What is the best way to compare (personality) data from two time points? I have collected personality data (big five) for N = 50 at two times, approximately 10 years apart. I simply want to see how stable the traits are across this time point (i.e. is there a statistical difference in say, agreeableness between from collection time 1 to collection time 2). I know you can use t-tests/ANOVAs for each of the traits, but I wondered if there are other ways which may be better/more sophisticated/more reliable?
Any thoughts would be greatly appreciated. 
 A: You might consider some form of longitudinal structural equation modelling (see Little, 2013), like a latent panel model. You would not only be able to look at stability or change in levels of big five factors, but you could also assess longitudinal invariance of personality factors (Little, 2013, provides good coverage of longitudinal invariance, specifically, but Vandenberg & Lance, 2000, is a good general conceptual intro to invariance testing), which isn't something you can do with the more typical approaches. In a nutshell, this would allow you to ask the more foundational question (before comparing mean-levels of a personality factor over time) of whether the structure of personality is stable over those 10 years. I'm not a personality psychologist, so I don't know how intuitively plausible that possibility is, but it doesn't seem wholly unreasonable to suggest that the way personality manifests in a person might change over a decade (i.e., the distinctions between agreeableness, extraversion, openness, neuroticism, and conscientious might become more/less nuanced). 
If you're new to SEM, this CV thread here has a number of really good answers outlining the benefits of this approach to analyzing data.
References
Little, T. D. (2013). Longitudinal structural equation modeling. New York, NY: Guilford Press.
Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational researchers. Organizational Research Methods, 3, 4-70.
