An introduction to modeling longitudinal data with generalized additive models: applications to single-case designs

Area of Science:

• Psychology
• Education
• Statistics

Background:

• Single-case designs (SCDs) are crucial for evaluating intervention effectiveness in psychological and educational research.
• Analyzing SCD data presents challenges, particularly in accounting for trends over time.
• Existing analytical methods often require pre-specifying the data's functional form, which may not accurately reflect complex trends.

Purpose of the Study:

• Introduce generalized additive models (GAMs) as a novel statistical technique for analyzing SCD data.
• Demonstrate how GAMs can flexibly model trends in SCDs without imposing a priori functional forms.
• Provide a procedure for using GAMs to test for treatment effects and assess trend presence in SCDs.

Main Methods:

• Review the challenges of trend analysis in SCDs and current analytical approaches.
• Describe the principles of generalized additive models (GAMs).
• Develop and illustrate a GAM-based procedure for analyzing SCDs, including a simulation study and examples.

Main Results:

• GAMs allow the data to inform the functional form of the trend, offering a more flexible alternative to traditional parametric regression.
• The proposed GAM procedure effectively tests for treatment effects and examines trend presence in SCD data.
• Simulation results indicate favorable statistical properties of GAMs for SCD analysis.

Conclusions:

• Generalized additive models (GAMs) show significant promise as both a primary analysis strategy and a sensitivity analysis tool for SCDs.
• GAMs can enhance the rigor of intervention effect evaluation by providing a data-driven approach to trend modeling.
• Further research is warranted to explore the full potential and address limitations of GAMs in SCD research.