Date: Apr 24, 2008 12:04 AM
Author: Seth Myers
Subject: temporal dependence?

Hi,

I'm not sure where to look for help with this problem. I don't even know the right search terms for it.

First let me describe the analysis.

I have land use data from satellite imagery (individual pixels or cells) for years 1985 and 1990. I am recoding development as 1 and non-development (forest, etc) as a zero. I am attempting to predict the probability of transition by cell over these 5 years from 0 to 1 as a function of several variables (slope, etc). I'm quite sure there will be spatial autocorrelation since development breeds new development. I know of ways to deal with this (autoregression, mixed models). I also expect a time dependency, if this is the correct term, for the following reason. Development that occurs in 1986 will affect future time periods and 1987 will also, etc. So, the dependent variables are not independent from each other either in space or time. I do not know from the data what year a particular cell was developed only that it occurred between 1985 and 1990. So, development will occur near other development that occurred prior to it, but I don't know the time ordering other than to say that development either occured before 1985 or between 1985 and 1990.

I can think of a way to do this via simulation by starting at 1985 and assuming a basic relationship between development, past development, and other covariates (like slope). I would then apply this relationship to the landscape as of 1985 to assign probabilities of development. Next, I could develop some cells using a random number generator (creating a binary landscape that is a possible realization of the model) and repeat the process for 1986 and each year until 1990. I could do this many times and see the frequency with which each cell was developed and use this to estimate the likelihood. I could then adjust the functions in an attempt to maximize likelihood. This is very brute-force and I don't want to do it, if avoidable.

Thanks for reading,
Seth