Hi everyone,

This is a bit long-winded, but I respect everyone's mind on this list and would like any criticism and suggestion, if your time allows.

I would like to include a spatially-lagged variable in logistic regression in order to decrease some autocorrelation problems in a land-use change model.  The model is for the probability of a cell not developed in 1985 becoming developed by year 2006.  I would like to use Moran's I to estimate my spatially-varying weights.

The problem is this: I am modeling the probability of land becoming developed from 1985 to 2006 (to capture contemporary dynamics) but developed land pre-1985 likely has an influence, and, so, there is a mismatch between the areas having an influence and the response.  For background, the response is binary (0=undeveloped, 1=developed).

I could just calculate Moran's I for all areas, but this would also include the autocorrelation of cells developed pre-1985 with other cells developed pre-1985  (which is not of interest for several reasons including that the areas developed long ago were influenced by 'accidents' of history which are wholly unobservable, plus the decision-making process for land development changes over time).  I could just calculate Moran's I on the increment of growth from 1985 to 2006 (masking out pre-1985 developed areas) but this would neglect a source of contagious effect.

My possible solution is this.  Allow, cross products in the numerator in the usual manner between observations in the recent growth increment (1985 to 2006) but add a restriction that cell values for pre-1985 growth (minus the mean) are only multipliled with the cell values of the current increment (0=not developed in 1985 or 2006, 1=not developed in 1985 but developed in 2006).  So, I am trying to get at how autocorrelated the new increment is with itself and the previous growth (but not previous growth with itself).  The mean for use in subtraction would possibly be the mean over all cells in the lattice.  This seems in a sense to be the cross-correlation between: 1) all developed cells and 2) cells potentially developed from 1985 to 2006 (the response).   When stated this way, it seems that possibly two means should be used (all development and current increment), ala' the usual covariance and cross correlation formulation.

Seth Myers
PhD Candidate
SUNY ESF


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