Different results on tetrachorical correlations in Mplus and Stata--Stata announces modified procedure

To identify the structure of mental disorders in large-scale epidemiological data sets, investigators frequently use tetrachoric correlations as a first step for subsequent application of latent class and factor analytic methods. It has been possible to do this with Stata since 2005, whereas the corresponding Mplus routine has been on the market for some years. Using an identical data set we observed considerable differences between the results of the packages. This paper illustrates the differences with several examples from the Early Developmental Stages of Psychopathology Study data set, which consists of 3021 subjects, with diagnostic information assessed by the CIDI. Results reveal that tetrachoric correlations resulting from Mplus were often considerably smaller than those computed with Stata. The results were dramatically different, especially where there were few observation per cell or even empty cells. These findings were put to Mplus and Stata, whose responses clarified the discrepancies by describing the different mathematical assumptions and procedures used. Stata announced that it intended to launch a modified procedure.