Hello Emilio! I have seen few authors have used phi coefficient to test correlation among categorical variables. I have attached one document here for your kind reference. Below mentioned study has used this coefficient to test multicollinearity among independent variables....Hope that helps

Muir SW, Berg K, Chesworth B, Klar N, Speechley M. Balance impairment as a risk factor for falls in community-dwelling older adults who are high functioning: a prospective study. Phys Ther. 2010 Mar;90(3):338-47. doi: 10.2522/ptj.20090163. Epub 2010 Jan 7.

How about, do regression ommiting one variable each time and see how the coefficients and their relevant standard errors change. If they do not change too much, then you are ok. If you are not happy with this, then calculate the VIFs. Regress each of the indep variables on the others and calculate the pseudo-R-squared value.

McFadden’s R2 is defined as

R2McF = 1 – ln(L1) / ln(L0)=1-loglik with params/loglik with only constant.

You have the R2, then you have VIFs similar to OLS.

See the chi-squares between the variables and also Cramer's V measure of association (similar to correlation, but for categorical variables).

Hello, Michail.

I have taken into account your first advice with the two highest correlations observed in the matrix, with r values of 0.478 and 0.499.

Doing regression by steps and omiting each time these four covariates, B coefficients and standard errors remain with little changes (lesser than 0.04 of variation in standard errors). The multicollinearity effect does not seem relevant.

Thanks a lot.

Good, good luck.

He has categorical data, so the Pearson correlation is not that appropriate here.

I was confronting the problem just a few days ago. What helped me most is this paper:

Graham, Michael H. "Confronting multicollinearity in ecological multiple regression." Ecology 84.11 (2003): 2809-2815.

If your target is to avoid variance inflation by multicollinearity of predictors, I would suggest to fit the scores of their principle components in glms as predictors instead of the original variables. Setting a threshold to the correlation is still somehow done arbitrarily and I argue to what extent looking for linear relationship in the predictors makes sense when the glm assumption itself is non-linear.

Hope that helps.

Hello, Avit.

Interesting paper.

Besides the sequential regression and the pseudo-R2 that Michail pointed out, I will add your suggestion of an analysis of principle components in GLM to my statistical notes of the study.

Regards.

Sill, he has categorical data, his independent variables are categorical. This means that he should use the scores from the latent trait analysis and not principal component analysis.

Have a look here Emilio

http://www.bristol.ac.uk/cmm/team/fs/aimdss-2nd-ed/chapter8.pdf

and here

http://cran.r-project.org/web/packages/ltm/

Another possibility is to calculate the tetrachoric correlations between the dichotomous variables and apply factor analysis or principle component analysis on the correlation matrix.

I saw cases where VIF was computed for logistic models using categorial variables. I believe it is the same procedure as for regular regression. What I saw was that the observations were weighted with the value of the predicted variable.

Thank you, Kremena and Adrian.

I have also read that the principles concerning multicollinearity can be applied both to logistic regression as to linear regression, the same diagnostics assessing multicollinearity can be used (e.g. VIF, auxiliary regressions), and the same dimension reduction techniques can be used (such as combining variables via principal components analysis).

Adrian, your suggestion of weighted observations sounds interesting.

You should try Liu-type estimators for the logistic regression models.

Since VIF concerns with independent variables, the nature of dependent variable does not matter. VIF can be used for logistic regression as well. 

Hello Emilio! I have seen few authors have used phi coefficient to test correlation among categorical variables. I have attached one document here for your kind reference. Below mentioned study has used this coefficient to test multicollinearity among independent variables....Hope that helps

Muir SW, Berg K, Chesworth B, Klar N, Speechley M. Balance impairment as a risk factor for falls in community-dwelling older adults who are high functioning: a prospective study. Phys Ther. 2010 Mar;90(3):338-47. doi: 10.2522/ptj.20090163. Epub 2010 Jan 7.

Hello, Neha

Having read your kind post and the paper, phi-coefficient (test of correlation for nominal data in a contingency table 2x2) seems an interesting procedure to assess the presence of multicollinearity between dichotomous independent factors.

In the paper, two variables were highly correlated if ɸ-value was ≥ 0.30 (Fleiss JL. Statistical Methods for Rates and Proportions. 2nd ed. New York, NY: John Wiley & Sons; 1981).

I like it. I will use it for future studies.

Thanks a lot!

You are most Welcome Emilio!  Best wishes :)

I am also testing for multicollinearity using logistic regression. I have all outcomes and predictors as categorical variables. I am using a method described by Paul Allison in his book Logistic regression Using the SAS System. He also gives the SAS code that you can adapt for your use. Adrian mentioned in his post, this method applies weights. The interpretation is then exactly like in linear regression.

When ever I use logistic regression I will see the coefficients and their corresponding SE. If SE is very high than the coefficient value then it indicates the presence of multicollinearity. I will remove that variable and try to fit other model. This process will continue till I get a final model with significant varaibles with SE lesser than coefficient value 

What about running a stepwise logistic regression for that purpose

Hello Perumal,

My question to you is what is the threshold for SE to be high ? We know that

for VIF it's >10. Please give me a reference for the SE threshold if there is any.

best wishes

Dear Sharad

Please post the link for SAS codes for detecting collineraity in logistic regression described by Paul Allison in his book Logistic regression Using the SAS System. If there is no link, please post the SAS codes. It will be of great help.  

Dear Sharad,

You could also use the collin command from UCLA. It is a stata command. 

"Net install collin"

Eric.