What is relationship between agile and OOP?

What statistical analysis method can I use to find the relationship between a disease (single variable) and environmental factors (multiple variables)?

• 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 (Empirical Orthogonal Function) but it requires time series data. CCA (Canonical Correlation Analysis) but it finds the relationship between two sets of multiple variables. So, 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.

• Answer:

  [Disclaimer: I'm a "punk statistician", not a real one :-P] You're saying that there may be an arbitrarily complex relationship between your variables and the target, and you want to model this relationship... that's generally a really difficult problem.  Typically the way one goes about this is to assume the relationship follows some parametric model: e.g., linear, polynomial, exponential.  Then you can try to fit the model to the data and see how good the fit is.  In the simplest case you'd test for a linear relationship and look at correlation or R2 score, as you mentioned.  As you pick more and more complex models, you need to start worrying about the bias variance dilemma [i.e., your model might get a perfect fit, but it'll be fitting noise in the training data; see http://en.wikipedia.org/wiki/Bias%E2%80%93variance_dilemma]. The obvious question is: how do I pick a model to fit?  No easy answer here, unfortunately.  One way to do this is to just look at the data and get a feel for what the possible relationships may look like.  Then pick the SIMPLEST model that you feel may capture the relationship (see again bias-variance).  The ultimate test is to see how well your model can predict the target for new (or held out) data points. Another option is to fit a non-parametric model.  These models are great if your ultimate goal is to make predictions for novel data points (e.g., what will be the disease incidence if temperature rises to 45, and elevation is X?).  You could try random forest regression [see http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html#sklearn.ensemble.RandomForestRegressor], or radial basis functions [see http://en.wikipedia.org/wiki/Radial_basis_function].  The main disadvantage to these types of models is that while they may be able to make good predictions, they are not as interpretable.  When relationships are really complex though, this is your best bet.