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

Ceiling or floor effects pose analytic challenges in behavioral and psychological research. In this study, we developed novel Tobit modeling approaches, estimated using maximum likelihood (ML) or Bayesian methods, to address these effects for widely used statistical analyses, including the dependent-sample t-test and moderated regression. Simulation studies were conducted to compare the performance of the proposed modeling approaches to the conventional approach where ceiling or floor data are treated as if true values. The conventional approach was found to yield biased estimates, inflated Type I error rates, and poor confidence interval coverage, even with as little as 10% ceiling data. In contrast, the proposed approaches with either ML or Bayesian estimation provided accurate estimates and inference results across most studied conditions (e.g., with 30% ceiling data). Real data examples further illustrated the impact of modeling choices. To facilitate implementations of the proposed Tobit modeling approaches, we provide simulated datasets along with R and Mplus scripts online. Implications of the findings and future research directions were discussed.