Consequences of sampling frequency on the estimated dynamics of AR processes using continuous-time models

Area of Science:

• Psychological modeling
• Longitudinal data analysis
• Statistical methods

Background:

• Continuous-time (CT) models offer a flexible framework for analyzing longitudinal psychological data.
• CT models allow for a single underlying continuous function assumption, overcoming limitations of discrete-time (DT) models.
• CT models facilitate cross-interval comparisons (e.g., daily, weekly, monthly) by rescaling parameters to a common time scale.

Purpose of the Study:

• To evaluate the accuracy of continuous-time autoregressive (CT-AR) models in recovering true process dynamics.
• To investigate the impact of differing sampling intervals on the recovery of CT-AR model parameters.
• To assess how varying strengths of the autoregressive (AR) parameter influence model recovery across different sampling frequencies.

Main Methods:

• A Monte Carlo simulation was employed to test CT-AR model performance.
• Two generating time intervals (daily and weekly) were simulated with varied AR parameter strengths.
• Model recovery was assessed across three sampling intervals: daily, weekly, and monthly.

Main Results:

• Sampling at a faster interval than the generating process generally allowed for accurate recovery of AR effects.
• When sampling slower than the generating process, stronger underlying AR effects were necessary for satisfactory parameter recovery.
• Inadequate sampling frequency led to biased estimations and poor coverage of true parameters.

Conclusions:

• Frequent data sampling, ideally faster than the underlying process dynamics, is recommended for reliable CT-AR model estimation.
• Researchers should align sampling intervals with theoretical knowledge of the psychological construct under investigation.
• The capability of CT-AR models to accurately represent longitudinal data is contingent upon appropriate sampling frequency.