ABSTRACT
Ordinary least squares linear regression with rates as the outcome suffers from two problems: (1) it treats all rates equally, regardless of their precision, and (2) it fails to weight rates by their person-time denominator. Some use ln(rate) as an outcome, but (1) rates of 0 have no ln, and (2) the ln of the average does not equal the average of the ln. These problems can be solved with weighted least-squares linear regression. Stata’s importance weights make this approach easy. Poisson, weighted least squares, and ordinary least squares are compared. The role of variance weighted least squares is reviewed and contrasted with the use of inverse-variance weights. Simulations used learn whether spurious correlation, discussed Chapter 1, is a problem. For counts unrelated to the population size, it is best to use the counts as variables. For counts related to population size, it is best to divide by population size to create a proportion. Simulation results shown for different modeling methods.
