on page 2 Mplus LANGUAGE ADDENDUM 7.1 is said that the The alignment optimization method consists of three steps: 1. Analysis of a configural model with the same number of factors and same pattern of zero factor loadings in all groups. 2. Alignment optimization of the measurement parameters, factor loadings and intercepts/thresholds according to a simplicity criterion that favors few non-invariant measurement parameters. 3. Adjustment of the factor means and variances in line with the optimal alignment. my question is why is that a model with ALIGNMENT = FREE (CONFIGURAL); give the same estimates as ALIGNMENT = FREE; because i was thinking you need to be able to compare the configural and the scalar but their estimates are the same.
Tait Medina posted on Tuesday, February 25, 2014 - 6:19 am
Is it possible to test the equality of regression coefficients across groups under the alignment method? For example, I am interested in regressing the factor on age and testing whether the coefficient for age is different across groups?
The alignment method currently doesn't handle covariates. But you can divide people into age groups and then you get a*b groups in the alignment run, where a is the number of age groups and b is the number of original groups.
Tait Medina posted on Tuesday, February 25, 2014 - 3:11 pm
Thank you for your reply.
I have a question about the output from Alignment=Fixed. How are the estimates given under MODEL RESULTS connected to the numbers given under “Item Parameters In The Alignment Optimization Metric”? I have read Web Note 18, but am having a hard time mapping the output in these two sections onto the equations.
Also, the R2 measures given in Table 7 in Web Note 18 need to be calculated by hand using Eq 13 and 14. Correct?
The “Item Parameters In The Alignment Optimization Metric” section contains the alignment results in the metric in which the alignment optimization is performed, i.e., after all indicator variables are standardized and also under constraint (10) from web note 18, also including the factor mean fixed to 0 in the corresponding group. These parameters are scale reversed back to the original metric of the variables and also to factor variance fixed to 1 in the corresponding group if that is the requested parameterization. There is a way to get these parameters as your final model estimates. You will need to standardize your variables using the standardized option of the define command as well as the analysis option METRIC=PRODUCT;
R2 is computed with the upcoming Mplus 7.2 but you can compute it by hand as well.