Conditional decomposition diagnostics for regression analysis of zero-inflated and left-censored data

Area of Science:

• Biostatistics
• Health and Safety Science
• Statistical Modeling

Background:

• Health and safety studies often yield semi-continuous outcomes (zero or positive continuous values).
• Traditional zero-inflated left-censored models use latent structures, making assessment challenging.
• Evaluating model fit requires focusing on observable characteristics.

Purpose of the Study:

• To develop and illustrate a conditional decomposition approach for assessing zero-inflated left-censored models.
• To partition model assessment into components for boundary (zero) and above-boundary (positive) values.
• To improve the evaluation and refinement of statistical models in health and safety research.

Main Methods:

• Employed a conditional decomposition approach to partition model assessment.
• Utilized conditional likelihood decomposition for statistical assessment.
• Investigated conditional mean and quantile functions for events above the boundary and marginal probabilities of boundary events.
• Derived large sample standard errors for graphical assessment and conducted simulations for finite-sample behavior.

Main Results:

• The conditional decomposition effectively partitions model assessment into observable components.
• Graphical and residual analyses based on conditional and marginal probabilities enhance model evaluation.
• Simulations demonstrated the finite-sample behavior of the proposed methods.
• The approach successfully identified sources of model lack-of-fit in health and safety data.

Conclusions:

• The conditional decomposition approach provides a robust framework for assessing zero-inflated left-censored models.
• This method leads to improved model identification and refinement in health and safety studies.
• Enhanced graphical assessment aids in understanding model performance and identifying areas for improvement.