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Comparison of Estimation Procedures for Multilevel AR(1) Models.

Tanja Krone1, Casper J Albers1, Marieke E Timmerman1

  • 1Department of Psychometrics and Statistics, Heymans Institute, University of Groningen Groningen, Netherlands.

Frontiers in Psychology
|June 1, 2016
PubMed
Summary
This summary is machine-generated.

For multilevel time series, random estimation in Autoregressive model 1 (AR(1)) is preferred over fixed estimation due to lower bias and higher power. Bayesian and Maximum Likelihood Estimation methods showed comparable performance in this simulation study.

Keywords:
Bayesian MCMCautocorrelationmaximum likelihood estimationmultisubjectsimulation studytime series analysis

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Area of Science:

  • Statistics
  • Psychometrics
  • Econometrics

Background:

  • Multilevel models are essential for analyzing time series data from multiple individuals.
  • Autocorrelation estimation is crucial for understanding temporal dependencies within these models.
  • Comparing Maximum Likelihood Estimation (MLE) and Bayesian Markov Chain Monte Carlo (MCMC) is vital for robust statistical inference.

Purpose of the Study:

  • To compare Maximum Likelihood Estimation (MLE) and Bayesian Markov Chain Monte Carlo (MCMC) for estimating autocorrelation in Multilevel Autoregressive model 1 (AR(1)) models.
  • To investigate the impact of modeling individual parameters as fixed versus random effects.
  • To evaluate how varying simulation parameters (time series length, number of individuals, autocorrelation mean and standard deviation) influence estimation accuracy.

Main Methods:

  • A simulation study was conducted with a fully crossed design.
  • Key simulation parameters included time series length (10 or 25), number of individuals (10 or 25), autocorrelation mean (-0.6 to 0.6), and standard deviation (0.25 or 0.40).
  • Two estimation methods (MLE and Bayesian MCMC) and two parameter modeling approaches (fixed vs. random effects) were compared.

Main Results:

  • Random estimators demonstrated less bias and higher statistical power compared to fixed estimators for population autocorrelation.
  • Increasing the number of individuals significantly benefited random estimators, with a smaller effect on fixed estimators.
  • Fixed estimators showed a slight advantage with more time points, while random estimators performed better overall when feasible.

Conclusions:

  • Random effect modeling is generally preferred over fixed effect modeling for estimating autocorrelation in multilevel AR(1) models.
  • Both MLE and Bayesian MCMC methods offer comparable results, with Bayesian methods showing slightly less bias and MLE showing lower variability.
  • Optimal estimation is achieved with a higher number of individuals and time points, and lower individual variability in autocorrelation.