gibbon lab posted on Tuesday, December 04, 2012 - 8:34 pm
I was just wondering what is the difference between a path analysise and a set of seperate regressions. I tried to do a simulation to understand the difference.
First, I generated three variables x, y and z based on a multivariate normal distribution with 1000 observations. Then I did two seperate simple regression models y=a+b*x+epsilon,z=alpha+beta*y+eta. After that I ran a path analysis in Mplus specifying x->y->z. I noticed that I actually got the same results for estimating a,b,alpha and beta in the path analysis. However, if I specify "y with z" in mplus, I get different results in the path analysis for estimating alpha and beta.
I understand that the command "y with z" correlates epsilon and eta which can not be done in seperate regressions. That is why I got different results.
My question: is correlating different residuals the only difference between a path analysis and seperate regression models? Do you recommend any references if I want to know more about this topic? Thanks a lot.