[R-sig-Geo] Inference of local Gi*

[Jose Ramon Martinez Batlle]

Thanks Roger for your feedback and clarification.

Best regards.


El lun., 27 abr. 2020 a las 5:04, Roger Bivand (<Roger.Bivand using nhh.no>)
escribió:

> On Sat, 25 Apr 2020, Jose Ramon Martinez Batlle wrote:
>
> > Dear Anaïs.
> >
> > I am sure more experienced members will give you a better answer, but
> until
> > that I will try to help.
> >
> > 1) If I understood correctly, the spatial objects have 15 000 and 30 000
> > points in each case study, respectively. If this is the case, I am afraid
> > that nb objects of such large datasets surely would have an impact on the
> > system performance when used in subsequent tasks. The best I can suggest
> is
> > to try some sort of spatial binning if possible (e.g. hexbins), but at
> the
> > same time accounting for the modifiable areal unit problem.
> >
> > 2) The spdep:localG help page states that "For inference, a
> Bonferroni-type
> > test is suggested in the references, where tables of critical values may
> be
> > found". The source mentioned is free access, and can be found here:
> >
> > Ord, J. K. and Getis, A. 1995 Local spatial autocorrelation statistics:
> > distributional issues and an application. Geographical Analysis, 27,
> 286–306
> >
> https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1538-4632.1995.tb00912.x
> >
> > Standard measures (critical values) for selected percentiles and number
> of
> > entities, are included in Table 3 of the cited reference. Since the
> values
> > returned from localG are Z-values, you can use them to determine whether
> > the critical value chosen is exceeded and thus infer significant local
> > spatial association for each entity.
>
> Thanks, José, you are quite correct that false discovery rate problems are
> among the main reasons why so-called "hot-spot" analyses may be very
> misleading, in appearing to give an inferential basis for apparent map
> pattern.
>
> In our survey paper with David Wong referenced on ?localG,
> https://doi.org/10.1007/s11749-018-0599-x, we show that the analytical
> and
> bootstrap-based inferences are similar - the normality is related not to
> the underlying variable seen globally, but the the local behaviour of the
> statistic. For this reason, bootstrap permutation implementations are not
> included in spdep, though the code is available if need be. Please
> indicate whether users would like this code included for comparative
> purposes here or in a github issue on
> https://github.com/r-spatial/spdep/issues/.
>
> Further, the LOSH statistic, which is a measure of local spatial
> heteroscedasticity building on local G, provides a little insight into the
> problems raised for so-called "hot-spot" analyses by variability across
> the study area in the behaviour of the variable of interest. If, for
> example, the variable of interest is influenced by a background variable
> with a spatial pattern, we will probably find "hot-spots" which look like
> the omitted background variable on a map.
>
> While local G cannot take residuals of a linear model, local Moran's I can
> do so. For local G, we do not have exact case-by-case standard deviates;
> we do have these for local Moran's I as discussed in the article with
> David Wong, and they very typically reduce strongly the counts of
> apparently significant local statistcs even before adjusting p-values for
> FDR. Finally, only some local measures can adjust for global
> autocorrelation - unadjusted local measures also respond to the presence
> of global autocorrelation.
>
> On balance, judicious choice of class intervals in mapping a variable of
> interest may prove more helpful than trying to present wobbly inferences
> from ESDA.
>
> Hope this isn't too discouraging,
>
> Roger
>
>
> >
> > Kind regards.
> > José
> >
> > El vie., 24 abr. 2020 a las 14:00, Anaïs Ladoy (<anais.ladoy using epfl.ch>)
> > escribió:
> >
> >> Dear list members,
> >>
> >> I'm currently working on a point dataset, from which I want to conduct
> >> a Hot Spot Analysis with local Gi* statistics (Getis-Ord).
> >>
> >> I'm trying to find a way of computing its significance. I see two ways
> >> of computing significance in this case:
> >>
> >> 1) Compare the obtained local Gi from spdep::localG to a normal
> >> distribution. But here I have several questions :
> >> a) In my first case study (BMI value of 15 000 participants in a cohort
> >> study), the distribution of local Gi is far from normal (it is bimodal
> >> with a mode around very negative values and a mode around 0). However,
> >> I do need a normal distribution of Gi in order to compare it with a
> >> normal distribution, right? Or am I missing something here? What should
> >> I do in this case?
> >> b) In my second case study (Years of life lost for 30 000 individuals),
> >> the distribution of Gi returned by spdep::localG is approximately
> >> normal but the standard deviation is far from 1. In fact, in
> >> spdep::localG, the Gi values are supposedly standardized (from what I
> >> understood using an analytical mean and variance). Should I use these
> >> to compare to a normal distribution, or should I use raw G values
> >> (using return_internals=TRUE) and standardize them with the observed
> >> mean and variance of Gi? Does it cause a problem that my observed
> >> variance does not match the analytical variance?
> >>
> >> 2) Compute permutations
> >> However this is not implemented in R for localG. I tried using PySAL
> >> but the initial file is big and the weight file is huge, and my
> >> computer crashes. Any thoughts to solve this issue?
> >>
> >> Thank you for any feedback.
> >> Kind regards,
> >> Anaïs
> >>
> >> --
> >> Anaïs Ladoy
> >> PhD student, Laboratory of Geographic Information Systems, Swiss
> >> Federal Institute of Technology in Lausanne (EPFL), Switzerland.
> >>
> >> _______________________________________________
> >> R-sig-Geo mailing list
> >> R-sig-Geo using r-project.org
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> >>
> >
> >
> >
>
> --
> Roger Bivand
> Department of Economics, Norwegian School of Economics,
> Helleveien 30, N-5045 Bergen, Norway.
> voice: +47 55 95 93 55; e-mail: Roger.Bivand using nhh.no
> https://orcid.org/0000-0003-2392-6140
> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en



-- 
*José Ramón Martínez Batlle*
*Investigador/Profesor Universidad Autónoma de Santo Domingo (UASD)*
Correo electrónico: jmartinez19 using uasd.edu.do
Página web: http://geografiafisica.org

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