Latent Profile Analysis and Statistical Methods in Psychology There has been a popular phenomenon that has several ‘hallmark’ components, and are uniquely associated with sexual abuse survivors. I would like to verify that the components can stand as a construct, and that these components are indeed a unique phenomenon among sexual abuse survivors, more than other typologies.
Previously, I have carried out Structural Equation Modelling (SEM) and regression investigating risk factors, correlates, etc. I would like to use a different approach on this phenomenon. I also have data on potential risk factors, correlates, etc.
a) What statistical approach do you guys recommend me to use? All variables are continuous, but categorization is also possible. Is Latent Profile Analysis (LPA) appropriate here, given we would like to assess typologies based on several latent continuous variables? I intend to use LPA to examine the determined typologies and assess whether the phenomenon (let's give it a name: construct A) is more pronounced in the group with SEXUAL violence than on the other groups.
Or are another statistical methods more appropriate (including SEM, Factor Analysis, etc)?
b) For Latent Profile Analysis, is it possible to use Mplus? Otherwise, what are application recommended for that?

Latent Profile Analysis (LPA) is a term typically used for a model which identifies latent sub-populations within a population based on a certain set of categorical variables. In your case, you have continuous variables, and the corresponding term used for this is Latent Class Analysis (LCA). Admitedly, there is some cross-over regarding the use of these terms.
So, if you want to identify latent subgroups, you can use LCA/LPA.
Yes, it is possible to fit both LCA and LPA models with Mplus
