Growth curve models: a Bayesian approach via Markov chain Monte Carlo (MCMC) methods

• Grant number: 22/13263-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): January 01, 2023
• Effective date (End): December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Mario de Castro Andrade Filho
• Grantee: Cícero Coimbra Fonseca
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The usage of growth curve models in the study of characteristics from longitudinal data has seena wide variety of applications in fields such as Forestry (Fekedulegn & Colbert, 1999), Developmental Psychology (Curran et al., 2010), Microbiology (Zwietering et al., 1990) and Zootechnics (Finco et al., 2016). The Bayesian methodology may be advantageous in modeling these curves as it allows for the inclusion of expert knowledge. Even when such information is not available, one may choose to use weakly or non-informative priors instead. In general, fitting Bayesian models requires approximate methods. In such cases, Monte Carlo Markov chain (MCMC) methods like the Metropolis-Hastings algorithm (Chib, 1995) are widely used; particularly, diffusion process-based methods such as Hamiltonian Monte Carlo (HMC) (Neal, 2011) and MALA (Metropolis-adjusted Langevin algorithm) (Girolami & Calderhead, 2011) tend to be more computationally efficient in practice. This project aims to analyse the implementation of growth curve models models in a Bayesian framework, considering a performance comparison of MCMC methods, appropriate prior selection and elicitation with alternative parameterizations.