Is there an analog to the five factor model for emotion?
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.