can you try this in SPSS as I think procedures like GLM and logistic regression where you have categorical and continuous you can test for interaction and confounding

Thanks, Deborah, for your suggestion. I could do the test in SPSS but only after recoding the categorical variables (e.g. recoding residence as '1' referring to 'villager', '2' referring to 'urbanite' and '3' referring to 'migrant'). Is there a way in SPSS to do the same with categorical variables without recoding? 

Dear Saudi,

You can't test for correlation between two categorical variables. I guess you mean to test for association between categorical variables, which can be done with a Chi-square test (chisq.test). See also: http://datascience.stackexchange.com/questions/893/how-to-get-correlation-between-two-categorical-variable-and-a-categorical-variab

In re coding your variables, it is imperative that  you have to create  K-1  dummy vectors of  ones (1s)  and zeros (0s). If you use the right coding scheme and interaction then, it becomes  easy to check for multicollinearity by looking for contradictory results between  F- test for the Full Model and T-Test for partial regression coefficients.

Look at the regression diagnostics in various R packages. For example there is a vif() in the car package. I'm not sure if this works on .mer objects but as multicollinearity is only about the predictors I would fit a model with those predictors using lm or glm and use vif() to look at the degree of collinearity. This is superior to looking at the pairwise correlations (which could be low even if multicollinearity is high).

I don't think using spearman's rho is helpful as collinearity depends on the linear correlation not the linear correlation between rank transformed data.

Dear Pepjin,

Thanks for your clarification. To make sure, do you mean that correlation tests continuous variables and association tests categorical variables? 

You can test for correlation between categorical predictors in a regression, but only with respect to the dummy/indicator variables. If you have predictors coded as factors in R, the regression function will create dummy/indicator codes appropriate to the contrasts setting in the main R options. Usually this is simple dummy coding. The correlation function doesn't I suspect work with factors, so you'd have to create the dummy codes yourself to use it. However, a function like vif() in car will not mind and will work on factors and continuous predictors.

Dear Sofia Cividini,

Does the vif function with categorical variables? I have tried it but got many warnings. 

Dear Thom S Baguley, Thanks for your answer. Do you mean that I should change the categorical predictors (e.g. gender) to dummy ones (e. g. '1' referring to males and '2' to females) and so on? If so, is it the same way to do with categorical variables of more than two levels? Best

Dear Abdulrazzak Charbaji,

Thanks for your answer. Do you mean categorical variables should be recoded as either '0' and '1' alone? If so, what about three- or four-level variables (e.g. education → 'primary', 'secondary' and 'university')? 

Note that level of education is not an interval variable.   Create K-1 Vectors of 1s    and 0s    for the categorical variable "level of Ed".

Dear Abdulrazzak Charbaji,

In this case, does this mean that recoding categorical variables is not suitable unless they are interval?

To get information on correlation among the categorical variables (k-levels), the contingency table analysis would be a good start.  If collinearity exists, you will see many near zero cells in the non-central part. This makes the estimation unaccurate and with larger errors. However, the multi –collinearity doesn’t affect model overall fitting and prediction, but have big effects on the effect of predictor identification.    

The "variance inflation factor" (VIF) is defined for an individual

Predictor including demy variable.  Conceptually, one uses that predictor as the dependent variable in a regression on all the other predictors, and

interprets 1 - R2 from the regression as the usable fraction of that predictor in the full regression model.  The VIF for that predictor is the reciprocal of that 1 - R2. The VIF is based on correlation and though you want to be careful using correlation between binary variables (or categorical

variable split up into different binary variables) when doing substantive research, it is perfectly ok to use that to diagnose multicolineartiy with categorical data.

A VIF gives information how badly the standard error for the estimate of that regression coefficient is degraded, but it does not show which predictors are involved in the collinearity (if a troublesome collinearity is present). Hence CATPCA (SAS)could be used to find which variables are involved.

In addition, change reference group for categorical factor may avoid collinearity.  You just run the same model by using different reference leve for each categorical predictor, and examine the VIF, then choose the model with all VIFs are smaller than other models. This may be easy.

The best codes are the binary 1s  and 0s . Don't use a vector of 1, 2, 3, etc for the different levels of education. Create K-1 vectors of dummy variables