Confounding and multicollinearity

1
Confounding and multicollinearity

• Confounding occurs 10000 times more frequently
  than multicollinearity
• Confounder An independent variable that changes
  the effect (the Bs) of other independent
  variables, when its 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

2
Collinearity

• Example Want to find the effect of weight on
  height
• For some reason, you have two independent
  variables Weight and weight1
• 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

3
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!)