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Visualisation of historical events using Lexis pencils

Visualisation of historical events using Lexis pencils

Brian Francis and John Pritchard

Centre for Applied Statistics
Fylde College,
Lancaster University
Lancaster LA1 4YF
United Kingdom

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This Case Study reports on the visualisation methods and tools developed under the ESRC Analysis of Large and Complex Datasets initiative for exploring such datasets. Longitudinal data collected over time typically consists of a large number of variables collected over a set of individuals - many of these variables will vary over time and will commonly be categorical in nature. Such social surveys will often have a start event, such as the date of marriage or the date of first criminal conviction, as well as temporal information on the individual such as age or date of birth, and this can be used in lining up or registering the pictorial representations of individuals.

The approach uses a pencil metaphor to represent an individual. Each face of a pencil represents a time-varying variable such as housing tenure, employment status or family composition - changes in state over time in these variables are represented by changes in colour along the faces of the pencil. Groups of individuals can be examined by positioning the pencils side by side ranked by some order such as number of criminal convictions or case number. However, where possible, it is often better to view the pencils in three-dimensional space by positioning the start of each pencil on a base plane defined by temporal variables such as age, calendar time or date of marriage. This has the effect of grouping similar individuals together. The method generalises the ideas of Lexis, a nineteenth century German demographer, and such plots are therefore known as Lexis pencil plots.

Special visualisation software is necessary to construct such images, and to provide the rotation, panning and zooming which the investigator needs fully to examine the dataset.

This case study used the AVS system, and a special module in AVS was written. This software tool allows the user to view any event history dataset, retaining control of the colour mapping, the width of the pencil faces, and the assignment of variables to faces. It allows subsets of cases to be viewed, cases to be identified, and selections of cases to be made partially transparent. Another necessary feature which the tool provides is the ability to rotate the set of pencils each around their its own axis while keeping the viewpoint fixed, to allow different sides of the pencils to face the viewer. The software provides hard copy output of any user view and can also write VRML format files to allow three-dimensional visuals to be disseminated.

Two short examples are presented. The first examines a criminological data set of sexual offenders and the second gives insight into a study of the employment of married couples. These studies show that Lexis pencils provide a useful way of viewing event history data and that practical insights can be obtained into complex datasets.

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