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M statistic commands: Interpoint distance distribution analysis

Author

Listed:
  • Pietro Tebaldi

    () (Bocconi University)

  • Marco Bonetti

    () (Bocconi University)

  • Marcello Pagano

    () (Harvard School of Public Health)

Abstract

We implement the commands mstat and mtest to perform inference based on the M statistic, a statistic that can be used to compare the interpoint distance distribution across groups of observations. The analyses are based on the study of the interpoint distances between n points in a k-dimensional setting to produce a one-dimensional real-valued test statistic. The locations are distributed in a region of the plane. When we consider all (n 2) interpoint distances, the dependencies among them are difficult to express 2 analytically, but their distribution is informative, and the M statistic can be built to summarize one aspect of this information. The two commands can be used on a wide class of datasets to test the null hypothesis that two groups have the same (spatial) distribution. mstat and mtest return the exact M test statistic. Moreover, mtest executes a Monte Carlo–type permutation test, which returns the empirical p-value together with its confidence interval. This is the command to use in most situations, because the convergence of M to its asymptotic chi-squared distribution is slow. Both commands can be used to obtain graphical output of the empirical density function of the interpoint distance distributions in the two groups and the two- dimensional map of the n observations in the plane. The descriptions of the commands are accompanied by examples of applications with real and simulated data. We run the test on the Alt and Vach grave site dataset (Manjourides and Pagano, forthcoming, Statistics in Medicine) and reject the null hypothesis, in contradiction to other published analyses. We also show how to adapt the techniques to discrete datasets with more than one unit in each location. Finally, we report an extensive application on breast cancer data in Massachusetts; in the application, we show the compatibility of the M commands with Pisati's spmap package. Copyright 2011 by StataCorp LP.

Suggested Citation

  • Pietro Tebaldi & Marco Bonetti & Marcello Pagano, 2011. "M statistic commands: Interpoint distance distribution analysis," Stata Journal, StataCorp LP, vol. 11(2), pages 271-289, June.
  • Handle: RePEc:tsj:stataj:v:11:y:2011:i:2:p:271-289
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    References listed on IDEAS

    as
    1. White, Laura Forsberg & Bonetti, Marco & Pagano, Marcello, 2009. "The choice of the number of bins for the M statistic," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3640-3649, August.
    2. Scott Merryman, 2005. "USMAPS2: Stata module to provide US county map coordinates for tmap," Statistical Software Components S448404, Boston College Department of Economics, revised 24 Jan 2005.
    3. Maurizio Pisati, 2004. "Simple thematic mapping," Stata Journal, StataCorp LP, vol. 4(4), pages 361-378, December.
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    Cited by:

    1. Berrendero, José R. & Cuevas, Antonio & Pateiro-López, Beatriz, 2016. "Shape classification based on interpoint distance distributions," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 237-247.
    2. Modarres, Reza, 2016. "Multivariate Poisson interpoint distances," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 113-123.

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