Person-specific versus multilevel autoregressive models: Accuracy in parameter estimates at the population and individual levels

This paper compares the multilevel modelling (MLM) approach and the person-specific (PS) modelling approach in examining autoregressive (AR) relations with intensive longitudinal data. Two simulation studies are conducted to examine the influences of sample heterogeneity, time series length, sample size, and distribution of individual level AR coefficients on the accuracy of AR estimates, both at the population level and at the individual level. It is found that MLM generally outperforms the PS approach under two conditions: when the sample has a homogeneous AR pattern, namely, when all individuals in the sample are characterized by AR processes with the same order; and when the sample has heterogeneous AR patterns, but a multilevel model with a sufficiently high order (i.e., an order equal to or higher than the maximum order of individual AR patterns in the sample) is fitted and successfully converges. If a lower-order multilevel model is chosen for heterogeneous samples, the higher-order lagged effects are misrepresented, resulting in bias at the population level and larger prediction errors at the individual level. In these cases, the PS approach is preferable, given sufficient measurement occasions (T >= 50). In addition, sample size and distribution of individual level AR coefficients do not have a large impact on the results. Implications of these findings on model selection and research design are discussed.