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

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  • Maura Mezzetti

    (Università “Tor Vergata”)

  • Daniele Borzelli

    (University of Messina)

  • Andrea d’Avella

    (University of Messina
    IRCCS Fondazione Santa Lucia)

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.

Suggested Citation

  • Maura Mezzetti & Daniele Borzelli & Andrea d’Avella, 2022. "A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1245-1271, December.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:5:d:10.1007_s10260-022-00625-6
    DOI: 10.1007/s10260-022-00625-6
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    References listed on IDEAS

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    Cited by:

    1. Maura Mezzetti & Ilia Negri, 2024. "Hierarchical Bayesian model to estimate and compare research productivity of Italian academic statisticians," Scientometrics, Springer;Akadémiai Kiadó, vol. 129(12), pages 7443-7474, December.

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