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Bridging the Gap between Different Statistical Approaches: An Integrated Framework for Modelling

Author

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  • Petra M. Kuhnert
  • Kerrie Mengersen
  • Peter Tesar

Abstract

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well‐known and long standing traditional idea of ‘good practice in statistics’ by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non‐parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non‐parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response. Cet article propose un cadre pour modéliser des ensembles complexes de données qui combine les approches traditionnelles de modélisation statistique avec de plus récentes avancées en statistique et modélisation à travers une structure exploratoire. Notre approche élargit l'idée traditionnelle, bien connue et de longue date, de “bonne pratique en statistiques”, enétablissant une structure complète pour la modélisation qui se concentre sur l'exploration, la prédiction, l'interprétation et l'estimation de la fiabilité, une idée relativement nouvelle qui permet l'évaluation individuelle de prédictions. La structure intégrée que nous présentons comprend deux stades. Le premier fait appel à l'utilisation de méthodes exploratoires pour aider à comprendre visuellement les données et identifier un ensemble limité de variables explicatives. Le second recouvre un processus de modélisation en deux étapes, qui encourage l'utilisation de méthodes non paramétriques, telles que les arbres décisionnels et les modèles additifs généralisés, afin d'identifier les variables importantes et leurs relations de modélisation avec la réponse avant d'examiner un modèle prédictif final. Nous nous concentrons sur l'ajustement du modèle prédictif en utilisant des approches paramétriques, non paramétriques et bayésiennes. L'article est motivé par un problème médical où l'intérêt se concentre sur le développement d'un système de stratification de risque de morbidité de 1710 patients cardiaques en fonction d'une suite de variables démographiques, cliniques et préopératives. Bien que les méthodes que nous utilisons soient appliquées spécifiquement à l'étude de ce cas, elles peuvent être appliquées à n'importe quel champ, sans tenir compte du type de réponse.

Suggested Citation

  • Petra M. Kuhnert & Kerrie Mengersen & Peter Tesar, 2003. "Bridging the Gap between Different Statistical Approaches: An Integrated Framework for Modelling," International Statistical Review, International Statistical Institute, vol. 71(2), pages 335-368, August.
  • Handle: RePEc:bla:istatr:v:71:y:2003:i:2:p:335-368
    DOI: 10.1111/j.1751-5823.2003.tb00202.x
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    References listed on IDEAS

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    1. Kuhnert, Petra M. & Do, Kim-Anh & McClure, Rod, 2000. "Combining non-parametric models with logistic regression: an application to motor vehicle injury data," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 371-386, September.
    2. Friedman, Jerome H., 2002. "Stochastic gradient boosting," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 367-378, February.
    3. De Gooijer, Jan G. & Ray, Bonnie K. & Krager, Horst, 1998. "Forecasting exchange rates using TSMARS," Journal of International Money and Finance, Elsevier, vol. 17(3), pages 513-534, June.
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