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Graphical Representation of Transitions and Sequences

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Advances in Sequence Analysis: Theory, Method, Applications

Part of the book series: Life Course Research and Social Policies ((LCRS,volume 2))

Abstract

A sequence is an ordered list of categorical values of a variable which, in the social sciences, corresponds to social processes or trajectories, such as school-to-work transitions or family formation. Sequence analysis presents the possibility of dealing with complex information because sequences are usually based on longitudinal data and cover a large number of cases. Even scholars who apply elaborated methodological statistical approaches necessarily need to reduce this complexity by restricting their analyses to certain events. For example, many researchers within the field of school-to-work transitions who apply event history analysis reduce the event “labour market entrance” to the status change into employment. The algorithmic approach of sequence analysis has the ability to handle the complexity of social processes empirically. However, the problem of graphical representation persists because the use of categorical time series involving many individuals requires multidimensional visualisation, but the general form of (printed) scientific publications is still black and white.

This article explores the different visualisation possibilities of sequential information that are typically used in the social science literature. It presents conventional (e.g., sequence index plots) as well as less common types of graphs (such as parallel coordinates plots, status proportion plots, and transition plots) and discusses their particular advantages and limitations. The arguments for this assessment are based on the particular scientific interest in certain features of sequences and on Cleveland’s rules of perception. Additionally, an attempt is made to find practical solutions to avoid problems in the depiction of sequential and transition data.

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Notes

  1. 1.

    One major objective of the life-course approach is the examination of the embedding of aggregate individual life courses into macro-level contexts and in the linkage between life-courses (cp. Elder et al. 2004).

  2. 2.

    This is only true for those sequences based on a time-scale mostly used in sociology. But, there are also studies about sequences that have no time dimension, such as the original application of optimal matching (OMA) on distance or DNA strands.

  3. 3.

    There are many trials of assembling rules for graphical display (Tufte 1983; Wallgren et al. 1996; Blasius and Greenacre 1998; Good and Hardin 2003), but I decided for Cleveland’s principles, because his work is most comprehensive, that is that other rules are included in his aggregation.

  4. 4.

    The majority of the principles are already implemented by the most statistical software packages, such as Stata. For example, the principle that the data rectangle should be smaller than the scale-line rectangle (Cleveland 1994, p. 31) is followed by Stata for every graphical command.

  5. 5.

    The graphs of this chapter are generated with the software Stata and the user-written sq-commands (Brzinsky-Fay et al. 2006); the data are mainly the same as in Brzinsky-Fay (2007).

  6. 6.

    Figures 14.2 and 14.3 show monthly employment status sequences of 250 randomly chosen school leavers from a sample of around 4,000 school leavers in ten European countries. The sequences consist of 60 months (12 years) and are from the European Household Panel (ECHP).

  7. 7.

    In Stata, the graph command plots the graph category by category, so that categories (statuses) with a higher number overplot those with a lower number.

  8. 8.

    This is implemented in the TraMineR package (Gabadinho et al. 2011a; b) for the software R under the name of ‘sequence frequency plots.’

  9. 9.

    Figures 14.4 and 14.5 show monthly employment sequences from school leavers in Belgium, France, and Spain.

  10. 10.

    In Stata, the standard colors are chosen in order to provide more contrast on color screen and when converted to black-and-white. However, apart from the explorative research procedure being an iterative, experimental process, the choice of the best color scheme is also iterative, and the proof of the pudding is in the eating. For more discussion on the choice of colors for representation of categorical data, see Zeileis et al. (2009).

  11. 11.

    The user-written package TraMineR available for the software R (see footnote 8) offers the possibility to produce so-called sequence frequency plots (Gabadinho et al. 2011a). These plots also show most frequent sequences, and have the form of a weighted bar chart.

  12. 12.

    However, the original application differs a bit regarding the structure, because each of the vertical axes refers to another dimension, whereas the usage in sequence analysis mixes the Cartesian system with the ‘real’ parallel coordinates in a way that the time points are represented by the horizontal axis.

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Author information

Authors and Affiliations

  1. WZB Berlin Social Science Center, Berlin, Germany

    Christian Brzinsky-Fay

Authors
  1. Christian Brzinsky-Fay
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Correspondence to Christian Brzinsky-Fay .

Editor information

Editors and Affiliations

  1. Inst of Political & International Studies, University of Lausanne, Lausanne, Austria

    Philippe Blanchard

  2. Centre LINES/LIVES, University of Lausanne, Lausanne, Austria

    Felix Bühlmann

  3. Centre LINES/LIVES, University of Lausanne, Lausanne, Austria

    Jacques-Antoine Gauthier

Appendix

Appendix

This list contains a selection of graphing principles developed and assembled by Cleveland (1994). It is limited to those principles that are relevant for the graphs usually applied to sequence analyses.

Elementary principles of graph construction:

  • Make the data stand out & avoid superfluity.

  • Use visually prominent graphical elements to show the data.

    […]

  • Overlapping plotting symbols must be visually distinguishable.

  • Superposed data sets must be readily visually assembled.

  • Visual clarity must be preserved under reduction and reproduction.

Principles of clear understanding:

  • Put major conclusions into graphical form.

    […]

General strategy:

  • A large amount of quantitative information can be packed into a small region.

  • Graphing data should be an iterative, experimental process.

    […]

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Brzinsky-Fay, C. (2014). Graphical Representation of Transitions and Sequences. In: Blanchard, P., Bühlmann, F., Gauthier, JA. (eds) Advances in Sequence Analysis: Theory, Method, Applications. Life Course Research and Social Policies, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-04969-4_14

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