We collected perception data by having people compare photos side by side. Then we ranked them using an algorithm that scores images that "won" these comparisons more as 1 and images that lose all the time as 0.
We plot these images on the map, with their associated scores and I get the map attached. For each color cell, there were 2 images, facing opposite directions, each with their own score. The cell color is the mean of those two colors.
Any interpolation model I fit gives me an RMS value of around .12 so I know the model is terrible.
Is there any other analysis I can do on this spatially if I can't fit a model? I was planning on referencing that model to crime data and see if perception of safety and actual crimes align in anyway. I was also going to look at housing pricing, etc. But since I can't make a good model, am I hosed?
The first place to start is to do some exploratory data analysis. Look for clustering or spatial autocorrelation in both the perceived and real data. Do the patterns look similar?
The data you are describing sound almost ideal for Geographically Weighted Regression (GWR). There are myriad resources available online to help you get through that, with many walk-through examples using ArcGIS.
Forget about interpolation completely. It's not right for this problem.