I am using Local Moran's I in the spdep in R.

See this question: https://stackoverflow.com/questions/44104008/spatial-autocorrelation-between-time-series-in-r?noredirect=1#comment75251231_44104008

Does this look right? And I'm reiterating the question in the end of that post.

How do I collapse all the Iis to come up with one Ii for the entire time span for that cluster?


Fisher's method?

What do you do with a test statistic value that has some relevance (like Ii = -0.357682) but a high p-value (like p-value = 0.59281) {arbitrary values, but same general idea}?

Assume a 95% confidence interval.

  • If you really want to stick with a Moran's-I (LISA) approach you could implement the recent Lee & Li (2016) approach but, they point out the same caveats regarding correlation through time. onlinelibrary.wiley.com/doi/10.1111/gean.12106/full May 22 '17 at 17:23
  • I think that you may be mistaking Moran's eigen vectors, in temporal analysis, for the straight Moran's-I autocorrelation statistic. And yes, you could apply a transformation to the time-series but, you are missing the importance of potential disparity in the spatial process through time. This could make the results quite incorrect. What if the distribution at any given point is skewed? If the correlation structure is fairly homogeneous through time, then collapsing the data would be warranted. May 22 '17 at 17:27
  • As per the Tour there should be only one question asked per question.
    – PolyGeo
    May 22 '17 at 21:42

Unfortunately, the global or local Moran's-I is not at all appropriate for multi-temporal data. There is a bivariate version of the statistic, available in GeoDa that can be used to compare two time-periods but not a time-series. Please note that there are some know issues with a bivariate Moran's-I (or by extension LISA) where the matrix is not symmetric and can be non-positive definite. The postulation on the spatial process in Wartenberg is in regard to a lapse rate. This brings up questions regarding the assumption of any given y being correlated at point i through time.

If you want to collapse the time-series data into a single spatial process, for a single evaluation of the spatial structure, I imagine that one would have to meet an assumption of a minimal correlation structure thorough time. Otherwise, resulting spatial clustering would be completely erroneous. For example, say you have one point in the time-series that is considerably different than the others yet you still collapse it into the overall data, how could you adequately be representing a temporally homogeneous spatial process and have relevant clustering?

A better approach may be Kulldorff (1997) scan statistics and its many extensions. Various implementations are available in the software SaTScan, the R interface to SaTScan "rsatscan" and the "kulldorff" function in the SpatialEpi package. This method allows for spatial-temporal models using specified distributional forms (eg., Binomial, Poisson, Gaussian), which provides a distinct advantage in hypothesis testing and inference.

Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics - Theory and Methods. 26(6):1481–1496.

  • Sup, it's me. Different account, Don't know why I can't comment on stuff. But why is that? Most of the researchers I've seen that use either the Global or Local Moran's I uses a time series of multiple different locations, provided they have the same time span and resolution.
    – ace_01S
    May 22 '17 at 17:06
  • @Ace_01S You need to merge your two accounts. Please see I accidentally created two accounts; how do I merge them?.
    – Midavalo
    May 22 '17 at 18:03

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