The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.

Mezzetti, M., Borzelli, D., D’Avella, A. (2022). A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves. STATISTICAL METHODS & APPLICATIONS, 31(5), 1245-1271 [10.1007/s10260-022-00625-6].

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

Maura Mezzetti;Andrea d’Avella
2022-01-01

Abstract

The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/01 - STATISTICA
English
Con Impact Factor ISI
Bayesian mixed model; Cluster analysis; Growth curve; Individual differences; Motor control
Mezzetti, M., Borzelli, D., D’Avella, A. (2022). A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves. STATISTICAL METHODS & APPLICATIONS, 31(5), 1245-1271 [10.1007/s10260-022-00625-6].
Mezzetti, M; Borzelli, D; D’Avella, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/313326
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