I want to find the relationship between a disease incidence in a region and a number of other environmental factors such as temperature, elevation etc.
I have tables containing this data for a particular country. The data files are raster files of the country map with each pixel having certain numeric value for the particular parameter. Example [126, 540, 359...] say disease cases or [23.34, 19.02...] for temperature etc.
I have read about multiple regression, Pearson Chi square test, t-tests etc. But I didn't find them suitable: Multiple regression because what I read it assumes a linear relationship between the variables. Chi square test applies to categorical data. t-tests for small datasets. I've also read about EOF analysis (Empirical Orthogonal Function) but it requires time series data. CCA (Canonical Correlation Analysis) but it finds the relationship between two sets of multiple variables.
Which statistical method can I use to find the relationship between these variables? I want to use a method that gives a relationship, say, more is the elevation, more is the number of disease incidence etc. Without assuming anything before hand like, "there'd be a linear relationship between the variables, so using linear relationship model." Also, is some method I mentioned appropriate but my understanding is not correct?
I don't necessarily need to find relationship one to many, it'd be fine to use one on one methods. On a side note, I'm working with GIS data and would use Python or R modules to find and plot the relationship. Thanks.