Hi Laura, the FIML estimation method takes care of missing data itself. Whereas other missing data methods use imputation or deletion of missing values, FIML uses the information available to do the estimation without needing to either impute or delete missing values. Dr. Paul D. Allison has several SAS conferences papers on missing data. Specifically, he presented a paper on how to handle missing data by maximum likelihood that you might find useful for understanding how to implement it. While Dr. Allison demonstration of the ML method was using different SAS Procs, hopefully translating it to the proc you are interested would be smoothly done. I hope this helps.

From SAS documentation related to FIML.

"The data set, the number of observations, the model type, and analysis type are shown in the first table of Output 25.13.1. Although PROC CALIS reads all 32 records in the data set, only 16 of these records are used. The remaining 16 records contain at least one missing value in the tests. They are discarded from the analysis. Therefore, the maximum likelihood method only uses those 16 observations without missing values. "

"The maximum likelihood method, as implemented in PROC CALIS, deletes all observations with at least one missing value in the estimation. In a sense, the partially available information of these deleted observations is wasted. This greatly reduces the efficiency of the estimation, which results in higher standard error estimates. "

They are careful to point out that you need to be careful because FIML does not apply generally.  I suspect that this type of FIML can only be used in a very, very narrow range of situations.

One of the standard references is the missing data book of Little and Rubin (2002)..  I would never use FIML.

Thanks to you both! I emailed Bobby Jones (one of the creators of PROC TRAJ) and he let me know that METHOD=FIML doesn't work with PROC TRAJ, but another command using the drop out method should work just fine. I tried it out and was successful. 

I have attached the examples he gave me if anyone is interested. Note: the example command in the word doc is for Stata but the attached example is for SAS

For FIML to be valid methodologically, the set of records with no missing data need to be an exactly correct representation of the patterns that would be present in a large set (say superset) that is all the data.  Almost all the examples in Little and Rubin (2002) show that using only the records with no missing data will lead to incorrect maximum likelihoods or Bayesian inference.  In other words, you almost always reach wrong conclusions.

The fact the a SAS Proc or any other procedures in other statistical packages will run if you only use the records with missing data can lead to problems at the inferential end.