Path analysis: how to interpret total...
Message/Author
 Byungbae Kim posted on Wednesday, June 01, 2011 - 11:16 am
Hi. Drs. Muthen. My name is Kim.

I am currently working on a path model where all the mediating variables are binary and the dependent variable is continuous. (For the reference, I have 5 exogenous, 3 mediating, and 1 dependent variable, and am using only observed variables.) Following the example (3.14) in the manual, it seems that I have the right output. However, I still have a few questions since I am new to M-plus.

1. I wonder how I could substantively interpret "total (indirect) effectsˇ± because I am using both OLS regressions and probit regression to get total effects here within this framework.

2.The results of analysis show that two of my exogenous variables have the coefficient of 0.000 along with the standard error of 0.000, and they are statistically significant. Could you give me an explanation and remedies for this?

3.My data set has a clustering issue; I am analyzing the court and sentencing data. The defendants (n=10,000) are nested with over 90 district courts. Within this framework, I know there is something called ˇ°two level path analysis,ˇ± but here in this model, I am only interested in correcting for the clustering issue. Is employing robust standard errors one of the options?

4.Finally, Could you direct me to a reference paper that would include the above questions?

Thank you very much for your time in advance.

Best regards

Kim
 Bengt O. Muthen posted on Friday, June 03, 2011 - 9:14 am
1. With a binary mediator m and probit, you still have a linear relationship between the m* and the covariate as well as between m* and y. Here, m* is the continuous latent response variable underlying m. So, with 2 linear relations, the indirect effect is as usual with a continuous mediator.

2. Small coefficients are typically due to large scale (large variances) of covariates. Do a Basic run to see their variances and then use Define to divide those variables by 10 or 100.

3. Use Type = Complex (see UG)

4. There aren't really general references on this (yet), but you can start with

Xie, Y. (1989). Structural equation models for ordinal variables. Sociological
Methods & Research, 17, 325-352.

3.