Latest Contributions by EricKrause

Hi @joshgGIS, We apologize for the very long delay in responding, and we really appreciate you pointing this out.  The formula shown in the documentation is not correct; however, the correct formulas are implemented in the tool. The formula for S_i^2 should not have "j=/=i" in the subscript.  And there's no need for S^2 to have the subscript i at all, since it is just the global variance of the data values and is the same for every feature. Just to doubly certain, I compared the code and several test cases between the tool and a different implementation in R (spdep module), and all results matched exactly. Thank you again so much for alerting us to this error and doing this deep digging. This will be corrected in the documentation of the next version of ArcGIS Pro. - Eric Krause ... View more

Hi @Lumera, As you figured out, the coordinate polynomials in Universal Kriging will be calculated and used automatically.  They cannot be manually overridden. The closest equivalent is EBK Regression Prediction, where you can use a raster that will be used in a regression equation to determine the mean.  However, the regression coefficients are not configurable, so the mean surface will be in the form: Mean(s) = B0 + B1*RasterCellValue(s).  That's not exactly the same as defining the mean surface, but it's close. ... View more

Hi @deryolr , You can convert a .dbf (or any other ArcGIS table) to a spatial weights matrix using the Generate Spatial Weights Matrix tool.  The Conceptualization of Spatial Relationships parameter has a "Convert table" option that will allow you to provide your dbf. Making a custom SWM usually involves first making a template SWM using Generate Spatial Weights Matrix tool. You then convert it to a table using Convert Spatial Weights Matrix to Table tool, and manually edit the table.  Finally, you convert it back to a SWM using Generate Spatial Weights Matrix. Before trying to convert your dbf to a SWM, I would try to add it to a map and make sure it displays as a table layer in the Contents pane.  That will verify that it is configured such that ArcGIS Pro recognizes it as a valid table. -Eric Krause ... View more

Hi @CStandley_1 , There seems to be a bit of confusion in that the word "confidence" isn't exclusively used for confidence intervals, and here it is referring to something slightly different.  Here, it is referring to a confidence level, not a confidence interval. The confidence level is tied to the significance (alpha) level.  There are several ways to say exactly the same thing: A feature is statistically significant at significance level 0.05. The p-value of a feature is less than 0.05. A feature is statistically significant with greater than 95% confidence. (This is the context that the label uses). A feature is not within a 95% confidence interval constructed assuming the null hypothesis is true. So the symbology of the features is based on the confidence level (or equivalently, the significance level).  While this is related to confidence intervals, to make the labels be about confidence intervals, they would have to change to something like: "Cold Spot (Not Within 90% Confidence Interval)".  People can certainly disagree, but I don't think this would help with understanding the output. Further, actually constructing confidence intervals for hot spot analysis results is much harder than you might suspect.  If you've done much work with confidence intervals, you're probably familiar with estimating the standard error, then creating a 95% confidence interval using a formula that looks like: Value +/- 1.96 * StandardError. However, this isn't really valid for hot spot analysis. This is honestly too complicated to try to explain in a forum environment, but there are nuances about when you can and cannot construct confidence intervals of this type (distinctions between sampling distributions and raw value distributions).  For hot spot analysis specifically, if you want to create a confidence interval for the level of "hotness" of a feature, you'd need to use something more sophisticated (like resampling), but the confidence intervals that you'd produce would be different than the confidence level of the symbology (because they would be estimating the variability of very subtly different things).  You're not expected to understand that, but just know that there is a reason that the hot spot analysis tools do not produce confidence intervals and only refer to the confidence level. ... View more

Hi @EugenioJairEscobarSánchez, There are a few things to keep in mind.  First, the GWR tool that you are using in ArcMap is not that same one that is only available in ArcGIS Pro. The newer GWR was designed to match the implementation of the GWR4 software (as it was at the time), and has been tested to give matching results. Second, there is not one single "correct" bandwidth, and there are a variety of methods to estimate it that agree/disagree with each other to varying extents.  I am not certain the method that ArcMap's GWR tool uses to optimize the bandwidth, but I can verify that Fatheringham (the "father" of GWR) approved of the methodology and created at least one tutorial using the ArcMap tool: https://gwr.maynoothuniversity.ie/wp-content/uploads/2016/01/GWR_Tutorial.pdf ... View more

Hi @GarethNash, I'm only seeing this thread now.  The "Custom 3D points" option will produce a netCDF file with predictions at the specified location, but it isn't configured in a way where it can be represented as a voxel layer.  Only the gridded points option can produce a voxel layer. ... View more

Apologies, the above reply was from me, but I accidentally posted from the wrong account. ... View more

The idea has been implemented in ArcGIS Pro 3.4 as the Directional Trend tool, available in the Geostatistical Analyst toolbox (Utilities toolset) and Spatial Statistics toolbox (Measuring Geographic Distributions toolset).  The tool re-creates the polynomial trend lines on the X-Z axis as a scatter plot chart on a feature layer. The tool is available at all license levels (a Geostatistical Analyst license is not required). ... View more

Hi @MasoodShaikh, Kriging is an "inexact" interpolation method, meaning that the prediction surface does not pass perfectly through the values of the input points and instead has a tendency to smooth predictions (meaning that the range of predictions is usually more narrow than the range of the original data values).  The weaker the autocorrelation and the more noisy the data, the more it tends to smooth.  For your data, it's likely that you have many locations where high values are very close to low values, and the kriging surface effectively smooths over the highs and lows. There are a couple things you can do.  First, you can use an interpolation method like Radial Basis Functions (aka splines) or Inverse Distance Weighting that will always honor the range of the input data values.   Second, you can disable the Nugget effect of kriging, which will force it to honor the input data range.  You can do this on the semivariogram page of the Geostatistical Wizard by changing the “Model Nugget” option to “Disable”.  However, not using a nugget effect can often create strange artifacts in the output, so it is generally not recommended.  If you do this, pay close attention to strange behavior in the resulting surface. -Eric ... View more

I mean the second.  And, yes, if the new dataset has fundamentally different properties than the first, it will be quite inaccurate.  This is only appropriate in cases like daily measurements of the same data, where the changes in the data values will be relatively small, and you're willing to sacrifice a small amount of accuracy in order to not have to manually perform kriging in the Geostatistical Wizard every day. Kriging is never particularly safe to do in an automated environment, but if it's something you really need to do, we recommend using Empirical Bayesian Kriging for it.  It is available as a geoprocessing tool, so setting up automation is relatively simple. ... View more

Hi @MWmep013, The reason for the discrepancy is that the GWR tool was reimplemented in ArcGIS Pro 2.3, and the previous version (equivalent to ArcMap) was deprecated.  Among other things, the newer version uses a different and more common formula for global and local R-squared and optimizes bandwidths differently.  The newer version follows the design and formulas of the GWR4 software (not from Esri). While you will not find it in the Geoprocessing pane, the deprecated version can still be used through arcpy (for example, in a Python Notebook or the Python Window) with arcpy.stats.GeographicallyWeightedRegression().  You can see the documentation for the deprecated version here:  https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/geographically-weighted-regression.htm Using the deprecated version should provide the same results as the ArcMap version.  As for why using Distance Band lowers the R-squared, I am not certain, but it likely has something to do with your particular data. Please let me know if you have any other questions. -Eric ... View more

Hi @ZhichengZhong, ArcGIS does not have a GTWR tool, but in principle, including time should not alter the question of if/how to test for significant explanatory variables.  While the GWR tools does provide significance results for local models, it's understandable that other softwares and publications do not.  The problem is that GW(T)R isn't really a single model: it is a collection of local models that are each estimated at the locations of the input features.  Further, these models are correlated with each other, as they often share the same features in their neighborhood.  This can create problems related to multiple hypothesis testing where you are effectively testing N times the number of explanatory variables, and you should definitely be cautious in interpreting any particular p-value when performing so many hypothesis tests.  This is why, generally, explanatory variables are chosen using global models like OLS, and statistics like R-squared and AIC are used to determine how much better GW(T)R does compared to the global model. ... View more