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Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data

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  • Beh, Eric J.
  • Lombardo, Rosaria
  • Alberti, Gianmarco

Abstract

Traditionally, simple correspondence analysis is performed by decomposing a matrix of standardised residuals using singular value decomposition where the sum-of-squares of these residuals gives Pearson’s chi-squared statistic. Such residuals, which are treated as being asymptotically normally distributed, arise by assuming that the cell frequencies are Poisson random variables so that their mean and variance are the same. However, studies in the past reveal that this is not the case and that the cell frequencies are prone to overdispersion. There are a growing number of remedies that have been proposed in the statistics, and allied, literature. One such remedy, and the focus of this paper, is to stabilise the variance using the Freeman–Tukeytransformation. Therefore, the properties that stem from performing correspondence analysis will be examined by decomposing the Freeman–Tukey residuals of a two-way contingency table. The application of this strategy shall be made by studying one large, and sparse, set of archaeological data.

Suggested Citation

  • Beh, Eric J. & Lombardo, Rosaria & Alberti, Gianmarco, 2018. "Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 73-86.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:73-86
    DOI: 10.1016/j.csda.2018.06.012
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    References listed on IDEAS

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    1. Chiara Mazzetta & Steve Brooks & Stephen N. Freeman, 2007. "On Smoothing Trends in Population Index Modeling," Biometrics, The International Biometric Society, vol. 63(4), pages 1007-1014, December.
    2. Read, Campbell B., 1993. "Freeman--Tukey chi-squared goodness-of-fit statistics," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 271-278, November.
    3. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
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    Cited by:

    1. Rodrigues Teixeira, Ana Carolina & Machado, Pedro Gerber & Borges, Raquel Rocha & Felipe Brito, Thiago Luis & Moutinho dos Santos, Edmilson & Mouette, Dominique, 2021. "The use of liquefied natural gas as an alternative fuel in freight transport – Evidence from a driver's point of view," Energy Policy, Elsevier, vol. 149(C).
    2. Yoshio Takane & Eric J. Beh & Rosaria Lombardo, 2025. "A theory of contrasts for modified Freeman–Tukey statistics and its applications to Tukey’s post-hoc tests for contingency tables," Computational Statistics, Springer, vol. 40(3), pages 1423-1446, March.
    3. Eric J. Beh & Rosaria Lombardo, 2024. "Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics," International Statistical Review, International Statistical Institute, vol. 92(1), pages 17-42, April.
    4. Ting-Wu Wang & Eric J. Beh & Rosaria Lombardo & Ian W. Renner, 2025. "Profile transformations for reciprocal averaging and singular value decomposition," Computational Statistics, Springer, vol. 40(3), pages 1217-1251, March.

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