tommy lake posted on Thursday, August 17, 2006 - 10:27 pm
Dear Prof. Muthen,
I am modling a reciprocal connection between two continuous latent variables Y1 and Y2:
Y1 on Y2 x1; Y2 on Y1 x2;
I got Y1 on Y2 negatively significant while Y2 on Y1 positively significant. Yet theoretically I believe both links should be positive. If I model the two equations separately, i.e., as recursive models, then both are positive. Would you suggest me to do the two equations separately, or are there any strategies to "correct" the non-recursive model?
In addition, I also need to do this model in two groups then compare which group has stronger relationship between Y1 and Y2. What parameters should I use to compare? structural coefficients, standardized coefficients, or just significance?
Reciprocal interaction models can be tricky to understand. You should look at the literature on reciprocal interactions, e.g. Bollen's SEM book. For instance, the limit on eigenvalues plays a part here - and that is checked for if you ask for indirect effects in Mplus. Perhaps other covariates should be included, perhaps the model doesn't fit.
I would argue for testing structural coefficients.
tommy lake posted on Friday, August 18, 2006 - 7:54 pm
Thank you for your answer. By "testing structural coefficients," do you mean looking at the amount of structural coefficients, or looking at their t-scores, aka, significance?
Comparing the parameter estimates, their significance, and perhaps also testing their equality by also running a model with them held equal and then computing the 2*loglikelihood difference for the two models, resulting in a chi-square test.