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
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