Transformed mixed-effects modeling of correlated bounded and positive data with a novel multivariate generalized Johnson distribution. (English) Zbl 1493.62276
Summary: 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.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62J05 | Linear regression; mixed models |
| 60E05 | Probability distributions: general theory |
Keywords:
elliptical distributions; Gauss-Hermite quadrature; hierarchical representation; median regression; multiple correlated responses; multivariate Johnson transformationReferences:
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