2. Nov 5, 2009

### bpet

Abstractly, sounds like you want to estimate a conditional distribution (conditional on several random or non-random variables). Before doing this, what techniques do you have to visualize the multi-dimensional data set?