Chapter Random effects regression trees for the analysis of INVALSI data
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 specifica...
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| Format: | Online |
| Langue: | anglais |
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Firenze University Press
2022
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| Accès en ligne: | ONIX_20220601_9788855183048_524 |
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| _version_ | 1869514804718206976 |
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| author | VANNUCCI, GIULIA GOTTARD, ANNA Grilli, Leonardo Rampichini, Carla |
| author_browse | GOTTARD, ANNA Grilli, Leonardo Rampichini, Carla VANNUCCI, GIULIA |
| author_facet | VANNUCCI, GIULIA GOTTARD, ANNA Grilli, Leonardo Rampichini, Carla |
| author_sort | VANNUCCI, GIULIA |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-82527 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Firenze University Press |
| publisherStr | Firenze University Press |
| record_format | ojs |
| spelling | doab-20.500.12854ir-825272022-06-02T04:12:29Z Chapter Random effects regression trees for the analysis of INVALSI data VANNUCCI, GIULIA GOTTARD, ANNA Grilli, Leonardo Rampichini, Carla Regression trees Multilevel models Random effects Hierarchical data 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. 2022-06-02T04:12:28Z 2022-06-02T04:12:28Z 2022-06-01T12:19:54Z 2021 chapter ONIX_20220601_9788855183048_524 2704-5846 https://library.oapen.org/handle/20.500.12657/56339 9788855183048 https://directory.doabooks.org/handle/20.500.12854/82527 eng Proceedings e report open access image/jpeg Attribution 4.0 International https://library.oapen.org/bitstream/20.500.12657/56339/1/16978.pdf Firenze University Press 10.36253/978-88-5518-304-8.07 10.36253/978-88-5518-304-8.07 2ec4474d-93b1-4cfa-b313-9c6019b51b1a 9788855183048 6 Florence open access |
| spellingShingle | Regression trees Multilevel models Random effects Hierarchical data VANNUCCI, GIULIA GOTTARD, ANNA Grilli, Leonardo Rampichini, Carla Chapter Random effects regression trees for the analysis of INVALSI data |
| title | Chapter Random effects regression trees for the analysis of INVALSI data |
| title_full | Chapter Random effects regression trees for the analysis of INVALSI data |
| title_fullStr | Chapter Random effects regression trees for the analysis of INVALSI data |
| title_full_unstemmed | Chapter Random effects regression trees for the analysis of INVALSI data |
| title_short | Chapter Random effects regression trees for the analysis of INVALSI data |
| title_sort | chapter random effects regression trees for the analysis of invalsi data |
| topic | Regression trees Multilevel models Random effects Hierarchical data |
| topic_facet | Regression trees Multilevel models Random effects Hierarchical data |
| url | ONIX_20220601_9788855183048_524 |
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