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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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General location multivariate latent variable models for mixed correlated bounded continuous, ordinal, and nominal

Elham Tabrizi1, Ehsan Bahrami Samani1, Mojtaba Ganjali1

  • 1Department of Statistics, Faculty of Mathematical Science, Shahid Beheshti University, Tehran, Iran.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

This study introduces novel statistical models for analyzing complex, correlated data, including continuous and categorical variables with missing values. These methods enhance the analysis of health and economic datasets, improving understanding of related factors.

Keywords:
62J0562J12Beta regressionconditional grouped continuous modelgeneral mixed data modellatent variablethe maximal normal curvature

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Analyzing correlated continuous and categorical data is complex, especially with missing values.
  • Existing models may not adequately handle bounded continuous responses or non-ignorable missingness.

Purpose of the Study:

  • To propose new multivariate latent variable models for analyzing correlated bounded continuous and categorical responses.
  • To address models with and without non-ignorable missing values.
  • To extend models for bounded continuous responses using beta and Dirichlet distributions.

Main Methods:

  • Multivariate latent variable approach.
  • Regression methods for jointly analyzing continuous, nominal, and ordinal responses.
  • Maximum-likelihood estimation for regression parameters.
  • Sensitivity analysis for missing data mechanisms.

Main Results:

  • Developed general location models accommodating bounded continuous and categorical variables.
  • Successfully applied models to BMI, Steatosis, Osteoporosis data, and Tehran household expenditure budgets.
  • Demonstrated the utility of beta and Dirichlet distributions for bounded continuous responses.

Conclusions:

  • The proposed models offer a flexible framework for analyzing complex correlated data with mixed response types and missing values.
  • The methods provide robust tools for applications in health and economic research.
  • Sensitivity analysis confirms model stability concerning missing data mechanisms.