Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data.

Area of Science:

• Psychological Research Methods
• Longitudinal Data Analysis
• Time Series Modeling

Background:

• The Experience Sampling Method (ESM) collects intensive longitudinal data with high ecological validity.
• ESM data often features unequal spacing due to varied measurement intervals within and across days.
• Discrete-time (DT) modeling approaches assume equally spaced data, posing a challenge for ESM analysis.

Purpose of the Study:

• To evaluate the practical relevance of violated model assumptions in DT AR(1) and VAR(1) models for unequally spaced ESM data.
• To investigate the bias in parameters of interest under different DT model implementations compared to continuous-time (CT) models.
• To illustrate the practical implications of DT versus CT modeling using empirical affect data.

Main Methods:

• Simulated data under an ESM measurement design were used to assess parameter bias.
• Four model implementations were compared, ranging from a true CT model to a crude DT model.
• Empirical affect data were analyzed to demonstrate real-world differences between DT and CT modeling.

Main Results:

• The bias in DT (V)AR models for unequally spaced ESM data is significantly influenced by the true parameter and data characteristics.
• The magnitude and direction of bias vary considerably depending on the specific model implementation and data properties.
• Differences between DT and CT modeling can be substantial in practice, as shown by the empirical data analysis.

Conclusions:

• Continuous-time (CT) modeling is recommended for analyzing unequally spaced ESM data whenever feasible.
• DT modeling approaches may introduce significant bias when applied to ESM data due to violated spacing assumptions.
• Advancements in CT modeling software make its implementation more accessible for researchers studying intensive longitudinal data.