Comparison of Estimation Procedures for Multilevel AR(1) Models

Tanja Krone, Casper J. Albers, Marieke E. Timmerman

To estimate a time series model for multiple individuals, a multilevel model may be used. In this paper we compare two estimation methods for the autocorrelation in Multilevel AR(1) models, namely Maximum Likelihood Estimation (MLE) and Bayesian Markov Chain Monte Carlo. Furthermore, we examine the difference between modeling fixed and random individual parameters. To this end, we perform a simulation study with a fully crossed design, in which we vary the length of the time series (10 or 25), the number of individuals per sample (10 or 25), the mean of the autocorrelation (-0.6 to 0.6 inclusive, in steps of 0.3) and the standard deviation of the autocorrelation (0.25 or 0.40). We found that the random estimators of the population autocorrelation show less bias and higher power, compared to the fixed estimators. As expected, the random estimators profit strongly from a higher number of individuals, while this effect is small for the fixed estimators. The fixed estimators profit slightly more from a higher number of time points than the random estimators. When possible, random estimation is preferred to fixed estimation. The difference between MLE and Bayesian estimation is nearly negligible. The Bayesian estimation shows a smaller bias, but MLE shows a smaller variability (i.e., standard deviation of the parameter estimates). Finally, better results are found for a higher number of individuals and time points, and for a lower individual variability of the autocorrelation. The effect of the size of the autocorrelation differs between outcome measures.