I have been explained this technique in class. However, I did not understand some stuff.
The professor said that a model to be estimated needs to be at least identified. Identified meaning to be when Number of observations > Number of parameters. In CFA, number of observations are the number of elements of the covariance matrix under the diagonal + the variances. Number of parameters are the number of loadings we do not constraint to 0 in the Loading Matrix + the variances of unique factors (errors) + Variances of the factors.
However, something is not working here.
My model has 12 variables and 5 factors. The first factor affects the 3 first variables, the next factor the following 3 variables, and the rest of factors are affecting 2 variables each one.
For example, a model with 78 observations from the covariance matrix (as I defined above), and 39 parameters (12 loadings, 12 error terms, 10 correlation factors, 5 factor variances) cannot be estimated in R in Lavaan. 78 > 39 so I don't understand what is happening here.
However, if I fix the 5 variances of the factors to 1, everything is computed. So estimating 34 parameters instead of 39 is working, but the number of observations is sufficiently high to estimate whatever model I pursue.
Furthermore, in case it is not possible, what is the point of fixing loadings of the rest of factors to 0? I could let that all variables are affected by all factors, to see some unexpected relationship...
Thank so much