Generalized Least Squares (GLS) transformation in analyzing Single-Case Experimental Design (Poster 7)

• In Event: Innovative Methodologies and Systematic Reviews in Analyzing Single-Case Experimental Design Data

Abstract

Multilevel models (MLMs) were proposed to be a flexible and promising method for accounting for the time trend and the heterogeneity across subjects (Ferron et al., 2009). MLMs estimate fixed effects to determine the average treatment effect and use variance components to account for between-case variability.
There are several methodological challenges in the analysis of single-case data. The first challenge is autocorrelation, which refers to the degree of correlation between successive data points that are serially dependent due to repeated measurements of the outcome from the same individual (Barnard‐Brak et al., 2021). Data analyzed from SCEDs inherently exhibit some degree of autocorrelation because of the within-subject time-series nature of the data points. Ignoring autocorrelation leads to biased estimation of fixed effects and inflated Type-I error rates. Another challenge is the underfitting of the variance-covariance structure when fitting an MLM for single-case data (Li et al., 2022). Previous studies have often fitted single-case data using a diagonal covariance structure, which makes a strong assumption that the treatment effect is uncorrelated with the baseline level. This underfitting can result in biased estimation of random effects and inflated Type-I error rates for the inference of fixed effects.
Previous research has addressed these issues separately, such as fitting the MLM with autocorrelated residuals to handle autocorrelation and using degrees of freedom adjustment methods to correct for inflated Type-I error. However, no studies have focused on the evaluation of fixed effects estimation and inference when both unstructured variance and autocorrelated residuals exist.
The primary objective of this study is to evaluate fixed effects estimation and inference within the context of unstructured variance and autocorrelated residuals. Specifically, this research aims to assess the effectiveness of using the Generalized Least Squares (GLS) transformation for estimating fixed effects with autocorrelation and the application of Satterthwaite’s adjustment for making inferences on these fixed effects with unstructured covariance. The simulation for this proposed study aims to evaluate the MLMs with autocorrelated residuals and unstructured variance-covariance matrix in the fixed-effects estimation and inference using GLS transformation. Simulation conditions will vary by different numbers of subjects, number of measurements, effect sizes, and strength of autocorrelation. We anticipate that accurate specification of the autocorrelation and variance-covariance matrix will result in reliable inferential statistics and reduced bias in fixed-effects estimation.
The proposed study is the first study on evaluating the MLM with autocorrelated residuals and an unstructured variance in SCEDs using GLS transformation. The findings highlight the effectiveness of using the GLS transformation for estimating fixed effects in the presence of autocorrelation and the application of Satterthwaite’s adjustment for inference with unstructured covariance.

Authors

• Chendong Li, Texas A&M University

• Eunkyeng Baek, Texas A&M University

• Wen Luo, Texas A&M University