How does AMOS or other SEM/path analysis software estimate missing data?

Question

I'm currently writing a paper as a hopeful publication. I'm using AMOS to run path models. But I think my question can apply when utilizing other path analytical software.

I have one path model that had missing data in the dependent variable so I had to allow Amos to 'estimate means and intercepts'

How does AMOS or other SEM/path analysis software estimate missing data?

Using a multiple regression allegory, does it run the analysis without the missing data, finds the beta's and intercepts, and use that to estimate the missing dependent variable data? And then run the analysis again with the full dataset of both missing subbed with the estimates and the non-missing data?

Answer 1

SEM programs (generally) use full information maximum likelihood (FIML) estimation. It doesn't really think about missing data as it calculates a likelihood for all of the data points that exist, it does not try to estimate what the missing values are. What you are describing is a little like multiple imputation (MI), which is asymptotically equivalent to FIML, but FIML can be model dependent, where MI is not.

Some people argue that the Full Information part is redundant, as ML should use full information (e.g. mixed models estimated with ML are equivalent to SEM models with FIML estimation, but people don't talk about FIML with mixed models, just ML).

Using your favorite search engine, you'll find lots of information on SEM and FIML, including some answers on this site, e.g. Full information maximum likelihood for missing data in R . The level of technical sophistication required to read papers on FIML varies a lot - so if you don't find things at your level, keep looking. However, the book chapter that first helped me to understand it (although it's getting a bit old now) is this one: Arbuckle, J. L. (1996). Full information estimation in the presence of incomplete data. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 243– 277). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.