Friends, I need help and insights.
I have 4 predictor variables with each assessed by no of questions given below:
Directive Leadership- 07
Transactional Leadership- 07
Transformational Leadership- 13
Empowering Leadership- 10
This makes a total of 37 variables.
I have two questions:
1. How many cases will I need for assessing if multicollinearity exists or not? Will it be 37*5= 185 or 37*10=370
2. How do I regress to find the IVF value? Should I take one question of Directive Leadership as IV and balance all 36 questions as dependent variable for checking the VIF value? And repeat it by checking rest of the variables in similar manner?
Your help will be deeply valued.
Warm regards,
Vikas.
The proper way to find out if you have multicollinearity in your data is to generate a matrix X with all those variables with their values and find their determinant (if 0 then linear dependency exists), or you could use the condition number of a matrix where large condition numbers signal that the matrix X has collinearity. Also, if your data X is not square, you can use Gaussian Elimination and see if you have zeros in your row-reduced form.
As for finding the VIF, your suggestion is correct. Repeat VIF for each X_i.
Thank you Faris for your response. As you see, I have 37 predictor variables and have done a pilot with 60 cases. Is it sufficient for me to run a multicollinearity test?
When I do a VIF test of only Directive Leadership that has 7 variables, and repeat by taking each variable as dependent and others as independent, I get no multicollinearity. However, when I do it for only Transformational or Empowering Leadership, I get multicollinearity. Ideally, I think I should do it for all 37, with one variable as dependent and balance 36 as independent and then check the outcomes. However, for doing this, my cases should be 370 and not just 60 that I have now. Is my understanding correct?
Will deeply value your inputs.
Regards,
Vikas.
You are welcome Vikas. Yes you should do the VIF test for all the 37 variables. Take one X_i as the independent variable, and all X_{-i} as your dependent variables. I am unclear where 10 vs 5 came from. Please elaborate.
As for the multicollinearity test, my suggestion is to put all your data in a matrix X and if it is not square, perform Gaussian Elimination.
Best wishes!
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