Abstract
Multivariate Conditional Transformation Models (MCTMs) were recently proposed as a new multivariate regression technique. These models characterize jointly the covariates effects on the marginal distributions of the responses and their correlations without requiring parametric assumptions. Flexibility, in both the responses and covariates effects are achieved using Bernstein basis polynomials. In this paper we compare MCTMs estimations with the well established Copula Generalized Additive Models (CGAMLSS). MCTMs conditional correlation estimations outperform the CGAMLSS ones, showing lower estimation error, and variability. Finally, MCTMs were applied to the joint modelling of three thyroid hormones concentrations – Thyroid Stimulating Hormone (TSH), triiodothyronine (T3), and thyroxine (T4) – conditionally on age. Our results show how the marginal distribution and correlations of the hormones concentrations are influenced by the age of the patients.
Supported by Grant from the Program of Aid to the Predoctoral Stage (ED481A-2018/154) of the Galician Regional Authority (Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia) and European Social Fund 2014/2020. Developed under the project MTM2017-83513-R and co-financed by the Ministry of Economy and Competitiveness (SPAIN) and by the European Regional Development Fund (ERDF). Also supported by the project ED431C 2020/20, financed by the Competitive Research Unit Consolidation 2020 Programme of the Galician Regional Authority (Xunta de Galicia).
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Díaz-Louzao, C., Lado-Baleato, Ó., Gude, F., Cadarso-Suárez, C. (2021). Multivariate Conditional Transformation Models. Application to Thyroid-Related Hormones. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_25
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