Longitudinal data analysis - is correlation of random effects with fixed effects an issue?

[Daniel]

Hi,

in frequentist framework, I typically analyse longitudial data with lme4/mixed models, using time as random slope and groups/subjects as random intercept - see, classical, the sleepstudy-example: lmer(Reaction ~ Days + (1 + Days | Subject)).

1) First question: In a Bayesian framework, I assume that I would use the same formula, but just replace "lmer" with "brm" to fit a longitudinal model?

2) Especially from colleagues who come from the field of health economics, I often read they use fixed effects models because "FE regressions only use changes within units (individuals) over time (intraindividual changes)" - so, no time-invyaring predictors are included. The explanation is the correlation between random and fixed effects, which would violate proper assumptions to run a mixed model: "Many panel regression models consider unobserved effects as random variables. The success of this methodology hinges on whether the unobserved effects are associated with the explanatory variables. A violation of this assumption would result in inconsistent estimates when, e.g., pooled OLS estimates or random effects (RE) strategies were used, whereas fixed effects (FE) regressions would deliver consistent estimates (Cameron AC, Trivedi PK. Microeconometrics: methods and applications. Cambridge University Press, New York, 2005)". My 2nd question is: Is this also a concern in Bayesian framework? Or is using a mixed model with brms the way to go for longitudinal data analysis? I know that many problems that occur during to MLE do not occur with MCMC sampling, that's why I'm asking.

Thanks in advance

Daniel

[Paul Buerkner]

1) This is correct.

2) I don't really know to be honest. If this *really* was an issue, I assume it would be one also in a Bayesian framework.

That said, I think the multilevel models are definitely a very good way to analyse longitudinal data in general, but I can't really comment on

the concerns raised for panel regression.

--
You received this message because you are subscribed to the Google Groups "brms-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to brms-users+unsubscribe@googlegroups.com.
To post to this group, send email to brms-...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/brms-users/6302b99b-042e-4306-ba4a-6f3c4e9ff5d5%40googlegroups.com.
For more options, visit https://groups.google.com/d/optout.