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    Chapter Random effects regression trees for the analysis of INVALSI data

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    Author(s)
    VANNUCCI, GIULIA
    GOTTARD, ANNA
    Grilli, Leonardo
    Rampichini, Carla
    Language
    English
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    Abstract
    Mixed or multilevel models exploit random effects to deal with hierarchical data, where statistical units are clustered in groups and cannot be assumed as independent. Sometimes, the assumption of linear dependence of a response on a set of explanatory variables is not plausible, and model specification becomes a challenging task. Regression trees can be helpful to capture non-linear effects of the predictors. This method was extended to clustered data by modelling the fixed effects with a decision tree while accounting for the random effects with a linear mixed model in a separate step (Hajjem & Larocque, 2011; Sela & Simonoff, 2012). Random effect regression trees are shown to be less sensitive to parametric assumptions and provide improved predictive power compared to linear models with random effects and regression trees without random effects. We propose a new random effect model, called Tree embedded linear mixed model, where the regression function is piecewise-linear, consisting in the sum of a tree component and a linear component. This model can deal with both non-linear and interaction effects and cluster mean dependencies. The proposal is the mixed effect version of the semi-linear regression trees (Vannucci, 2019; Vannucci & Gottard, 2019). Model fitting is obtained by an iterative two-stage estimation procedure, where both the fixed and the random effects are jointly estimated. The proposed model allows a decomposition of the effect of a given predictor within and between clusters. We will show via a simulation study and an application to INVALSI data that these extensions improve the predictive performance of the model in the presence of quasi-linear relationships, avoiding overfitting, and facilitating interpretability.
    URI
    https://library.oapen.org/handle/20.500.12657/56339
    Keywords
    Regression trees; Multilevel models; Random effects; Hierarchical data
    DOI
    10.36253/978-88-5518-304-8.07
    ISBN
    9788855183048, 9788855183048
    Publisher
    Firenze University Press
    Publisher website
    https://www.fupress.com/
    Publication date and place
    Florence, 2021
    Series
    Proceedings e report, 127
    Pages
    6
    Rights
    https://creativecommons.org/licenses/by/4.0/
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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