Hello. I'm doing a multinomial logistic regression using SPSS and want to check for multicollinearity. My predictor variables are all categorical (some with more than 2 levels). I assume this means that VIF and Tolerance stats are not useful in diagnosing multicollinearity. I have tried examining an Anti-Image Correlation Matrix as you would for factor analysis, having entered all my variables as ordinal data. All the r values are below .9. I'm not sure if that is the right thing to do or if I should find another method for assessing multicollinearity. Any advice would be greatly appreciated! Thanks in advance.
Dear Francesca,
Try to see these to attachment files which are very useful:
https://socialsciences.mcmaster.ca/jfox/Courses/soc740/lecture-7-notes.pdf
For a categorical and a continuous variable, multicollinearity can be measured by t-test (if the categorical variable has 2 categories) or ANOVA (more than 2 categories)
For categorical variables, multicollinearity can be detected with Spearman rank correlation coefficient (ordinal variables) and chi-square test (nominal variables).
Something equivalent to the variance inflation factors (VIP) but for categorical data it would be an option.
In R, you can use rms package
In this forum (see link) an example is exposed. https://stackoverflow.com/questions/33397689/multi-collinearity-for-categorical-variables.
I suggest you take into account the suggestion of one of the forum members:
«Categorical variables cannot be colinear. They do not represent linear measures in Euclidean space .... A chi-square test can be used to test for independence of categorical variable»
Thanks Pablo Antúnez Mohammad Ebrahim Ghaffari and Ahmad Al-shallawi for taking the time to answer my question. Really helpful.
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