Specializing in Quantitative Methods

[coldsweat]

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Short story: I am searching for advice as a doctoral student interested in learning advanced quantitative methods.

Long story: As an undergraduate, I took one statistics class, and while I enjoyed it, I didn't take another class in it. I didn't take any math classes either, which were not required by my university because it had an open curriculum. When I entered my master's program, however, I was exposed to psychometric theory and became really interested in the field. I took a course on multiple regression in my master's program, but there was a lot of hand waving regarding the derivation of formulas and their relationships to each other. This knowledge wasn't absolutely necessary to interpret the output, but I would have loved to develop a more conceptual understanding of the procedures.

I'm starting a doctoral program this fall and our department has a strong quantitative methods program, so I'm looking forward to taking as many quantitative courses as possible and using the methods and concepts I learn in my research (specifically, EFA, CFA, SEM, latent variable growth curve modeling, latent class analysis, and item response theory). For those on the board with experience in advanced quantitative methods, what would you recommend I do to prepare myself? I'm self-studying linear algebra this summer in the hope of unlocking the secrets of correlation/covariance matrices, which has been interesting. However, my last math course was calculus was in high school and I'm slowly becoming accustomed to the proofs. Do you believe that studying linear algebra, calculus, probability, and other fundamental math areas will help me significantly or is it overkill considering the methods I want to learn? What books/online resources have you found useful in learning psychometrics/advanced statistical techniques? How did you learn the techniques - was it through self-study, taking courses, performing analyses and consulting with professors/colleagues, or wrestling with problems with analyses by yourself? I'm supposing it was a combination of these methods, but which if any was the most important? What advice in general would you have for a doctoral psychology student interested in the quantitative path?

Thanks!

 

[IOPsych]

I think you are on the right path. Most people I have talked said if you know calculus you are good to go. But then again, I am also not talking to Cheryshenko, Judea Pearl, etc. Although the people I have talked to do have a fair amount of publications in methodology journals. It can never hurt to know linear algebra 🙂

 

[AcronymAllergy]

Semi-random comment, but I know that concepts from matrix algebra can be useful in obtaining a deeper understanding of some of the multivariate stats.

 

[IOPsych]

Semi-random comment, but I know that concepts from matrix algebra can be useful in obtaining a deeper understanding of some of the multivariate stats.

Yes, matrix algebra is definitely useful. Matrix algebra is a component of linear algebra.

 

[Pragma]

Semi-random comment, but I know that concepts from matrix algebra can be useful in obtaining a deeper understanding of some of the multivariate stats.

Ahhh, matrix algebra - brings back fond memories of my multivariate class.

OP, I am sure that self-study won't hurt you. But I think the actual coursework is where it's at, and sitting down with your research group to go over analyses.

 

[Ollie123]

A solid background in matrix algebra and calculus should place you in a great position for understanding most things covered in statistics. Familiarity with statistical programming would also be helpful.

That said, the more experience I get, the more I realize those are far from necessary. I'd wager > 95% of folks using such techniques have little to no understanding of the underlying mathematics. Of course, if you want to do true quant work (i.e. DEVELOP new statistical techniques) a much stronger math background is of course necessary. I've developed a reputation as a "stats guy" and I certainly could not explain to someone the underlying math behind most of those techniques, though could run most of them with at least a moderate degree of confidence and am certain I could figure out the ones I haven't used. That said - I'm continually amazed at the things actual statisticians don't know/can't explain either. Its somewhat frightening, but I think a lot of people are happy to just trust in the syntax/menus and not peak inside the black box. For better or worse, it doesn't seem to impact one's ability to publish widely cited papers in top tier journals - at least from what I've seen.

That said - I wish I did know the math and am continually striving to learn it. That's me though. I'm obsessively detail-oriented, but also amazingly inefficient. Grad school is as much about finding a balance between those things (I'm still working on that one!) as anything else.

 

[Member6523]

Bruce Thompson is an excellent writer who lays out basic concepts of factor analysis and canonical correlational analysis to those who only have a basic understanding of matrix algebra. If you learn a bit about CCA, you can see how it is the most "raw" statistic, in that different iterations of it basically translate into familiar inferential statistics (ANOVA, regression, chi-square). If you feel up to it, read Thomas Knapp's article "Canonical correlation analysis: a general parametric significance-testing system" to see its potential. If Thompson whets your appetite, try reading some of the older texts by Mardia and Tatsuoka - they also provide much of the quantitative background underlying multivariate techniques. Tabachnick and Fidell's book is a gold standard of multivariate analysis that includes a few appendices on matrix algebra as well.