Dealing with missing data by EM in single-case studies.

Area of Science:

• Behavioral Science
• Psychology
• Research Methodology

Background:

• Single-case experimental designs (SCED) are crucial for evidence-based practices.
• Missing data is a common challenge in SCED due to multiple behavioral measures.
• The expectation-maximization (EM) algorithm shows promise for handling missing data in SCED.

Purpose of the Study:

• To systematically examine the performance of the EM algorithm in SCED with AB designs.
• To evaluate EM's effectiveness under varying missing rates, autocorrelation, intervention lengths, effect sizes, and models.
• To assess the impact of autocorrelation and missing data on intervention effect estimates.

Main Methods:

• Applied the expectation-maximization (EM) algorithm to simulated SCED data (AB design).
• Varied missing data rates, autocorrelation levels, intervention phase lengths, and effect magnitudes.
• Utilized two fitted models and assessed three intervention effect indicators (baseline slope, level shift, slope change).
• Evaluated performance using relative bias, root-mean squared error, and relative bias of standard error estimates.

Main Results:

• Autocorrelation was the most significant factor affecting the quality of estimates.
• Autocorrelation interacted with missing rate, influencing estimate bias and root-mean squared error.
• Autocorrelation also interacted with the fitted model, affecting the bias of estimated standard errors.
• A simpler model without autocorrelation is suitable for estimating baseline slope and slope change.

Conclusions:

• The expectation-maximization (EM) algorithm is a principled and recommended method for handling missing data in SCED studies.
• Researchers can use simpler models for specific estimates when autocorrelation is accounted for.
• Decision trees are provided to guide the application of EM in SCED research.