I have a question that needs clarification as I am getting two different answers from various sources. I read through your handout in multi group analysis and you compare more constrained model to the less constrained model (chi-square difference (df difference)), rather than the configural (baseline) model. However, I found one book which suggests that no matter which level of the restrictiveness the model has, it has to be compered against the baseline model.
Are they just two different approaches, or what I have read is not correct?
There is no one right way to do this. The configural, metric, and scalar models can be tested against the unrestricted model. Metric and scalar can also be tested against configural. And scalar can be tested against metric. I think it is most common in testing for measurement invariance to test configural against the unrestricted model, and metric and scalar against the configural model.
Many thanks for your reply. Just to clarify-isn't configural model you are referring to the most unrestricted model, which is often referred to as "totally free multiple group model (TF)" (Hair et al., 2010). It seems that there is one model that is even less restricted than configural model in your explanation. Please could you elaborate on this? Many thanks in advance.
Hi, I would like to estimate the ratio of two chi-square values (e.g., from a multi-group model) but more so to get a variance estimate of that ratio. Can Mplus model the chi-square value as a parameter?
I think you would want to use bootstrap to get SE for the ratio. Generate the bootstrap samples outside of Mplus and then estimate the model with multiple data sets using the type=montecarlo option of the data command. Repeat for the other model and you can get the distribution that way.