Equation of Bivariate Local Moran's I

[Nan Ding]

I'm a graduate student in GISDE program at Clark University. 

My partners and I are doing a python project. 

Since Bivariate Local Moran's I only exist in Geoda, our project objective is creating a tool of Bivariate Local Moran's I for users to use it in ArcMap. 

While we are kind of confused with the formula of BV. While we are kind of confused with the formula of BV. 

Could you offer us the equation of BV? Thank you very much!

Nan Ding

nad...@clarku.edu

[Dr. Sergio Rey]

Hi Nan,

You might want to have a look at PySAL: https://pysal.readthedocs.org/en/v1.9.1/library/esda/moran.html#pysal.esda.moran.Moran_BV

hth,

s.

--

Sergio (Serge) Rey
Professor, School of Geographical Sciences and Urban Planning
GeoDa Center for Geospatial Analysis and Computation
Arizona State University
http://geoplan.asu.edu/rey

Editor, Geographical Analysis
http://wileyonlinelibrary.com/journal/gean

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[Isabel Kiefer]

Hello,

I'm using PySAL to compute the bivariate Moran's I for two variables drawn from remote sensing images. I would like to describe the formula that is used to obtain "I", but I have some problems understanding it...

Combining Moran_BV and the definition of the univariate Moran's I, I get this formula: 

Is this correct in your opinion? Shouldn't I divide by sum(i)(X(i)-mean(X))^2 ? 

Thank you very much in advance and sorry if my question might seem stupid..

Best regards,

Isabel Kiefer

[Dr. Sergio Rey]

hi isabel,

sorry if i didn’t get back to you on this.

in pysal (and opengeoda) the variables  x and y are first subjected to a standard-normal transformation:

zy = (y - ybar)/y_s

zx = (x - xbar)/x_s

where y_s is the standard deviation of y

so the sum of zy’zy  =  zx’zx = n-1

what matters is the order in the numerator (what has the j subscript and what has the i subscript).

also see: https://github.com/pysal/pysal/issues/695

hth

s.

--

Sergio (Serge) Rey
Professor, School of Geographical Sciences and Urban Planning
GeoDa Center for Geospatial Analysis and Computation
Arizona State University
http://geoplan.asu.edu/rey

Editor, Geographical Analysis
http://wileyonlinelibrary.com/journal/gean

[nicknic...@gmail.com]

Hi Serge,

I'd like to use a Bivariate Moran's I and LISA statistics using two variable at different times. For instance, population in 1990 and firms' localisation in 2000, since population in 2000 (market size) may affect the localisation of firms in the nearby location subsequently (10 years).

Kindly, I'd like to know if there are any issues with this. I have seen papers that use bivariate spatial autocorrelation using the same variable at different time, or different variables at the same time; but I have never seen papers that use different variables at different time.

Any advise is highly appreciated.

Thank you.

Nick