I am looking to model transit ridership based on demographics at the stop level. For each stop, I know:

  • ONS: Total boardings per day - averaged over the number of times a bus pulls up at the stop

  • POP: Number of people living withing 1/4 mi of the stop

  • DEM_i: Proportion of people living near the stop from demography i (0-1)

My initial model (Model1) is:

  • $ONS = \beta_0 + \beta_1 Pop + \beta_2 Dem_i$

This model is fine (see results below) and my vif scores very close to 1. However, the term $\beta_2 Dem_i$ is't doing much here because it is the number of people by demographic that affect transit usage, not the proportion. So I add the interaction term (model 2):

  • $ONS = \beta_0 + \beta_1 Pop + \beta_2 Dem_i + \beta_3 Pop Dem_i$

Which gives me a much better fit. The problem is that now my coefficients are switched. The $Dem_i$ coefficient, $\beta_2$, went from -4.6 to 5.3. In addition, the $\beta_2$ and $\beta_3$ parameters have opposite signs. I have read online that one should not worry about co-linearity in interaction terms. But in this case it seems to be making my model unstable. The vif values for $POP$ and $POP*Den_i$ are close to 1000 each. How should I interpret this model? Which coefficients should I trust?

Screen Capture of Model 1 and Model 2


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