Collinear Variables

Question

I have a dataframe with 20 variables describing the situation of the students in a school while the do two different courses. Now, I am studying if there are multicollineality between some columns and I have the next question:

I have two categorical variables (with the same 4 categories) describing if a student has a good mod (1-bad mood, 4-awesome mood) while he does the two different courses:

 ~              goodmood_course1          goodmood_course2
 student1             0                       3
 student2             1                       1
 ...

I found that the two columns are almost the same:

    table( df$goodmood_course1 == df$goodmood_course2 )
    ... FALSE TRUE
        5     375

How can I deal with this multicollinarity? Could I remove one of the columns or would be better to do a mean of the values. Should I do a chi test with the data? Thank you so much!

Answer 1

In this case, I think removing one variable is fine. The number of cases that are not equal is so small that very little information is lost by dropping one variable.

Taking the mean of ordinal variables (which these are) is often done, but, technically, is not proper. Here, there is no need to violate the nature of the data by adding ordinal variables.

Answer 2

Multicollinearity is a problem of regression analysis and occurs when two or more explanatory variables have a very strong correlation with each other. On the one hand, with increasing multicollinearity, the procedure for estimating the regression coefficients becomes unstable and statements on estimating the regression coefficients increasingly inaccurate. On the other hand, the model interpretation is no longer unambiguous. The classical symptom of strong multicollinearity is a high coefficient of determination accompanied by low t-values for the individual regression parameters.

Basically I would advise to exclude one of them in a regression equation if there is a high correlation between two predictor variables.

In your example, however, I would be cautious. What exactly do you want to find out? What is your target variable?

I would be curious, for example, whether the mood is independent of the course. I would assume that - despite the correlation - this is not the case.