Finding the independent variable interactions for statistical models I am looking to find out ways in which I can check if there exists any kind of relationship between the various independent variables in a model. I understand that checking for correlations is a good starting point but correlation analysis is unable to capture any statistically significant non linear relationships between the variable. I am looking for a robust measure that might be helpful in finding any sort of linear/ non-linear relationships between the independent variables in a dataset.
 A: Spearman's rank correlation coefficent will show a correlation while reducing dependency on linearity by looking at how the variables are correlated after ranking the independent and dependent observation pairs by their ascending dependent variable magnitude.
This rank correlation non-parametric method then shows approximately how good the correlation could be if a best non-linear (or sometimes linear) relationship between the two variables can be found. To then find that relationship, one may have to modify the variables by taking logarithms, reciprocals, squares, square roots, exponentiation or other procedures. Alternatively, one may need to find a non-linear function that best agrees with the path that the data takes, for example, on plotting, by using non-linear regression. These procedures are done so that the residuals are well behaved after regression, where the residuals are the difference between the model used evaluated at the dependent variable sample values minus the data magnitude corresponding to those dependent variable values. 
Well behaved residuals for the purpose of finding a correlation means that there are no wild type values, called outliers, especially for the dependent variable. Spearman's rank correlation would be unaffected (relatively) by such outliers, but ordinary correlation is quite sensitive to them. Sometimes a modification of the variables, for example reciprocation, can eliminate these outliers, in which case, they are not really wild type outliers, and sometimes, these outliers have to be censored or dropped, either following observation of a plot or by testing by various procedures.
