Is there an analog to the five factor model for emotion? To the best of my understanding, the five factor model of personality comes from a factor analysis on a large list of adjectives that can be used to describe an individual's personality. It is validated, in some sense, by its usefulness in predicting behavior and life outcomes in a wide range of contexts.
It seems like something very similar could be done for emotion. I.e. list words describing a persons present state (angry, remorseful, sad, bitter, frustrated, etcetera) and do a factor analysis on those. Then, see if the resulting model (assuming that the analysis yields something useful) is predictive of shorter term / state dependent behavior.
Has any work like this been done?
The recently published Atlas of personality, emotion and behaviour is possibly what you are looking for(Mobbs, 2020).  Over 3,000 emotions are included in the analysis, a summary of which is below.  The article has a more comprehensive version.  The five factor model was derived through factorisation whereas the atlas was developed using a lexical/network approach.

References
Mobbs AED (2020) An atlas of personality, emotion and behaviour. PLOS ONE 15(1): e0227877. https://doi.org/10.1371/journal.pone.0227877
Declared Interest
I am the author of the atlas paper.