Hello... Background: I am testing the measurement invariance of 2 constructs each measured at two time points across 4 groups. The delinquency factors are represented by 8 observables treated as ordinal. The internalizing factors are represented by 3 observables treated as continuous. The model is parameterized so each construct has a factor representing the 1st time point and a factor that represents the change in the factor from wave 1 to wave 2. The model (with across time equality constraints on loadings and thresholds/intercepts) fits well for all four groups. Now I am trying to test the across group invariance of these latent change models.
Problem: The default for Mplus for multiple group data is to contrain factor means in the first group to 0. I'd like to free the factor means for the change constructs as I believe that these parameters will be identified due to the across time invariance constraints. However, I can't figure out how to get Mplus to allow me to freely estimate these latent means. I have used [internch*]; - yet, the parameter is still set to 0 in the output.
Identification Question: I am familiar with the identification requirements for both congeneric continuous and categorical measurement (Millsap & Tein, 2004) models across multiple groups. However, I am not certain how these requirements would change when there are two time points. For example, if the latent means are identified in the single group models, do I need any across-group constraints on item thresholds or intercepts for a test of a baseline (noninvariant) multiple-group model? Also - pending adequate measurement invariance, I plan on incorporating these constructs as outcomes in a larger structural model. Is there a problem with fixing factor means at 0 when these factors become endogenous and the means now become intercepts - thus requiring another way of identifying the model. I hope that I am clear enough with my questions for you to assist me. Thanks! Scott
You sent your output to Mplus support. The problem is that you did not free that mean in the first group where it is fixed to zero as the defualt. You must free it in the first group using a group-specific MODEL command.
You would still need threshold or intercept equalities even if you have only two timepoints in order to establish measurement invariance. Fixing the intercepts to zero when the factors are endogenous is not a problem
Thank you Linda for looking at my output. I did not know that you could have (or needed) a separate MODEL statement for the first group. As for the identification question - I know that I would need threshold/intercept equalities for invariance across groups - but I am taking the approach of starting with a baseline, noninvariant model and then will systematicaly add equality constraints on the loadings and then thresholds/intercepts. I am wondering if all mean-level parameters are identified in single-group models, do I need the standard across group constraints (e.g., factor means set to 0 in first group and reference indicator thresholds invariant across groups) for a baseline - non-invariant model? It seems to me that if all parameters are identified in the single group models (facilitated by measures captured at 2 time points and appropriate constraints), then I would not need to begin the multiple group, baseline model with the "usual" identification constraints. Thanks, Scott
bmuthen posted on Saturday, November 27, 2004 - 2:08 pm
That correct; parameters that are identifiable in a single-group analysis need not be constrained across groups when doing a baseline - minimum-invariance - multi-group analysis.