# pointpats.mantel

pointpats.mantel(s_coords, t_coords, permutations=99, scon=1.0, spow=-1.0, tcon=1.0, tpow=-1.0)

  Standardized Mantel test for spatio-temporal interaction. [Man67]

  Parameters:
    s_coords array

      (n, 2), spatial coordinates.

    t_coords array

      (n, 1), temporal coordinates.

    permutations int, optional

      the number of permutations used to establish pseudo- significance (the default is 99).

    scon float, optional

      constant added to spatial distances (the default is 1.0).

    spow float, optional

      value for power transformation for spatial distances (the default is -1.0).

    tcon float, optional

      constant added to temporal distances (the default is 1.0).

    tpow float, optional

      value for power transformation for temporal distances (the default is -1.0).

  Returns:
    mantel_result dictionary

      contains the statistic (stat) for the test and the associated p-value (pvalue).

    stat float

      value of the knox test for the dataset.

    pvalue float

      pseudo p-value associated with the statistic.

  Examples

      >>> import numpy as np
      >>> import libpysal as lps
      >>> from pointpats import SpaceTimeEvents, mantel

  Read in the example data and create an instance of SpaceTimeEvents.

      >>> path = lps.examples.get_path("burkitt.shp")
      >>> events = SpaceTimeEvents(path,'T')

  Set the random seed generator. This is used by the permutation based inference to replicate the pseudo-significance of our example results - the end-user will normally omit this step.

      >>> np.random.seed(100)

  The standardized Mantel test is a measure of matrix correlation between the spatial and temporal distance matrices of the event dataset. The following example runs the standardized Mantel test without a constant or transformation; however, as recommended by [Man67], these should be added by the user. This can be done by adjusting the constant and power parameters.

      >>> result = mantel(events.space, events.t, 99, scon=1.0, spow=-1.0, tcon=1.0, tpow=-1.0)

  Next, we examine the result of the test.

      >>> print("%6.6f"%result['stat'])
      0.048368

  Finally, we look at the pseudo-significance of this value, calculated by permuting the timestamps and rerunning the statistic for each of the 99 permutations. According to these parameters, the results indicate space-time interaction between the events.

      >>> print("%2.2f"%result['pvalue'])
      0.01