Multiple Imputation for Bounded Variables.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Missing data present a significant challenge in statistical analyses across various research fields.
• Existing multiple imputation methods primarily address unbounded continuous variables, often using inadequate ad hoc solutions for bounded variables.
• Current approaches for bounded variables can lead to inaccurate statistical inferences and conclusions.

Purpose of the Study:

• To propose a flexible, quantile-based imputation model specifically designed for variables with singly or doubly bounded support.
• To ensure that imputed values maintain proper support within the defined bounded intervals.
• To offer a statistically sound alternative to existing methods for handling missing data in bounded variable scenarios.

Main Methods:

• Development of a quantile-based imputation model tailored for distributions over bounded intervals.
• Utilization of a family of transformations to ensure imputed values fall within the specified bounded range.
• Evaluation through simulation studies comparing the proposed method against log-normal imputation and predictive mean matching.

Main Results:

• The proposed method effectively handles skewness, bimodality, and heteroscedasticity in bounded data.
• Simulation studies indicate superior performance compared to log-normal imputation and predictive mean matching.
• Demonstrated successful application on datasets from the Millennium Cohort Study (mathematical development scores) and a psychiatric dataset.

Conclusions:

• The developed quantile-based imputation method provides a robust and statistically valid approach for handling missing data in bounded variables.
• This method offers improved accuracy and reliability in statistical inferences compared to existing techniques.
• The approach has broad applicability in fields such as education, psychology, and other areas utilizing bounded data.