James Algina posted on Wednesday, November 13, 2013 - 4:32 pm
I have data for which a parallel process growth model has been formulated. The data also include three observed variables that are not used to define growth latent variables. I estimated two models. In Model 'WITH' I use a 'with' statement for each growth latent variable and each of the other three variables. In Model 'ON' I treat some of the growth latent variables as endogenous, some of the growth latent variables as exogenous, two of the additional variables as endogenous, and the last additional variables as exogenous. I estimated two versions of each model. In Models 'WITH_OPC' and 'ON_OPC' I used orthogonal polynomials as factor loadings to define the latent growth variables In Models 'With_C_OPC" and 'ON_C_OPC' I centered the factor orthogonal polynomial loadings so the loading for the earliest time point was 0 Models 'WITH_OPC' and 'WITH_C_OPC' resulted in the same log-likelihood for the H0 model. Models 'ON_OPC' and 'ON_C_OPC' did not.
Can you suggest any reason why the centering would affect the log-likelihood in the 'ON" models but not in the 'WITH' models.
James Algina posted on Thursday, November 14, 2013 - 9:01 am
Removing some restrictions in the 'ON' models resulted in the same log-likelihood for the 'ON_OPC' and 'ON_C_OPC' Models. The failure of the initial 'ON_OPC' and 'ON_C_OPC' Models to have the same log-likelihood may be an illustration of the issue Roger Millsap identified in When Trivial Constraints Are Not Trivial: The Choice of Uniqueness Constraints in Confirmatory Factor Analysis.