Confounding and multicollinearity Confounding occurs 10000 times more frequently than...
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Transcript of Confounding and multicollinearity Confounding occurs 10000 times more frequently than...
Confounding and multicollinearity
• Confounding occurs 10000 times more frequently than multicollinearity
• Confounder: An independent variable that changes the effect (the B’s) of other independent variables, when it’s included in the model
• A confounder is differently distributed for different values of the variable it confounds
• Multicollinearity is when two independent variables measure (almost) the same thing
• Of course, both problems means that the indepedent variables are correlated
Collinearity• Example: Want to find the effect of weight on
height• For some reason, you have two independent
variables: Weight and weight+1• Both are obviously related to height• If both are included in the model
– Impossible to tell which one explains the difference in height in the data!!
– Impossible to get precise B-estimates for any of them, S-E.’s would be huge!!
• Of course, real data will involve much less obvious collinearity than this example, but the same thing will happen
Trial exam exercise:• Gender and treatment cannot be collinearily
related, because only the effect of gender changes from the univariate to the multivariate analysis
• Also, gender and treatment measure two intuitively different things, it is arbitrary which treatment you give to each individual
• If we had made sure that an eual number of males and females got each treatment, the confounding would disappear!! (I.e. gender would not have been significant in the univariate analysis either)
• Whereas, if you had collinearity, you could not ”design away” the problem (because the two variables measure almost the same thing!)