Mantel's test
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Indications/Recommendations for use:
When space-time interaction is present cases near in space will also be near in time, and the
test statistic will be large (more).
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Description:
A test for space-time interaction using space and time distances.
Mantel (1967) circumvented problems associated with
selecting the critical distances for the Knox test by first calculating time
and space distance matrices. His test statistic is the sum, across all case
pairs, of the time distance multiplied by the spatial distance.
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Test statistic:
The sum of the products of the space and time distances between all possible pairs of
cases.
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Null Hypothesis:
Spatial distances between cases is independent of the time distance between those
cases.
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The usual approach to determining the significance of Mantel’s test statistic under H0 is to use a Monte Carlo method, permuting the elements of one of the distance matrices while holding the other constant. This is equivalent to repeatedly scrambling the time observations across the localities, and calculating Z each time.
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Alternative Hypothesis:
Nearby cases tend to occur at about the same time.
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GeoMed Inputs:
Space and time
distances between pairs of cases. Mantel's test
requires the names of the space and time
distance files, and, if desired, the distance transformation. Mantel suggested the use of the reciprocal
distance, 1/[d(ij)+C], to reduce the impact of large distances. Here `d(ij) is the distance between cases i
and j and C is a constant.
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GeoMed Outputs:
- Mantel’s r and its significance
- Scatterplot of time distances on space distances
- association between time and space distances appear as patterns in the scattergram
- A frequency distribution of r under H0 is plotted
An approximate randomization is used to generate the distribution of
Mantel's statistic under the null hypothesis that the space and time
distances are independent. The observed value of Mantel's statistic is
then compared to this distribution.
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Example Analysis
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Reference:
Manly, B. F. J. 1986. Randomization and regression methods for testing for associations with geographical, environmental and biological distances between populations. Researches on Population Ecology, 28:201-218.
Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research, 27:209-220.
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