Lavaan and Extraneous Variables Assumption

[Julia M]

I am trying to create a model that is predicting a latent variable.  None of the predictors are latent variables.  In standard path analysis (with all observed variables in the model), one must include an extraneous variable predictor onto endogenous variables.  From my experience, lavaan doesn't appear to be doing this automatically.  How can I included an unspecified extraneous variable predictor to an endogenous observed variable using lavaan?

Example:
X and Y are observed variables that are known to be predictors of Z.  I want a model that shows the indirect relationship between X and Y via Z to the latent variable L (which has three observed variable outcomes: a, b, and c).

right now my model code would be:
Z ~ X + Y
L =~ a + b + c
L ~ Z

I want to add an extraneous variable to the Z ~ X + Y equation, such that Z is caused by X, Y, and other things I didn't happen to measure at this time (i.e. the "e" bubble you would use see if you used STATA or AMOS to graphically set up a path analysis). 

Any advice?

[Terrence Jorgensen]

I want to add an extraneous variable to the Z ~ X + Y equation, such that Z is caused by X, Y, and other things I didn't happen to measure at this time (i.e. the "e" bubble you would use see if you used STATA or AMOS to graphically set up a path analysis). 

You can capture the residual with a phantom construct, and fix the residual variance to zero.

eZ =~ 1*Z   # phantom construct
eZ ~~ NA*eZ
 Z ~~  0*Z  # fix residual variance to zero

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen