This has been answered in part in many places but here I am asking again.
Background: I did calculus and vectors and advanced functions in high school. Then I did a bachelor's degree in social work and a master's in social work and now I'm looking to do a PhD. I consider myself statistically literate, more so than average social work students, and can navigate SPSS. But to conduct rigorous research that is firmly grounded in theory in the social sciences and in the math behind statistics I feel a need for a thorough understanding of mathematics so I can say why I actually did the analyses, why I use certain alpha scores, what I did, and what do the results really mean rather than relying solely on convention and audience ignorance.
What I've gathered so far is I should start with topics in linear algebra, and real analysis... and maybe avoid Discovering Statistics (although it is a favorite among many profs and students)... but otherwise I am totally lost.
Ultimately, I want to be able to run and understand multi-group confirmatory factor analysis to look at scalar invariance but later in the future also have the flexibility to do some SEM, IRT, Bayesian statistics, and natural language processing.
So for someone looking to self study with no undergraduate math experience....what is my trajectory (e.g. MOOCs, books, get another bachelor's degree)?
BTW I'm going to focus on learning R - for flexibility in the future.