Modelling non-linear psychological processes: Reviewing and evaluating non-parametric approaches and their...

Area of Science:

• Psychology
• Statistics
• Data Science

Background:

• Psychological concepts are increasingly viewed as dynamic systems requiring advanced statistical analysis.
• Intensive longitudinal data (ILD) reveal complex non-linear phenomena like growth, switching, and oscillations.
• Existing statistical methods in psychology are often insufficient for accurately modeling these non-linear processes.

Purpose of the Study:

• Introduce advanced statistical methods (local polynomial regression, Gaussian processes, generalized additive models) to psychological researchers.
• Evaluate the efficacy of these methods for analyzing non-linear processes within ILD.
• Empower researchers to accurately model psychological dynamics and select appropriate statistical tools.

Main Methods:

• Simulation study comparing polynomial regression with local polynomial regression, Gaussian processes, and generalized additive models (GAMs).
• Application of GAMs to explore idiographic processes and identify phenomena in ILD.
• Review and evaluation of non-standard statistical methods within the context of ILD.

Main Results:

• Local polynomial regression, Gaussian processes, and GAMs demonstrated superior accuracy in inferring non-linear processes from ILD compared to polynomial regression.
• Generalized additive models (GAMs) closely approximated the data-generating parametric models, showing high accuracy.
• The study provides a framework for applying these methods to psychological ILD.

Conclusions:

• Advanced statistical methods, especially GAMs, are crucial for accurately modeling non-linear psychological dynamics found in ILD.
• These methods enhance psychological theory development by providing tools to capture complex temporal changes.
• Researchers are encouraged to adopt these flexible methods to better understand individual psychological processes.