Generalized least squares transformation for single-case experimental design: Introducing the R package lmeSCED

Area of Science:

• Behavioral and social sciences
• Statistical modeling
• Psychology

Background:

• Single-case experimental designs (SCEDs) generate repeated observations, suitable for multilevel models (MLMs).
• SCED data often exhibit autocorrelation and small sample sizes, leading to biased standard errors and inflated Type I error rates in fixed effects.
• Existing statistical software has limitations in simultaneously addressing these SCED data challenges.

Purpose of the Study:

• To evaluate a two-step statistical approach combining generalized least squares (GLS) transformation for autocorrelation and Satterthwaite's adjustment for small samples.
• To implement these methods, alongside novel tests for random effects, in a user-friendly R package named lmeSCED.
• To assess the performance of this approach using Monte Carlo simulations and demonstrate its practical application.

Main Methods:

• A two-step method involving GLS transformation to handle AR(1) residuals and Satterthwaite's adjustment for fixed-effects inference.
• Development of the lmeSCED R package, incorporating a boundary-corrected restricted likelihood-ratio test and parametric bootstrapping for random effects.
• Monte Carlo simulation studies to evaluate parameter recovery and Type I error rates.

Main Results:

• Applying MLMs to GLS-transformed SCED data resulted in unbiased parameter recovery.
• The proposed methods maintained Type I error rates at nominal levels.
• The lmeSCED package effectively handles autocorrelation and small sample sizes in SCED data.

Conclusions:

• The evaluated two-step method provides a statistically sound approach for analyzing SCED data with multilevel models.
• The lmeSCED R package offers a practical and effective tool for researchers, enhancing the reliability of SCED data analysis.
• This work addresses critical limitations in existing statistical approaches for SCED data, paving the way for more accurate research findings.