Maybe the book by David Kaplan (2008) Structural Equation Modeling; Foundations and Extensions 2nd ed, 2008 Sage Publications can help you. This book treats ADF. I have used ADF, but it can go wrong quite easily. You need to be able to calculate the augmented matrices (for at least variance, but maybe also for the covariances).

You must keep in mind that ADF requires substantial sample sizes. Generally a lot higher than for a ML estimation. I had 10 variables, fixed a lot of parameters and had a polyserial correlation matrix and 730 respondents were required to run the model. I also had to turn off the admissibility check in LISREL. The article has never been finished as I did not trust what was going on. Two experts also could not help me fix the problem.

Can you describe the data you are trying to analyze? It could help to give you advice.

Respected Professor,

Thanks a lot for your response.

My data set comprise of 344 respondents. I am trying to test whether financial literacy could moderate the relationship of behavioral biases and financial well-being. Where, financial literary is a continuous variable, behavioral bias (Exponential Growth Bias) is a dichotomous variable (0,1) and financial well-being is a continuous variable. Moreover, there are 12 control variables in the SEM. Before applying ADF, I estimated a Standard Linear SEM with all my independent variables (behavioral biases) and found no significant moderation. Then, I found that there was an issue of multi collinearity among the independent variables as well as their interaction terms. So I tested each independent separately with Asymptotically distribution-free (ADF) technique as an estimation method and found evidence of significant moderation. However, now I am finding difficulty in justifying ADF as an estimation model. It would be grate if you suggest a way forward.

Regards

Khalil