0

i am trying to compare two regression models with different settings:

Model 1: Y ~ X + M + C, and

Model 2: M ~ X + Y + C

The purpose is to check which model is better. I think likelihood based methods will not work as the outcome variables are not the same, am I right? Then which kind of metrics can be used to compare such two models?

All advice and comments are appreciated! Thanks!

wenjia xu
  • 1
  • 2
    There isn't going to be a way to compare those two. You've just switched whether Y or M is on the left hand side of the regression equation. This amounts to determining whether you want to minimize vertical or horizontal deviations to fit the regression line (cf [here](https://stats.stackexchange.com/a/22721/7290)). If you are wondering whether Y *causes* M, or M *causes* Y, you need to run some experiments. – gung - Reinstate Monica Jul 06 '21 at 19:41
  • Thanks for your comment @gung-ReinstateMonica. Yes, you are right that I want to test if Y causes M or M causes Y. but the data I have is observational data, could you let me know what kind of experiments I could do? Or could you perhaps share some experience on how to test this given observational data? thanks! – wenjia xu Jul 07 '21 at 08:00
  • Recruit a new set of units (patients, consumers, mice, firms, whatever), & randomly assign them to groups. Independently manipulate levels of M between the groups, & see if Y differs by group. Likewise for manipulating Y & seeing if M differs. – gung - Reinstate Monica Jul 07 '21 at 11:29
  • Thanks for your reply. Unfortunately the survey has finished and there is no way to get new data or manipulate levels of M or Y as it is observational social survey. Is there any empirical way to compare two models? – wenjia xu Jul 07 '21 at 12:11
  • No, that was the point of my first comment. – gung - Reinstate Monica Jul 07 '21 at 13:12

0 Answers0