Analyzing the difference between regression equations of the same variables measured at different times

Question

I'm looking at the relationship between a set of IVs and one DV, measured at two different points in time. I want to know if the relationship is stable over time, that is, if the IVs predict the DV the same way at both times.

I've got a regression equation at each time point. How do I analyze the similarity or difference between these two regression equations?

I would like to be able to specify confidence intervals for a specific range of difference between two estimates of the same beta at different points in time, but I'm not sure if that is the optimal or conventional way to look at this.

Answer 1

I would use a regresson model with interaction effects. First, make sure your data is in long format, so that all observations for your DV have one row each, and with a binary variable (0/1) that indicates if the measure is at time A or time B (we'll call it time). You now run a multiple regression with DV as the dependent variable and include time and all interactions between your IVs and time in the model.

The regression coefficients for the interactions will indicate difference in the effect of IVs on the DV between the two points in time.

Using R code:

model <- lm (DV ~ time + IV1 + time:IV1 + IV2 + time:IV2)
summary(model)

In the output, you will get a list of regression coefficients for time, your IV's and their interactions, as well as standard errors and p-values. The p-values for the interaction effects will tell you whether they are significant, i.e. if the IV in question has a statistically significant different effect for the two points in time. The regression coefficients will tell you the magnitude of that effect.

I hope this helps!