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High Leverage Points and Outliers in Generalized Linear Models for Ordinal Data

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Advances in Data Analysis

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

A generalized hat matrix based on Φ-divergences is proposed to determine how much influence or leverage each data value can have on each fitted value to a generalized linear model for ordinal data. After studying for evidence of points where the data value has high leverage on the fitted value, if such influential points are present, we must still determine whether they have had any adverse effects on the fit. To evaluate it we propose a new family of residuals based on Φ-divergences. All the diagnostic measures are illustrated through the analysis of real data.

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Acknowledgments

This work was partially supported by Grants MTM2006-00892 and UCM-BSCH-2008-910707.

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Authors and Affiliations

  1. Department of Statistics and O.R (I), Complutense University of Madrid, Madrid, Spain

    M.C. Pardo

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  1. M.C. Pardo
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Editors and Affiliations

  1. Data analysis & Forecasting Lab., Technical University of Crete, Chania, Crete, 731 00, Greece

    Christos H. Skiadas

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Pardo, M. (2010). High Leverage Points and Outliers in Generalized Linear Models for Ordinal Data. In: Skiadas, C. (eds) Advances in Data Analysis. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4799-5_7

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