Reconsidering the use of the general linear model with single-case data

Area of Science:

• Behavioral Science
• Statistical Modeling
• Research Methodology

Background:

• The General Linear Model (GLM) is increasingly used for single-case data analysis.
• Justification for GLM often relies on low estimates of autocorrelation.
• Potential biases in autocorrelation estimates can impact GLM validity.

Purpose of the Study:

• To question the sole reliance on low autocorrelation estimates for GLM justification in single-case data.
• To investigate the impact of linear model complexity on autocorrelation bias.
• To provide methods for assessing GLM appropriateness across plausible autocorrelation ranges.

Main Methods:

• Utilized Monte Carlo simulations to examine bias in autocorrelation estimates.
• Developed a method to determine the range of plausible autocorrelation parameters.
• Illustrated techniques for adjusting confidence intervals for GLM analysis.

Main Results:

• Autocorrelation bias in GLM analysis is dependent on the complexity of the linear model.
• A method was demonstrated to identify a reasonable range for autocorrelation parameters.
• GLM analysis validity can be confirmed when it performs adequately across plausible autocorrelations.

Conclusions:

• Relying solely on low autocorrelation estimates to justify GLM for single-case data is insufficient.
• Methods are provided to strengthen the argument for GLM use by assessing its performance across plausible autocorrelation ranges.
• Adjustments to confidence intervals can ensure adequate coverage probabilities when GLM performance is variable.