Ultimately I want to estimate a second-order factor structure in AMOS.
As such I am trying to compare the fit of a first-order model in which the first-order factors are (a) constrained to be uncorrelated, and (b) free to correlate.
I am running into two problems when I try to run these models.
- the chi-square and df's for the fully constrained and unconstrained models are coming out as the same (I am trying to constrain the model by naming the covariance parameters under the plugins tab which I think constrains them to be the same?) It is my understanding that they should be different and if the unconstrained model (factors free to correlate) has a smaller chi-square value then a second-order factor structure can be estimated.
- If I constrain individual correlations (setting the covariance of the curved arrows between the latent variables in the measurement model to be 0) in several instances I get an error message that one of the variances is negative and the chi-square is not estimated.
Additional Information: I have 3 factors with 2 observed variables each. My sample size is 202. The second order factor is not included in these models. I am looking to compare a constrained model (constrain factors to be uncorrelated) to the same model with unconstrained correlations (allowing factors to correlate) to determine whether I can estimate a second-order factor (2 models), then I am also constraining correlations individually (there are 3 as there are 3 factors). Can I constrain the correlations to be uncorrelated by setting the covariances between each of the 3 factors to be 1?