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Multivariate quasi-beta regression models for continuous bounded data.

Ricardo R Petterle1, Wagner H Bonat2, Cassius T Scarpin3

  • 1Department of Integrative Medicine, Federal University of Parana, Curitiba, Brazil.

The International Journal of Biostatistics
|August 1, 2020
PubMed
Summary

We introduce a new multivariate regression model for continuous bounded data, handling correlations without needing a full probability distribution. This model improves analysis of complex datasets like body fat measurements.

Keywords:
NORTA algorithmcorrelated dataestimating functionsmultiple continuous bounded outcomessimulation studyunit interval

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Analyzing multiple continuous bounded outcomes presents statistical challenges, particularly regarding inter-variable correlations.
  • Existing models often require specific multivariate probability distributions, limiting their applicability.
  • Continuous data bounded within [0, 1], including boundary values, necessitate specialized regression techniques.

Purpose of the Study:

  • To propose a flexible multivariate regression model for continuous bounded data.
  • To develop an approach that accounts for correlations between response variables without assuming a specific joint distribution.
  • To analyze body fat percentage data measured across multiple body regions.

Main Methods:

  • Developed a multivariate quasi-beta regression model based on second-moment assumptions.
  • Utilized quasi-score and Pearson estimating functions for parameter estimation.
  • Employed the NORmal To Anything (NORTA) algorithm in simulation studies for correlated beta distributions.

Main Results:

  • The proposed multivariate model effectively handles multiple correlated continuous bounded variables.
  • Simulation studies confirmed the properties of the estimating functions for correlated responses.
  • The model demonstrated a superior fit compared to univariate analyses for body fat data and quantified response correlations.

Conclusions:

  • The multivariate quasi-beta regression model offers a robust framework for analyzing correlated continuous bounded data.
  • The model's flexibility extends to data including zeros and ones within the [0, 1] interval.
  • Adapted diagnostic tools enhance the practical application and interpretation of the proposed model.