Although I have found on StackOverflow all answers I ever had on GIS matters using R, ArcGIS and QGIS in the past, I am currently faced with one question I can't find an answer to online.
For my final dissertation project, I am working on water quality data based on sampled I have collected across an aquifer. I am exploring faecal contamination patterns, so I am mostly interested in faecal bacteria count and my method (using R) is as follows:
2. Stepwise logistic regression for dimensionality reduction. That's because my dataset is very wide given that I only have 97 samples, and I am trying to predict a contaminated/non-contaminated status, not a level of contamination (hence logistic over linear regression) --> the best possible result is still a rather poor model with low predictive power and no spatial autocorrelation found in residuals (that excludes using a Geographically weighted Regression)
3. Geospatial modelling: still trying to run some form of interpolation --> I tried Moran's I, LISA, and even Mantel test (distance matrix against faecal contamination matrix) and found no spatial autocorrelation for the variable of interest. --> I used IDW, because unlike Kriging it doesn't make assumptions about spatial autocorrelation
4. Hierarchical clustering (unsupervised machine learning) to still extract some form of classification from this complex dataset despite the difficulty to predict anything with supervised methods tested above.
My main question right now is about step 3. Given that I found NO spatial autocorrelation, am I right to still go ahead and run an IDW interpolation? Or should I just stop my analysis right there and say: look, my result is "no significant result from a geospatial point of view"? I have read so many articles, tutorials and handbooks, that this useful question Choosing IDW vs Kriging interpolation summarizes pretty well, but it doesn't really lift my doubts.
@Spacedman has provided a very useful answer.
My sampling pattern was indeed quite poor due to more or less limited access to groundwater sources across the study area.
Initially I was testing a new real-time method for faecal matter detection, but it turns out it just doesn't work in this area and is shockingly uncorrelated with the actual contamination. That's what I am finding in step 1. So my study has become an exploration of contamination patterns across the aquifer. In step 2 I try to work out whether other hydrochemical parameters I registered would work as decent predictors and if I can build a regression model. Turns out: not really. So in step 3 I was hoping that I could still build some sort of classification of the study area and display contaminated vs non-contaminated areas. In step 4 I rely on Machine Learning, and I use Gower distance (which combines all parameters into a single distance metric) to classify different "families" of contamination, if that make sense?
Could @Spacedman clarify what he means by "you have demonstrated that a non-spatially correlated model is adequate"?
Does it mean I should just stick with my logistic regression or the clustering?