Path Coefficient of alternative models

[Md. Shahin]

Hi 

I am beginner in SEM. I am using SEM for my research project. I am confused with the changes in the path coefficient in alternative models with same variables. 

Form Example, I have 7 observed variables. In the first model, 7th variable is predicted (regression) by other 6 variables and I got path coefficient. In the second model, I have added a latent variables with three observed variables. Then, the latent and 4 variables are predicting 7th variables. The path coefficients in second model are different from first model. My question, why the path coefficient is changed with latent? I warmly welcome your reply. 

#First Model 

ECON1<- '

#regression

G ~ 1+ A+B+C+D+E+F

'

#2nd Model 

ECON2<- '

#measurement

K=~ A+B+C

#regression

G ~ 1+ K+C+D+E+F

'

[Edward Rigdon]

Md.--

     The two models have different predictors for G. The first model includes A through F, while the second includes both a common factor for A, B and C plus C again and D, E, and F. A common factor carries only the variance that is common to its indicators, while your first model allows all of the variance of all of the predictors to predict G. Now C appears twice in the second model, both as an indicator of K and as a separate predictor of G, which complicates interpretation. The first model is entirely saturated, while the second includes some constraints. In the second, the relation between A, B and G is mediated by K, while the relation between C and G is not mediated by the common factor K.

     It is possible that the constraints in your model have affected parameter estimates. The full mediation of the (A, G) and (B, G) relations by the common factor K may induce lack of fit, if those constraints are not fully consistent with the model, and that may induce bias in the parameter estimates.

     The impact of collinearity will also be different across the two models. In the first model, all other variables directly predict G, so collinearity among all those variables may alter parameter estimates (and standard errors). In the second model, only K and C, D, E, and F directly predict G. So making common factor K mediate the relation for A and B may change how much collinearity affects the parameter estimates for the regression of G.

--
You received this message because you are subscribed to the Google Groups "lavaan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/d86cb156-0db2-4b65-baee-ac8a8eff3759n%40googlegroups.com.