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Updated: Jul 15, 2026

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Bayesian marginalized zero-inflated Poisson model with random effects for single-case experimental designs: A

Chendong Li1, Wen Luo1

  • 1Department of Educational Psychology, Texas A&M University.

Psychological Methods
|July 13, 2026
PubMed
Summary

This study introduces a Bayesian marginalized zero-inflated Poisson (mZIP) model for analyzing single-case experimental designs. The mZIP model accurately estimates intervention effects, outperforming other methods with zero-inflated count data.

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Area of Science:

  • Behavioral Science
  • Statistical Modeling
  • Psychometrics

Background:

  • Single-case experimental designs (SCEDs) often involve zero-inflated count data.
  • Traditional zero-inflated models estimate conditional effects, not the marginal effects typically of interest to researchers.
  • Existing methods face interpretational and estimation challenges with small sample sizes common in SCEDs.

Purpose of the Study:

  • To introduce and evaluate a Bayesian marginalized zero-inflated Poisson (mZIP) model for SCEDs.
  • To estimate the marginal intervention effect, aligning with applied research questions.
  • To compare the mZIP model's performance against existing methods for zero-inflated data in SCEDs.

Main Methods:

  • Developed a Bayesian marginalized zero-inflated Poisson (mZIP) model with random effects.
  • Conducted a Monte Carlo simulation study to assess model performance.
  • Compared mZIP with the log response ratio (LRR), Poisson GLMM, and negative binomial GLMM for marginal effect estimation.

Main Results:

  • The Bayesian mZIP model consistently provided unbiased estimates of the marginal treatment effect and reliable statistical inference.
  • LRR, Poisson GLMM, and negative binomial GLMM yielded biased estimates and invalid inference under high zero-inflation and small sample sizes.
  • The mZIP model demonstrated higher statistical power compared to the LRR.

Conclusions:

  • The Bayesian mZIP model is a robust and accurate tool for analyzing zero-inflated count data in single-case experimental designs.
  • It effectively estimates marginal intervention effects, offering a valid alternative to traditional conditional models.
  • The study highlights the importance of distinguishing between conditional and marginal estimands in SCED research.