1. Jun 14, 2009

### wvguy8258

Hi,

Does anyone have advice on a good statistical model for the following? I have a dependent variable that is the day that something occurs for an individual. It can occur on any of X number of days for any of Y individuals. It occurs once for each individual, so once it happens the probability of it occurring again is zero. There are a set of independent variables for each day and individual. I would like to model this as a probability that an individual has the occurrence on a specific day, so this would have to take into account what has happened before. I do not believe that logistic regression will work, because of the fact that once the occurrence happens, that individual is out of the data set. Perhaps a multinomial logistic regression with the reponse being day of occurrence and a set of cumulative independent variables to keep track of what happened previous to each day. I do not think a survival/time-to-event analysis is appropriate because time in this case doesn't matter. If conditions for an occurrence are right on day 1, the fact that it is only 1 day into the study doesn't matter.

By the way, the study is looking at factors that contribute to the timing of first migration to breeding ponds during a year's breeding season of a breeding population of a species of amphibian. All animals in the study (those observed to have migrated to breed) are known to have bred that year. It is common knowledge that warm temperatures in early spring with rain cause this migration, but no good analysis has been done so far using several data sets from different years and geographic locations. Thanks. -seth

Last edited: Jun 14, 2009
2. Jun 15, 2009

### EnumaElish

What you described ("a multinomial logistic regression with the reponse being day of occurrence and a set of cumulative independent variables to keep track of what happened previous to each day") sounds right.

One place you might look at is the marketing ("sales") literature. I am not very familiar with all aspects of it, but I know that they've used models like this that track cumulative sales growth. There may be other variants that track an individual's disposition to make a purchase, and the timing of it.