Parallel Measures - Fixing Residuals?

[Peter Burnett]

I'm a PhD student learning SEM and CFA, so take my lack of understanding with a grain of salt.  I'm attempting to look at parallel measures vs Tau-equivalent vs congineric measures of modelling.  For the Tau-equivalent measures it assumes that the parameters for the variables are all equal, while the residuals are allowed to freely vary, which I am able to do with-in the model.  However, for the parallel measures it adds in the additional stipulation that the residuals of each variable need to be equal to each other and I can't figure out how to force the model do this in the code.

I can figure out how to fix variance of latent factors and how to set parameters of initial variables equal, but can't figure out how to set the variance (residuals) of the variables equal to each other.  Is there a way to do this using Lavaan?

Thank you.

[Peter Burnett]

For reference, I'm doing a two factor model with 3 variables each (6 variables total).  So the base model is:

         Ex5.Model <-   'Factor1 =~ X__1 + X__2 + X__3

                                  Factor2 =~ X__4 + X__5 + X__6 '

And for Tau-Equivalent measures to set factor parameters equal:

         Ex5.Model <- 'Factor1 =~ v1*X__1 + v1*X__2 + v1*X__3

                                Factor2 =~ v2*X__4 + v2*X__5 + v2*X__6 '

         Ex5.fit<- cfa(Ex5.Model, data = Example5_1_n200,estimator="MLR",std.lv=TRUE)

I obviously don't know the parallel measures code to use.

[Edward Rigdon]

Peter--

     Label the variances of the observed vaiables:

X_1~~a*X_1

If the variable is dependent (as these are), then you are referencing the residual variance, which is what you want. Here, "a" is the residual variance of X_1. So another line that says

X_2~~a*X_2

would constrain residual variances to be equal for X_1 and X_2.

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