The Interval-Censored Biplot

Abstract

The principal components biplot is a useful visualization tool for the exploration of a samples by variables data matrix. In several data analysis situations, the data values are interval censored so that only the interval of a data value is available, but not the value itself. For such data, we propose the interval-censored biplot (IC-Biplot), a new exploratory and graphical method that is an extension of the principal component analysis biplot. It provides not only a two-dimensional graphic representation of respondents and their attributes, but also point estimates for the data values that are constrained to be in their interval. Two applications of the IC-Biplot are discussed. The first application considers data on emergence times of permanent teeth focusing on the pattern of emergence. The IC-Biplot confirms rank orders suggested earlier in the literature. Goodness-of-fit measures show that the present model seems to fit these data very well. The second application discusses a regular sample by attribute matrix from the literature on characteristics of several types of oils. This article has online supplementary materials.

Key Words:

• Biplot
• Interval-censoring
• Principal component analysis

ACKNOWLEDGMENTS

Data collection was supported by Unilever, Belgium. The Signal Tandmobiel${}^{}$ study comprises following partners: D. Declerck (Dental School, KU Leuven), L. Martens (Dental School, University Ghent), J. Vanobbergen (Oral Health Promotion and Prevention, Flemish Dental Association), P. Bottenberg (Dental School, University Brussels), E. Lesaffre (L-Biostat, KU Leuven, and Department of Biostatistics, Erasmus Medical Centre, Erasmus University Rotterdam), and K. Hoppenbrouwers (Youth Health Department, KU Leuven, and Flemish Association for Youth Health Care).

Additional information

Notes on contributors

Silvia Cecere

Silvia Cecere, MSc (E-mail: [email protected]), and Patrick J.F. Groenen is Professor, Econometric Institute, Erasmus School of Economics (ESE), Erasmus University Rotterdam, Rotterdam, The Netherlands (E-mail: [email protected]). Emmanuel Lesaffre is Professor, Department of Epidemiology and Biostatistics, Erasmus Medical Centre, Erasmus University Rotterdam, Rotterdam, The Netherlands; L-Biostat, KU Leuven, Leuven, Belgium (E-mail: [email protected]).

Patrick J. F. Groenen

Silvia Cecere, MSc (E-mail: [email protected]), and Patrick J.F. Groenen is Professor, Econometric Institute, Erasmus School of Economics (ESE), Erasmus University Rotterdam, Rotterdam, The Netherlands (E-mail: [email protected]). Emmanuel Lesaffre is Professor, Department of Epidemiology and Biostatistics, Erasmus Medical Centre, Erasmus University Rotterdam, Rotterdam, The Netherlands; L-Biostat, KU Leuven, Leuven, Belgium (E-mail: [email protected]).

Emmanuel Lesaffre

Silvia Cecere, MSc (E-mail: [email protected]), and Patrick J.F. Groenen is Professor, Econometric Institute, Erasmus School of Economics (ESE), Erasmus University Rotterdam, Rotterdam, The Netherlands (E-mail: [email protected]). Emmanuel Lesaffre is Professor, Department of Epidemiology and Biostatistics, Erasmus Medical Centre, Erasmus University Rotterdam, Rotterdam, The Netherlands; L-Biostat, KU Leuven, Leuven, Belgium (E-mail: [email protected]).