I take it from your question that you are interested in residual spatial dependency when modellling discrete outcomes but have only found  papers that condition on geographical coordinates.

There is such a literature - which for  technical reasons often uses a probit approach - see

http://www4.fe.uc.pt/spatial/doc/lecture5.pdf

You could also look at the last chapter of https://www.researchgate.net/publication/260772180_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_2

CHapter  16 has the final example of Self-rated health of the elderly in China: the response is whether an individual is in good as opposed to fair/poor health. The model is a binomial logit model based on individual survey data with additional spatial effects between Chinese provinces.

Book Developing multilevel models for analysing contextuality, he...

I have calculated the spatial autocorrelation via "Morans I " to revealing neighbor effect in spatial data. You can refer to the Fortheringham's book about Geographical weighted regression. He well show that how can reveal spatial auto-correlations using the GWR.  

This might be worth a look, especially chapter 2.

http://link.springer.com/book/10.1007/978-0-387-21811-3

http://link.springer.com/book/10.1007/978-0-387-21811-3

Standard Logistic Regression is a technique that allows to look for a functional relationship between dependent continuous variables with a response that is categorical binomial (two possible cases), It is used to determine the probability that a measurement point belongs to one of the two classes. If the numbers of classes is more than 2, in this case the Multinomial Logistic Regression must be used. If the objective of your research is different from the objective described before, may be you will need to use a different techniques. I am interested in how to apply Logistic regression, in other areas and I would be happy to get more information on how this technique has been used.

Gianmarco, have you looked into Spatial Logistic Regression? There is a good R function slrm written by Adrian Badderly which can do this. It's in the spatstat package.

Are you working with xy presence/absence data for you dependent variable? If so, the slrm function works by converting the point data to a binomial raster (1's where the events are located, zeros elsewhere), and the independent variables are also converted to raster format. I used a GIS to do the preprocessing, and then loaded the files into R and presto. Once I had the coefficients, I went back into my GIS program and used raster math to create a final map. You can color the map using whatever threshold is appropriate for your data

I can give you more details on how I've used this if you wish.

Hello All, and thank you for your prompt feedback. First of all, I wish to make one of my point clearer: I was not referring to Trend Surface Analysis. Rather, as @Ingrid Luffman noted, I was referring to the issue of spatial autocorrelation which hamper one of the main assumption of, e.g., Logistic Regression since the latter (as many other statistical approaches and tools) relies on the independence of the observation.

That's way I was asking about strategies to cope with autocorrelation in modelling geographic data. In this respect, one of the simplest approach I have found so far is to include geographic coordinates as covariates in the model (see the article by Hu and Zo, that I cited in my original thread). In other (more complex) instances, an 'autocovariate term' is added to the model again as covariate: see, for example, Latimer AM, Wu S, Gelfand AE, Silander JA. Building statistical models to analyze species distributions. Ecol Appl. 2006;16: 33–50. doi:10.1890/04-0609, besides the other one that I already cited in my original thread.

Now, as far as ArcGIS is concerned, I find quite straightforward to implement the first (more simple) approach, i.e. coordinates as covariates. As for the 'more complex' approach, I am having difficulties in translate it into actual ArcGIS procedures.

As for @Ingrid Luffman reply, I will surely look into the R package that you mentioned. Usually, I use a ArcGIS, preparing all the rasters I need (the one of the binary dependent Vairable, and the ones of the predictors), and than extract all the relevant data and process them in R, and then I go back to ArcGIS to produce the final LR raster. I am wondering if that package allows to input that 'autocovariate' term I was referring above.

Thanks all again. If you have further comments, feel free to reply.

Cheers

You might want to look at the literature on indicator kriging, it is not quite the same as logistic regression but may be appropriate depending on your application. For example see

1990, M.Ali, E. Nowatzki and D.E. Myers, Probabilistic Analysis of Collapsing soil by Indicator Kriging Mathematical Geology 22, 15-38

Hi Gianmarco, 

Thanks for starting this thread. I am working on a similar problem. Did you find a good solution?

I am trying to figure out how to calculate a Join Count statistic for my model and then incorporate the correlation structure into my logistic regression. Have you tried this approach? 

Thanks, 

Nathan

I have used auotocorrolation analysis in spatial data in my thesis and research, please visit my published article and hope find your answer:

Application of geographically weighted regression model to analysis of spatiotemporal varying relationships between groundwater quantity and land use changes (case study: Khanmirza Plain, Iran)

Thank @Shahabeddin for the references. I will give them a read.

@Nathan: I do not know if the procedure I used may apply to your case. What I have been doing so far is to follow some of the procedures described in the Hu-Lo article which I mentioned in my original question.

Since the starting point of my analysis has been creating a number of sampling points within the study area, I created them with a given arbitrary spacing, which should (in principle) downplay the effect of autocorrelation. After this first step (producing thousand of points), I took a random sample (stratified across the Dependent Variable, in order to keep unchanged the ratio between negative and positive outcome of the DV) in order to further increase the inter-point distance relative to the whole dataset. As third step, I added the X and Y coordinates as extra predictors. After fitting the model, I checked the residuals for spatial autocorrelation, and quite fortunately the values of Moran's I at different lags are both extremely low and not significant.

This is what I did so far. Maybe you want to try the SAMv4.0 software (freeware) which allows to fit autoregressive models, and has many other interesting features as well. Unfortunately, as for Logistic Regression, it does not handle categorical predictors, so if you have some you have to dummy-code them.

Hope this helps

Gianmarco, 

Thanks for your insight. I like the simplicity of using coordinates as explanatory variables. Your answer raised another question: Can you use Moran's I on residuals from a logistic regression? I thought Moran's I could only be used for continuous data. 

Thanks again, 

Nathan

Coordinates...PLUS the previous sampling strategy, do not forget!!!

As for the residuals: what do you mean? The residuals of LR are...residuals. They are continuous. I have read a number of articles in which the (logistic) model residuals were tested for spatial autocorrelation. If you want, tomorrow I could try to locate those references.

UPDATE:

for instance, in the following publication the authors use Moran's I to test for auto-correlation in (auto)LR model residuals:

Analyzing spatial autocorrelation in species distributions

using Gaussian and logit models (doi:10.1016/j.ecolmodel.2007.04.024)