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Seriation by constrained correspondence analysis: a simulation study

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  • van de Velden, M.
  • Groenen, P.J.F.
  • Poblome, J.

Abstract

One of the many areas in which Correspondence Analysis (CA) is an effective method, concerns ordination problems. For example, CA is a well-known technique for the seriation of archaeological assemblages. A problem with the CA seriation solution, however, is that only a relative ordering of the assemblages is obtained. To improve the usual CA solution, a constrained CA approach that incorporates additional information in the form of equality and inequality constraints concerning the time points of the assemblages may be considered. Using such constraints, explicit dates can be assigned to the seriation solution. In this paper, we extend the set of constraints that can be used in CA by introducing interval constraints. That is, constraints that put the CA\\ solution within a specific time-frame. Moreover, we study the quality of the constrained CA solution in a simulation study. In particular, by means of the simulation study we are able to assess how well ordinary and constrained CA can recover the true time order. Furthermore, for the constrained approach, we see how well the true dates are retrieved. The simulation study is set up in such a way that it mimics the data of a series of ceramic assemblages consisting of the locally produced tableware from Sagalassos (SW Turkey). We find that the dating of the assemblages on the basis of constraints appears to work quite well.

Suggested Citation

  • van de Velden, M. & Groenen, P.J.F. & Poblome, J., 2007. "Seriation by constrained correspondence analysis: a simulation study," Econometric Institute Research Papers EI 2007-40, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:10559
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    1. Yoshio Takane & Haruo Yanai & Shinichi Mayekawa, 1991. "Relationships among several methods of linearly constrained correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 667-684, December.
    2. Ulf Böckenholt & Ingo Böcknholt, 1990. "Canonical analysis of contingency tables with linear constraints," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 633-639, December.
    3. Caitlin E. Buck & Sujit K. Sahu, 2000. "Bayesian models for relative archaeological chronology building," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 423-440.
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    1. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    2. Schoonees, P.C., 2015. "Methods for Modelling Response Styles," ERIM Report Series Research in Management EPS–2015–348–MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Antonello D’Ambra & Pietro Amenta, 2011. "Correspondence Analysis with Linear Constraints of Ordinal Cross-Classifications," Journal of Classification, Springer;The Classification Society, vol. 28(1), pages 70-92, April.
    4. Pieter Schoonees & Michel Velden & Patrick Groenen, 2015. "Constrained Dual Scaling for Detecting Response Styles in Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 968-994, December.
    5. D'Ambra, Luigi & Amenta, Pietro & D'Ambra, Antonello & de Tibeiro, Jules S., 2021. "A study of the family service expenditures and the socio-demographic characteristics via fixed marginals correspondence analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).

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