Bayesian Model Selection for Derived Responses

Area of Science:

• Statistics
• Biostatistics
• Bayesian inference

Background:

• Traditional Bayesian model selection criteria (AIC, DIC, WAIC) assess predictive accuracy for original response variables.
• These criteria are limited when the variable of interest is derived (e.g., BMI from weight and height), as optimal models for components may not optimize derived variable prediction.

Purpose of the Study:

• To adapt the Widely Applicable Information Criterion (WAIC) for derived response variables.
• To introduce a new criterion, Derived WAIC (DW AIC), specifically designed to measure out-of-sample predictive accuracy for derived quantities.
• To enable direct comparison of models predicting derived variables, irrespective of whether they model original components or the derived variable directly.

Main Methods:

• Adaptation of the Widely Applicable Information Criterion (WAIC).
• Development of the Derived WAIC (DW AIC) to assess predictive accuracy of derived response variables.
• Application of DW AIC to compare a bivariate growth model for height and weight against a spline smoothing model for BMI.

Main Results:

• DW AIC provides a method to evaluate models based on their predictive performance for derived variables.
• The study demonstrates that the best model for original variables (height, weight) may not be optimal for derived variables (BMI).
• DW AIC facilitates model comparisons that are not possible with standard criteria like AIC or WAIC.

Conclusions:

• DW AIC is a valuable tool for Bayesian model selection when dealing with derived response variables.
• This new criterion enhances the ability to choose models that best predict key derived health metrics like BMI.
• The proposed method allows for more accurate and relevant model selection in complex biological and health-related data analysis.