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Tobit modeling for dependent-sample t-tests and moderated regression with ceiling or floor data.

Lijuan Wang1, Ruoxuan Li2

  • 1Department of Psychology, University of Notre Dame, 390 Corbett Hall, Notre Dame, IN, 46556, USA. lwang4@nd.edu.

Behavior Research Methods
|December 10, 2025
PubMed
Summary

Novel Tobit modeling approaches effectively address ceiling and floor effects in behavioral research, offering accurate estimates and reliable inference compared to conventional methods that yield biased results.

Keywords:
Ceiling effectsFloor effectsModerated regressionTobit modelingt test

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Area of Science:

  • Behavioral Science
  • Psychological Research
  • Quantitative Psychology

Background:

  • Ceiling and floor effects present significant analytical challenges in behavioral and psychological research.
  • Conventional statistical methods struggle when data are constrained by these effects, leading to inaccurate conclusions.

Purpose of the Study:

  • To develop and evaluate novel Tobit modeling approaches for handling ceiling and floor effects.
  • To compare the performance of these new methods against traditional approaches using simulations and real data.

Main Methods:

  • Development of Tobit modeling approaches estimated via maximum likelihood (ML) and Bayesian methods.
  • Simulation studies comparing proposed Tobit models with conventional methods for dependent-sample t-tests and moderated regressions.
  • Application to real-world datasets to demonstrate practical utility.

Main Results:

  • Conventional methods produced biased estimates, inflated Type I error rates, and poor confidence interval coverage, even with minimal ceiling data (10%).
  • Proposed Tobit modeling approaches (ML and Bayesian) yielded accurate estimates and reliable inference, performing well even with substantial ceiling data (30%).

Conclusions:

  • Novel Tobit modeling approaches offer a robust solution for analyzing data with ceiling and floor effects in behavioral and psychological research.
  • These methods provide more accurate and reliable statistical inference than conventional approaches, enhancing research validity.
  • Accessible R and Mplus scripts are provided to facilitate the adoption of these advanced Tobit modeling techniques.