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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: similarity statistic for heatmaps (or any cartesian plane) |

Date |
Wed, 20 Jun 2012 15:44:14 +0100 |

OK, but it still seems to me that different problems are being conflated: 1. Is y similar to x, compared observation by observation? 2. Is the distribution function of y similar to that of x, pooling observations? 3. Is the spatial pattern of y similar to that of x, focusing on locations as well as values? On #1, people often use correlation techniques, but correlation tests linearity not agreement. More at e.g. Cox, N.J. 2006. Assessing agreement of measurements and predictions in geomorphology Geomorphology 76: 332-346. Nick On Wed, Jun 20, 2012 at 3:26 PM, Raymond Lim <rl2240@columbia.edu> wrote: > Thanks for the feedback Nick. Yes, my latter statement is dubious. I > should have said akin to Kolmogorov-Smirnov and not referred to > spatial 1-dimension. Essentially, I want to test whether the > distribution function of two surfaces are statistically different. For > example, say I measure pollution levels in a city in two different > time periods. I want to test whether the distribution of pollution is > the same (I don't care about volume of pollution, just distribution of > it across parts of the city). Alternatively, a correlation measure > would be good too. > > Computing the difference between heatmaps sounds like a good start. > Thanks again! > > - - > The latter statement is at best dubious and at worst fallacious. > > A Kolmogorov-Smirnov test compares distribution functions and says > nothing whatsoever about spatial distribution, as you can shuffle the > locations and keep the same distribution functions. Indeed it wouldn't > surprise me if it were based on an assumption of independent > measurements likely to be challengeable for most interesting spatial > data. > > Similarly, you can compare heatmaps aspatially and spatially: > something like concordance correlation compares element by element but > says nothing about spatial patterns. If I were obliged to choose a > single single-number statistic to compare heatmaps it might be > something like a spatial autocorrelation of differences. > > But why choose a single statistic any way? Or rather, a map is a > sample statistic, just map-valued, and the best measure of similarity > of two heatmaps may be a heatmap of the difference between them (or, > e.g. their ratio). > > Nick > > On Tue, Jun 19, 2012 at 4:30 PM, Raymond Lim <rl2240@columbia.edu> wrote: >> Is there a statistic for computing similarity of two heatmaps (or any >> sort of Cartesian plane)? I know in 1 dimension, you can compared >> distributions using a Kolmogorov-Smirnov test, but not sure about >> 2-dimensions. > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: similarity statistic for heatmaps (or any cartesian plane)***From:*Raymond Lim <rl2240@columbia.edu>

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