# Characterize the shape of a career path

I have data on a few hundred people in a certain career. The rows are individual people and the columns are years (first year of their career, second year, etc. to retirement). Each year a certain number of events happen to the person, here is a graphical representative:

The graph is: x axis is years, y axis is total cumulative events for each person, and each line is a person.

My colleagues and I are interested in mathematically describing these career paths in a few ways:

• The overall (vague) goal is to look for career paths that are similar to each other.
• We assume in order to do that, we would have be able to characterize individual lines and then find other lines within a certain percentage different. Does that sound reasonable?
• We already know we'd like to compare people who had careers that began in different decades (1980's, 1990's etc..)
• But we also assume we'll find "high performers" and "low performers" that could be clumped together, or people who had career paths that accelerated vs people who had career paths that flatlined. We'd love to know how we could examine these.
• I did ask my colleagues if it'd make sense to just get an aggregate shape for EVERYONE, i.e. end up with one line that described the aggregate career path curve for everyone, and they didn't think that made sense (given some people's careers are so different). I asked if a certain number of groups made sense (i.e. low, medium, high performers) and they weren't sure. Is there a recommendation out there based on anything mathematically that could help guide us to picking a certain number of "groups"?
• Any ideas?

I apologize that several of these questions are somewhat vague, and unfortunately at the moment I don't really have any info about these people besides name and event per year, the data was collected before I became involved.

• You could look into clustering of curves, see stats.stackexchange.com/questions/315096/clustering-curves Jul 19, 2020 at 4:15
• You need to model the curves and then cluster on the fits. Aug 5, 2020 at 1:13
• @kjetilbhalvorsen, what's your thinking behind adding the [multivariate-analysis] tag? It's not obvios to me that this is a multivariate analysis. Aug 5, 2020 at 1:15
• @gung: maybe functional data analysis would be a better fit, which is a subfiels of multivariate? Aug 5, 2020 at 1:46
• For measures of similarity between curves, see stats.stackexchange.com/questions/27861/…, stackoverflow.com/questions/10373062/…. Can you share (a link to) (part of) your data? Aug 6, 2020 at 2:06