It is often expected that we check that our indep vars do not show too high correlations with each other. If all our indep vars are quantitative, this poses no problem. What should I do if some of my indep vars are binary = dichotomous = dummies? Should I also take them into account when checking the correlations?
There are many measures of the association/correlation between pairs (and also larger sets) of binary variables. The odds ratio (and the log of it) are popular, but see Article Reconsidering the Odds Ratio as a measure of 2 × 2 associati...
for arguments about kappa. A Pearson correlation can be calculated too,. There is much discussion on these 2x2 cases. Agresti's textbook is a good starting point. My tangent question is why do you want to look at the pairwise associations of a large number of variables? Your answer may suggest other approaches.
@Daniel. I usually ran ordinary OLS, logits, etc. Say regress Y X1 X2 X3 X4... Usually the assumption is that to obtain good estimates of the effects of the indep vars, corr (X1 X2 X3 X4...) should be low. So usually I get that correlation. I am concerned that if some of my Xs are not quantitative, this may have no sense.
In your regression, you should include those predictors you deem sensible, on theoretical grounds. If you fear that some of the predictors will be superfluous, you could check the VIF instead. This will also detect the shared information (regarding the response) of linear combinations of the predictors (what you will not see if you just look at pair-wise correlations).
Note that if you don't include predictors based on a particular functional model (in which the coefficients do have some particular, desired meaning), it actually does not matter whether or not the individual coefficient estimates are statistically significant (under the null µ=0). It can only be of interest how well the model predicts the response in what regions of the predictor space.
@Jochen, thank you very much for your answer. As someone already commented elsewhere, many of us benefit from a daily dosis of @Jochen... Indeed I use VIF. I posed the question in terms of correlations because VIF is based on correlations, so it seemd strange to me. Actually, while Stata calculates VIFs for any type of variables, you have to "trick" R if you want to do so (basically, telling R that the variable is quantitative). This suggests that perhaps there may be anr alternative to VIF that may be preferrable if non quantitative Xs are involved. Am I wrong?
Regards
I saw that David's link didn't help either, and I am afraid that I can't really help you here. But I heard that there are other people around in RG ;)
You can also try StatsExchange...
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