is there a test for spurious correlations?

[Gns Met]

Im running a probit model and i would like to know if there is a test for being sure there is not spurious correlations between my variables.

[Joseph Coveney]

I'm curious: for prediction, why does it matter whether correlations between your predictors are spurious? For inference, you had better already know about the relationships between your predictors, independently of any "test" for spurious correlations.

[Nick Cox]

What is spurious in any case? You need some model or protocol that defines genuine results before you can decide on what is spurious.

[Richard Williams]

I agree that you need a model to address this issue. Suppose you believe B affects C, and the empirical results seem to support this. But, an alternative theory says A affects both B and C, and that it is this common cause (not a causal effect) that causes B and C to be correlated. So, you add A to your model and see if B continues to have an effect on C. If not, you can argue the correlation between B and C is spurious.

But, there is no way you can be certain. There might be some other variable not in your model that is a common cause of B and C. For example, not having good measures of socio-economic status can often be a major problem. Or, your model may just be wrong.

So, you have to have some theory to guide you. There isn't a simple post-estimation test for spuriousness. But, if you have a decent theory, you can make a case for believing or not believing that some relationship is spurious, produced by common causes rather than because one variable affects the other. Or, you can argue the relationship isn't spurious, because you have included in your model all the variables that might plausibly be common causes and yet the effect of B on C persists. Again, you never have certainly, but with a good theory and good data you can make a case for your argument.