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We developed a flexible multivariate regression model for continuous bounded outcomes. This approach efficiently estimates parameters and combines various distributions, offering a robust framework for complex data analysis.

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Area of Science:

  • Statistics and Biostatistics
  • Multivariate Data Analysis
  • Regression Modeling

Background:

  • Analyzing multiple continuous bounded outcomes presents statistical challenges.
  • Existing models may lack flexibility in handling diverse marginal distributions.
  • Accurate parameter estimation and inference are crucial for reliable results.

Purpose of the Study:

  • To propose a novel multivariate regression model for continuous bounded outcomes.
  • To enable the combination of different marginal distributions within a single model.
  • To provide an efficient computational implementation for parameter estimation.

Main Methods:

  • Maximum likelihood estimation for parameter estimation and inference.
  • Model specification using the product of univariate probability distributions.
  • Correlation structure captured through a random intercepts correlation matrix.
  • Utilized beta and unit gamma distributions for bounded variables (0, 1).
  • Computational implementation via Template Model Builder with Laplace approximation and automatic differentiation.

Main Results:

  • The proposed model efficiently estimates parameters using Template Model Builder.
  • Simulation studies confirmed the computational efficiency and properties of maximum likelihood estimators.
  • The model demonstrated robustness to distribution misspecification.
  • Analysis of body fat percentage data showed the model's practical applicability.

Conclusions:

  • The proposed multivariate regression model offers a general and flexible framework for multiple continuous bounded outcomes.
  • The efficient computational implementation facilitates practical application.
  • The model effectively handles complex correlation structures and diverse marginal distributions.