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Transformed mixed-effects modeling of correlated bounded and positive data with a novel multivariate generalized Johnson distribution

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  • Tourani-Farani, Fahimeh
  • Kazemi, Iraj

Abstract

Multivariate analysis of multiple correlated responses is often challenging due to the complex data structure. For analyzing such responses, this paper presents a pragmatic multivariate mixed-effects model. The model can flexibly accommodate both symmetric and asymmetric structures by utilizing a novel multivariate transformed distribution belonging to the family of elliptical distributions. It also offers a convenient alternative to most multivariate mixed models for analyzing bounded and positive correlated multivariate responses. The model is based on the median vector and a useful hierarchical representation, facilitating a theoretical investigation of its properties. An additional advantage is its flexibility in modeling correlated response vectors without assuming the existence of the mean. The maximum likelihood approach is proposed to estimate the model parameters. Results are illustrated by applying the proposed methodology to the health data sets for investigating the risk factors associated with childhood obesity.

Suggested Citation

  • Tourani-Farani, Fahimeh & Kazemi, Iraj, 2022. "Transformed mixed-effects modeling of correlated bounded and positive data with a novel multivariate generalized Johnson distribution," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000057
    DOI: 10.1016/j.jmva.2022.104954
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    3. Edilberto Cepeda-Cuervo & Jorge Alberto Achcar & Liliana Garrido Lopera, 2014. "Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 677-687, March.
    4. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
    5. Jianxin Pan & Robin Thompson, 2003. "Gauss-Hermite Quadrature Approximation for Estimation in Generalised Linear Mixed Models," Computational Statistics, Springer, vol. 18(1), pages 57-78, March.
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