Bootstrap Standard Error Estimates in Dynamic Factor Analysis

Area of Science:

• Statistics
• Psychometrics
• Time Series Analysis

Background:

• Dynamic factor analysis (DFA) models changes in manifest variables over time using latent factors.
• Estimating standard errors in DFA is complex due to the temporal dependence of observations.
• Traditional bootstrap methods are unsuitable for time-series data as they disrupt the order of measurements.

Purpose of the Study:

• To introduce and evaluate appropriate bootstrap methods for standard error estimation in dynamic factor analysis.
• To address the limitations of standard bootstrap procedures in time-series contexts.
• To provide reliable statistical inference for dynamic factor models.

Main Methods:

• The study describes two appropriate bootstrap procedures for DFA: the moving block bootstrap and the parametric bootstrap.
• The moving block bootstrap samples blocks of contiguous time points to maintain temporal structure.
• The parametric bootstrap involves a Monte Carlo simulation using sample estimates as population parameters.

Main Results:

• Demonstrated the application of moving block and parametric bootstrap methods using real-world data (affective mood, personality self-ratings) and a simulation study.
• Validated the effectiveness of these bootstrap techniques in providing accurate standard error estimates for DFA parameters.
• Confirmed that these methods overcome the limitations of standard bootstrap approaches for time-series data.

Conclusions:

• Moving block and parametric bootstrap methods are suitable for obtaining standard errors in dynamic factor analysis.
• These techniques correctly account for the temporal dependencies inherent in time-series data.
• The validated methods enhance the reliability of statistical inference in longitudinal studies using DFA.