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I'm doing a multivariate logistic regression where all my independent variables are categorical and binary. I have transformed all my categorical variables into dummies in order to have reference groups and interpret my odds-ratios. However, I would like to check if there are eventually multicollinearity issues.

I plan to calculate Spearman correlation between my independent variables and calculate VIF too. Nevertheless, I have several questions: Is Vif appropriate in this case? Do I have to calculate VIF and Spearman correlation on my categorical variables or their associated dummies?

I have tested other ways to detect multicollinearity (I check if the coefficients vary a lot if I increase my sample size or drop or add variables) and I'm pretty sure there is not a collinearity issue but I would like to have a "quantitative" proof.

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    $\begingroup$ Several small confusions here: Multivariate logit strictly means several response variables. Your title says "dependent variables", your text says "independent variables": you probably mean the second. The confusion is further evidence for those like myself who think both terms are better avoided. $\endgroup$
    – Nick Cox
    Aug 10 '16 at 9:22
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    $\begingroup$ Why Spearman correlation? There is precisely no reason to prefer its use here to Pearson correlation for investigating multicollinearity although in practice if all variables are binary, Spearman gives exactly the same answer, as 0 and 1 are just replaced by two distinct mean ranks, which is a linear transformation. $\endgroup$
    – Nick Cox
    Aug 10 '16 at 9:27
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Daryl Pregibon has written a key paper on LR diagnostics. It looks like it's only available from the publisher:

Daryl Pregibon. Logistic regression diagnostics. The Annals of Statistics, volume 9, pages 705–724, 1981

That said and from a practitioner's point of view, I would be comfortable using the metrics that have been developed for OLS regression such as the VIF or the eigenvalue-based collinearity index. The best source for this class of diagnostics is Belsey, Kuh and Welsch's book Regression Diagnostics: Identifying Influential Data and Sources of Collinearity:

http://www.amazon.com/Regression-Diagnostics-Identifying-Influential-Collinearity/dp/0471691178/ref=sr_1_sc_1?ie=UTF8&qid=1457527579&sr=8-1-spell&keywords=regression+diagnositcs+belsey

Of course, stringent purists or a PhD dissertation committee would likely object to leveraging these readily available and easily implemented methods but they stand as useful proxies for the real thing.

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    $\begingroup$ Pregibon's article is open access at projecteuclid.org/download/pdf_1/euclid.aos/1176345513 $\endgroup$
    – Nick Cox
    Aug 10 '16 at 9:15
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    $\begingroup$ Multicollinearity is a collective property of the predictors so methods for detecting, quantifying or exploring it are in practice fairly transferable, so I support this pragmatism as a first approximation. $\endgroup$
    – Nick Cox
    Aug 10 '16 at 9:18

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