I have two questions that I'm hoping you can help me with.
1) I'm doing path analyses with unstandardized data. Does Mplus fix residual path coefficients for each endogenous variable to 1.0 as a default? If not, how is a ULI constraint applied?
2) I'm starting with a model with 3 observed variables and 6 observations (Y1 Y2 on X1). I have 5 parameters to be estimated: Variance for X1, path from X1 to Y1, path from X1 to Y2, Y1 disturbance, and Y2 disturbance. Yet I get a just-identified model. Any idea why?
Thank you in advance for your assistance and for your wonderful product.
1) Yes the residual path coefficient is fixed at 1 just like in regular regression. I don't know what a "ULI constraint" is.
2) I assume that when you say you have 6 observations you mean that you have 6 sample statistics to estimate the model parameters from. The Mplus default is to correlate the residuals for y1 and y2 because these are identified and typically not zero.
Disturbance (residual) covariance is specified as y1 with y2. The WITH specification refers to a residual covariance when endogenous variables are involved, otherwise a covariane - see the User's Guide.