Thursday, January 9, 2014

Stacked structural models

Les Hayduk (1996, Ch. 5, 155-189) presented these special kinds of multi-group Structural Equation models, the 'stacked SEMs' with different numbers of indicators, and of course I did not understand them well... Nothing works better than trying it out for yourself (and better so in AMOS first).

So: When you don't have a variable in ONE of the groups which appears in another, you can still use the same larger multi-group model (with the 'limping' variable in!).
[see my 1st image posted here: ]

How? Les Hayduk proposes a way, simply put filling in ZEROS for the covariances of the missing ('phantom') variable with all other variables, and 1's for their variances, like so:

AMOS can run models off such Excel data (you can just save these 3 covariance matrices as different worksheets in the same file, as I did; thanks, Les for including in your book the Lisrel syntax, it helped!). NOTE: AnxFam and and Work were NOT present in the 2nd and 3rd groups, but the 3-group model includes them too.
The results I got seem to replicate Les' results, after some AMOS arm-twisting.

The morale? What appears as complicated merits a 1st reading (Hayduk's 2nd book...), there is always stuff you can grab and run with it (even if not so far at first).

PS: as suggested on Semnet one should include a covariance between the errors of the looped variables, which tests whether relevant outside influences on these 2 variables have been mitted, which in our case seems not to be the case, all 3 covariances e.g. here were NonSignificant (NS) (adding such a covariance between L2 and L3 makes the model non-identified, why? well that's why the chapter merits reading...).

Hayduk, L. A. (1996). LISREL issues, debates, and strategies: Johns Hopkins University Press.