# Accounting for Spatial Autocorrelation in ZINB Model?

I'm doing an analysis on disease in Chile. I'm using the rate as the `Dependent Variable` and both remote sensing and housing-type data as the `Independent Variables`. I have several questions regarding my methods:

1. The data appears to follow the zero-inflated negative binomial distribution. I checked with the countfit tool in Stata, and the data best fits this distribution. Is it ok to fit a ZINB model to continuous data?
2. I need to account for spatial autocorrelation in both the dependent, and the remote sensing data. I'm not sure exactly how to do this. After some reading, I thought that I needed to generate a spatial weights matrix (using ArcMap). If this is correct, how do I implement it? I generated one for the disease rate, and used it in Stata: `[pweight = weight]`, which greatly improved the model fit. However, I'm not sure if this is the correct usage.

Can anyone give me some pointers, or readings, or anything? I really want to complete this project!

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I would highly recommend looking into mixed effect models. You could then specify autocorrelation as a random effect. If you would like to incorporate autocorrelation into the estimate then an autoregressive (i.e., SAR, CAR) model is in order. Although, it may be quite tricky specifying spatial regression within in a zero-inflated model (especially in Stata).

You could try spatially lagging your dependent variable and adding it as a covariate but, in a zero-inflated model, it may make the model coefficients difficult to interpret if not down-out erroneous.

I should clarify that zero-inflated models assume that the zeros are generated by an different process than the count values and, as such, are modeled independently. Thus ZIP models have two components (and two sets of coefficients), a Poisson count model and a logit model for predicting the zeros. Because of this a single autoregressive term does not meet the ZIP assumption of separate process generating the zeros as well as working differently in the two types of regressions. Although, once you settle on a method, it should not be necessary to account for autocorrelation in the independent variables.

I would check to see how "redundant" your zero counts are. Often zero-count data can be substantially reduced thus, eliminating the need for a zero-inflated model.

As I already mentioned, your best bet is a mixed effects model or possibly a Hierarchical Bayesian approach. Sorry to be somewhat vague in my response but you are treading on some difficult statistical ground with little in the way of specific solutions. You may want to take a look at this paper "Zero-inflated models with application to spatial count data" before your proceed further.

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+1 Excellent advice. In some applications I have found that the (apparent) need for zero inflation may disappear once enough covariates have been included in the model. – whuber Jan 22 '13 at 19:00
Thanks, Jeffrey. It looks like I have some reading to do! I have been looking at mixed effect models in R, using the "nlme" package. Part of my hypothesis is that the zero counts are a result of the environment (too cold for the vector to survive in the zero-count areas). The variables I'm using for the inflated portion of the model are spatially autocorrelated. One add-on question: is it fine to use a "count model," such as poisson or negative binomial, for continuous data (the disease rate)? – Robert Wardrup Jan 23 '13 at 1:38
@whuber I wonder if your are observing this behavior because you are including a covariate that inadvertently acts as an autoregressive term or accounts for nonstationarity? What would be the effect on the coefficients if this were the case? If the hypothesis being tested is that zeros are generated by a different process, this may not be a desirable outcome. Your assertion seems like it could create a tenuous balancing act between parsimony, inference and fit. However, I find this interesting and would like to hear any insights you may have. – Jeffrey Evans Jan 24 '13 at 17:28
@RobertWardrup Sorry, but a continuous data distribution does not meet the assumption of the process following a Poisson/Bernoulli trial and as such, cannot be used in this type of model – Jeffrey Evans Jan 24 '13 at 17:32