# Dynamic factor analysis vs factor analysis on differences

I'm trying to wrap my head around dynamic factor analysis. So far, my understanding is that DFA is just factor analysis plus a time series model on the scores (the loadings remain fixed). However, in the cases that I've seen, the model on the scores is just a random walk with a diagonal correlation matrix. This seems identical to normal factor analysis applied to the differences. What am I missing?

If you know of any good references to get me started, I'd appreciate them. I'd actually like to find something that allows the loadings to be slowly-varying; my context for thinking about that is West&Harrison-style DLMs, which hasn't got me far.

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If your loadings slowly vary and your factor scores also vary its not immediately clear how you'd identify the model. Covariates on the factor scores perhaps? –  conjugateprior Jul 6 at 18:01
@conjugateprior Check this out –  bfoste01 Jul 16 at 2:31
After an (admittedly brief) skim of the paper my point is that one could not index both the loadings $\lambda$ and the factor scores $f$ with $t$. At most one of them. –  conjugateprior Jul 17 at 11:44