MTMM data in lavaan

[Kam Tai Tony Kwan]

I recently encountered a problem modelling multitrait–multimethod data in lavaan.

 I would like to adopt the CTCM-R model by Lance & Fan (2016) and I wonder if it is possible to set constraint to model square roots of residual errors (using phantom variables/other techniques) instead of directly modelling residual errors. I currently only constrainted the residual errors to be greater than 0 using A~~v1*A and v1>0.

Please advice if any improvements could be made to fit the model intended. Thank you.

[Terrence Jorgensen]

I wonder if it is possible to set constraint to model square roots of residual errors (using phantom variables/other techniques) instead of directly modelling residual errors

You mean (the square roots of) their variances?  You can indeed specify a phantom variable for any manifest variable to represent its residual.  So if A is your indicator, set its residual-variance parameter to zero, and specify a single-indicator phantom construct so all the residual variance goes to it.

A ~~ 0*A # usual residual variance == 0

A_ph =~ SD_A*A # phantom's loading == residual SD

A_ph ~~ 1*A_ph # phantom's variance == 1

Then you can specify any constraint for the parameter SD_A that conforms to the model you want.

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

[Kam Tai Tony Kwan]

I will definitely try that technique. Thank you so much!

Terrence Jorgensen 在 2022年1月26日 星期三上午6:47:13 [UTC+8] 的信中寫道：