Saturated models and assumptions of the twin method

When using raw data, Mx will generate a ?2ll statistic with a certain amount of df?s. This ?2ll statistic does not tell you how well this model describes the data. It is therefore necessary to compare the fit of a certain model to the fit a saturated model. In the context of twin analyses, a saturated model includes a covariance for each zygosity and a variance for each person-category (i.e. MZMtwin1, MZMtwin2, DZMtwin1 etc), as well as different means for each person-category.
In the saturated models several assumptions of the twin method can be tested (such as equal variances for MZ and DZ twins, for males and females etc). A variance components model should incorporate the results from testing assumptions in the saturated models (for example if males and females have different variances, an ACE males, KLM females model is preferred). Also statistically significant differences in means between MZ and DZ twins should be included in the final models.