I am a retired, but still active intellectually, professor in Psychology. When I was teaching advanced statistics, I used Mx to introduce SEM to students. I continue working on statistical development. I the short term, I want to investigate implementing PARAFAC (Parallel Factor Analysis) in SEM, to further my own understanding and to find out tricks to reduce the number of trivially equivalent but mathematically distinct minima in the OpenMx implementation. When working with convariance matrices, setting a factor loading to 1 may solve the polarity indeterminacy of a factor that is allowed to load on all observed variables, but factor permutation remains a source of multiple optima. Since PARAFAC rests on assumptions of non-proportional factor variances across groups, it seems that a SEM implementation with LR confidence intervals could indicate, by turning out huge, when the assumption does not hold. It is not clear how the LR based confidence intervals can be fooled by the numerous optima.