To investigate the impact of spatial effects in modelling of road deterioration and investment requirements.
Although I am not familiar with the topic of road deterioration I will give it a try since I believe your question is of a more general spatial nature.
In short I believe you should go for the second alternative. This does not mean that the first one is wrong, it is simply approaching the problem from two different ends. I`will try to explain.
When you fit a model to your data values, you are trying to describe its variability (in a general sense). A good model should closely approximate your observed values and leave some residuals that are randomly distributed; that means that they are not correlated to your independent variables (and if one of your independent variables is space you would like for them also to not be spatially autocorrelated). In this case, spatial autocorrelation becomes a measure of the quality of your model.
Following the second approach, the spatial autocorrelation becomes a diagnostic tool, which you can interpret to do a more educated selection for your model.
In both cases this may turn into an iterative process until you find a suitable model.
Hope it helps.
Hi Rafael Anleu,,
Thank you for the response.
I have little apprehension about using the second alternative because in the second alternative do I have to check for spatial autocorrelation for each and every independent variable (attributes) associated with road deterioration. What method should I use to check for spatial autocorrelation.
To make things more simple, we decided only to know whether a particular stretch of road is deteriorated or not (using logistic regression) and then infer about the road maintenance on a particular stretch. We may use Monte Carlo simulation in this case to calculate the statistics.
As you said that finding a suitable model will be an iterative process, from your experience which case can be more simple with less iterations.
Unless i understood incorrectly, you are talking about two fundamentally different approaches that are not necessarily linked. In spatial modelling what we are trying to avoid is spatial autocorrelation in the residuals of a fitted model.
The second approach implies that spatial autoccorelation in independant variables is a bad thing, which is not based in any statistical inferences. If we include all relevant predictors of a spatial process that is described by a set of spatially autocorrelated predictors, the residuals will be random and not spatially dependent.
The following might be an interested read http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2699.2012.02707.x/abstract
from which ''
We believe that within the arguments presented by Hawkins (2012), he has confounded the occurrence of SA in the raw data with SA in the residuals. If the spatial autocorrelation of an ecological response variable is caused by autocorrelated predictor variables (such as climate, land use, topography, human population densities or virtually any other spatial predictor), we are not alarmed. Of course we do not wish to remove this effect of such predictors. […] SA in the residuals is, however, a serious problem, because it
(1) indicates the violation of an independence assumption of any statistical model, be it regression or CART (classification and regression trees), resulting in incorrect error probabilities; and
(2) can seriously affect coefficient estimates.''
You can do it all in one fell swoop:
https://www.researchgate.net/publication/46552003_Estimating_a_Price_Surface_for_Vacant_Land_in_an_Urban_Area
Article Estimating a Price Surface for Vacant Land in an Urban Area
How do we know whether the impact of spatial autocorrelation on residuals is because of already auto correlated covariates or otherwise (how do we account for spatial autocorrelation of covariates and run the model to check if spatial autocorrelation still exists in residuals) ?
Maybe this helps you:
http://rstudio-pubs-static.s3.amazonaws.com/9687_cc323b60e5d542449563ff1142163f05.html
The attached file is a screenshot from QGIS providing information about stretches of road through point data (containing information about dependent variable which is road condition and a set of independent variables).
What is the best way to measure spatial autocorrelation in this case ? Moran's I or any other method since its point data?
Can spatial autocorrelation be measured in QGIS also or R will be a better tool?
How to draw the samples - What is the ideal distance between each sample point and how it can be calculated or it would be trial and error using sample points at specific intervals (50m or 100m or 500m etc.) ?
Break up the area into squares. Identify each of the data points by its barycentric coordinates relative to the vertices of the square they are in. Run a regression in which each vertex is an independent variable (minus an omitted vertex). See if you like the results. By the way, feel free to include other variables in the regression, such as road names for dummy variables.
https://www.researchgate.net/publication/5151500_A_Primer_on_Piecewise_Parabolic_Multiple_Regression_Analysis_via_Estimations_of_Chicago_CBD_Land_Prices
Article A Primer on Piecewise Parabolic Multiple Regression Analysis...
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