0

I would like to check for multicollinearity in logistic regression analysis. Independent variables are categorical (always binary) and continuous. Sample has limited size (N=176, 36 events), so I can use 2, max. 3 variables.

Can I use VIF as an indicator for multicollinearity in final model? What if I have in final model 2 categorical (binary) and one continuous? Does it make sense to use VIF? Are there any others SIMPLE options? (SPSS)

I have searched all over internet but could not find an SIMPLE (excluding complicated formulas) answer concerning VIF with categorical variables.

I am using SPSS 22.0 and my field is heart surgery, not statistic. Any suggestions? (instead of finding a statistician).

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Juraj
  • 103
  • 2
  • 7
  • Have been asked before: https://stats.stackexchange.com/questions/115915/how-to-evaluate-collinearity-or-correlation-of-predictors-in-logistic-regression, https://stats.stackexchange.com/questions/380708/how-can-i-use-linear-logistic-regression-for-inference-with-colinear-variables-a, https://stats.stackexchange.com/questions/342633/can-vif-and-backward-elimination-be-used-on-a-logistic-regression-model, – kjetil b halvorsen May 29 '20 at 19:58

1 Answers1

0

$$VIF_i = \frac{1}{1-R_i^2}$$

where $R_i^2$ is the $R^2$ of a linear model calculated for the regression of $X_j$ on the other covariates.

So you can calculate VIF for a quantitative variable with a categorial, but you can't do the contrary! That's because the regression of $Y$ categorial on $X$ (quantitative o categorial) would imply the use of logistic regression whose $R^2$ is just a pseudo-$R^2$.

From this question How to calculate pseudo-$R^2$ from R's logistic regression? I found a useful sentence for you:

"Technically, $R^2$ cannot be computed the same way in logistic regression as it is in OLS regression. The pseudo-$R^2$, in logistic regression, is defined as 1 - L1/L0, where L0 represents the log likelihood for the "constant-only" model and L1 is the log likelihood for the full model with constant and predictors."

Pitouille
  • 1,506
  • 3
  • 5
  • 16
jmarkov
  • 1
  • 2