I am analyzing the Collaborative Psychiatric Epidemiology Surveys public use data set, and their website explicitly states to use the clustering variable (SECLUSTR) as the PSU. Unfortunately, SECLUSTR has a maximum value of 2, and therefore there are far too many singleton PSU's to handle them by simply deleting those observations from an analysis.
In Stata 10/SE, one may handle this problem by using the "singleunit" option following the svyset command. According to ICPSR's CPES documentation, the singleunit option should be specified as "singleunit(certainty)". Does Mplus have a similar option for handling singleton PSU's for "type=complex"?. If so, what would it be? If not, how would you advise handling a complex survey dataset in mplus that has a substantial number of singleton PSU's that cannot be deleted?