In panel data analysis, I have used multi-level models with random/mixed effects to deal with auto-correlation issues (i.e., observations are clustered within individuals over time) with other parameters added to adjust for some specification of time and shocks of interest. ARMA/ARIMA seem designed to address similar issues.
The resources I’ve found online discuss either times series (ARMA/ARIMA) or mixed effect models but beyond being build on regression, I don’t understand the relationship between the two. Might one want to use ARMA/ARIMA from within a multilevel model? Is there a sense in which the two are equivalent or redundant?
Answers or pointers to resources that discuss this would be great.
I think the simplest way to look at it is to note that ARMA and similar models are designed to do different things than multi-level models, and use different data.
Time series analysis usually has long time series (possibly of hundreds or even thousands of time points) and the primary goal is to look at how a single variable changes over time. There are sophisticated methods to deal with many problems – not just autocorrelation, but seasonality and other periodic changes and so on.
Multilevel models are extensions from regression. They usually have relatively few time points (although they can have many) and the primary goal is to examine the relationship between a dependent variable and several independent variables. These models are not as good at dealing with complex relationships between a variable and time, partly because they usually have fewer time points (it’s hard to look at seasonality if you don’t have multiple data for each season).