The differences between the sex-based invariance procedure for the full sample and the results from the separate analyses for males and females reflect the different issues the two statistical approaches address. If the question is whether the two sexes are enough alike to combine, then the similarities across males and females in how LR relates to outcomes, the way potential mediators in the models relate to each other and to outcomes, and the similar ways the indicators for most latent variables relate in the SEM components, all support the conclusion that in many ways the models for the two sexes are similar. However, if the question is whether there are any potentially interesting differences in how males and females perform in the model, with the emphasis of the question on what differences exist, there can be a different answer.
