I am working on a project where I have to generate a model for road deterioration. I am using logistic regression but since the stretches of road are related in space so I have to test for spatial autocorrelation on the residuals of logistic regression. If spatial effects are present, how to account for those effects?
Any package in R that may be useful.
What is the response ? Bernoulli or binomial ? Also, what is your statistical unit ? By the way, I wonder whether you are more on the side of a binomial approach (fixed denominator), or a Poisson approach (modelling the counts, denominator treated as an offset). In both cases (binomial or Poisson) you might want to use a marginal model. Simple choices are the betabinomial model for proportions, or the negative-binomial for counts. In these two cases, the spatial auto-correlation is accounted for by the within-cluster correlation coefficients. Both models (and others) are implemented in the aods3 package.
Of course much more sophisticated approaches are possible, like fitting a spatial 'random-effect) logistic or Poisson model, with functions available in the INLA package.
http://www.r-inla.org/home
Book aods3: analysis of overdispersed data using S3 methods
There are few ways to test for spatial correlation like Moran's I test and spatial correlogram.
Dear Renaud Lancelot
Thank you for such a detailed response and sharing the documents related to INLA & aods3.
The approach in our case would be Poisson. We will count the number of 1's on stretches of road which will give us an idea about the level of deterioration. Once a particular threshold is reached that means there is a need for maintenance.
In absence of any specific test we were planning to use Monte Carlo simulation.
Dear Faye Anderson
Thank you for your response.
We thought of using Moran's I and joint count statistics but we are using point data that makes our problem bit complicated.
Is it a count by km or road segment ? You may consider this as a grouping factor and assess whether a negative binomial model fits the data better than a Poisson model. Indeed, the overdispersion parameter in the neg bin model should capture the spatial autocorrelation. You can also try the simpler quasi-likelihood model in aods3.
You can use the spatial correlation analysis Moran's index if the number of views is more than 30, Also Moran's I is the spatial evolution of Carl Pearson's analysis, which uses regression in the drawing of residual squares, but if your data less 30 you have to use Geary’s , Which depends on At the expense of the standard deviation of the data, there are many similar analyzes such as Semivariogram, Getis-Ord GI.
Hy Owais, i agrre with Sandie Geoda is nice an easy, free and strong in spatial autocorrelation. this is the link
http://geodacenter.github.io/
Thank you Manal Abdulrahman for your inputs.
Thank you Andres de la Rosa Portilla for sharing the link, it would be useful for my analysis.
Thank you all for your support. I will keep you updated about the final outcome of my project although it will take sometime.
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