I have two latent variable models which I have identified in separate analyses (we'll call them Model A and Model B). In each of the analyses, all parameters were freely estimated and I achieved excellent model fit. The latent variables in each model are thought to represent trait abilities measured via different assessment tools. I want to see how the latent variables from Model A predict the latent variables in Model B. Given that each model is believed to represent trait-level (static) abilities, is it acceptable to constrain each of the models based on the parameters identified in the separate analyses, and ONLY freely estimate the prediction parameters from Model A to Model B?
Brittany,
why did you estimate them separately in the first place?
And why do you want to constrain the combined model?
Sample size?
You can certainly test for the difference in fit between the constrained model and the freely estimated model.
Hello Heiko,
I estimated the models separately in the first place in order to answer different research questions, one pertaining specifically to each model. It really began as theory testing for the different trait constructs represented in each model. Now that I have proof of concept and have viable model structures, I'd like to combine them and determine whether one is predictive of the other. However, because each model should theoretically represent static traits, it makes a certain amount of sense that one model should not be able to change the nature of the other model. The only way I can think to represent the static models and test the relationships between the "pure" constructs is to constrain the models, but I'm not sure whether that is an acceptable practice. I have a sample size of 154 and large effects, approximately 60 parameters.
The short answer is no, it is not acceptable.
Generally, you would start with a model in which the measurement parts of the two models are specified (and estimated) as before, and the "structural" part between them is "saturated" (all covariances are freely estimated). In other words, a CFA model.
Then, you would run another model with the hypothesized paths between latent variables.
[Without having seen the model, I would guess that keeping the models separate before was probably not necessary.]
Hi Brittany,
If your sample size is sufficient, the only reason to constrain paremters in the combined model would be if you have an identification problem. Simply build the combined model. I would also refer you to multitrait-multimethod matrix models guide by David. A. Kenny: http://davidakenny.net/cm/mtmm.htm.
I would question whether having fewer than 3 observations per parameter is enough, since the smallest recommendation I have seen is 5.
Jeffrey M. DeVries Thanks for the great reference!
David L Morgan Thanks for the input. I know that sample size is a hotly debated topic, so it's always good to learn what others are using as benchmarks.
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