Question: Does someone know the 'proper' residual from binary logistic regression to use in creating a variogram of residuals if the variogram is to be used to inform the variance-covariance error matrix to account for spatial autocorrelation among residuals in a mixed model? I explain this more below.
I would like to use a mixed logistic regression model to account for spatial autocorrelation. To do this, I would like to use a variance-covariance error matrix in model fitting that is based upon a theoretical variogram with parameters estimated during model calibration. Identification of the proper form of the variogram and start values for its parameters can be accomplished, I believe, by first fitting a logistic regression with only fixed effects and then creating a sample varogram from the residuals. When modeling the probability of a binary outcome using a nonlinear model, especially when the response exhibits a high degree of spatial clustering, it seems there are several challenges. The reponse data (0,1) is highly spatially correlated, so a simple residual of observed minus probability as given by model will give clusters of negative and positive residuals. This is regardless of whether I standardize the residual or not, I believe. Also, there is the problem of how to interpret the residual into a form that could be placed back into the equation for logistic regression. For example, if the predicted probability is 0.5 and the observation is 1, it would require an infinite increase in the sum of predictors*coefficients to increase the probability from 0.5 to 1. So, it seems a 'residual' tacked onto the linear sum of the logistic regression equation is nonsensical and observed values minus probabilities is uninformative. Thanks, Seth
