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I am trying to generate a spatial weights matrix with individual level data. However, none of the default options (to my knowledge) correctly capture the conception of a neighborhood that I am trying to use. Specifically, I'd like to define each individual's neighborhood as their census tract (all individuals within each observation's tract gets a 1, all individuals not in the observation's tract get a zerothough it would be nice to also approximate the matrix using inverse distance, with a distance band equal to the tract boundary). I have a separate shapefile with the tract boundaries, as well as a column in my attribute table for the individual level data specifying the tract that each observation is in. Is there a way to do this? Thanks!
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03142011
09:19 AM

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I have a somewhat related question: does anyone know what default formula is used to calculate inverse distance, or where I can obtain this information? Is it as simple as 1/d (or e^d)? Thanks!
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01192011
11:36 AM

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Thank you for your response. That makes a lot of sense! I have a followup question about the formula that ArcGIS uses to calculate the local Moran's I statistic (from what I can tell, it does not match up with the formula in Anselin's 1995 articlenor, for what it's worth, with the one posted on Wikipedia). I found the formula here: http://resources.esri.com/help/9.3/ArcGISDesktop/com/GP_ToolRef/spatial_statistics_tools/how_cluster_and_outlier_analysis_colon_anselin_local_moran_s_i_spatial_statistics_works.htm My understanding is that a local Moran's I is calculated by taking the deviation of each observation from the global mean times the sum of the spatial weights matrix multiplied by the deviation of each neighbor observation from the global mean: x_ixbar(sum_j(w_ij*(x_jxbar))) This is very different form the formula posted by ESRI. I am in particular having trouble understanding 2 terms in ESRI's equation. The first is the denominator of the first termwhere the deviation of x_i is "normalized" by the average weight minus the global mean squared. This is not intuitive to me. Second, the equation does not take into account the difference of neighbor observations from the global mean. Instead, in the second term, the weights matrix is multiplied by the deviation of the observation i from the global mean. This seems like it might be a typo? Any insight you could provide as to where this formula is coming from is greatly appreciated! Thank you so much again for your help! Molly
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01192011
08:56 AM

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Hi, I computed Anselin's Moran's I and am trying to understand how ArcGIS moves from the test statistic to the classification of HH, HL, LH, or LL in the COtype field. From what I can tell, the test statistic only indicates whether an observation is similar (HH, LL cluster>high test statistic), or dissimilar (HL, LH>low test statistic) to its neighbor. However, I do not see how the magnitude of the test statistic distinguishes between the different types of cluster or outliers. That is, can I understand just by looking at the test statistic/zscore whether an observation is part of a HH as opposed to a LL, or a LH as opposed to a HL, cluster? If not, how does the program fill in the COtype field? Thanks! Molly
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01102011
11:55 AM

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