{"id":2614512,"date":"2025-01-10T16:09:50","date_gmt":"2025-01-11T00:09:50","guid":{"rendered":"https:\/\/www.esri.com\/arcgis-blog\/?post_type=blog&p=2614512"},"modified":"2025-01-10T16:25:55","modified_gmt":"2025-01-11T00:25:55","slug":"machine-learning-spatial-components-in-arcgis-pro","status":"publish","type":"blog","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro","title":{"rendered":"Machine Learning & Spatial Components in ArcGIS Pro"},"author":354322,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"_acf_changed":false,"_searchwp_excluded":""},"categories":[23341],"tags":[776862,35661,25581,23571],"industry":[],"product":[36561],"class_list":["post-2614512","blog","type-blog","status-publish","format-standard","hentry","category-analytics","tag-arcgis-pro-3-4","tag-machine-learning","tag-spatial-statistics","tag-whats-new","product-arcgis-pro"],"acf":{"authors":[{"ID":354322,"user_firstname":"Josiah","user_lastname":"Parry","nickname":"Josiah Parry","user_nicename":"jparry","display_name":"Josiah Parry","user_email":"jparry@esri.com","user_url":"https:\/\/josiahparry.com","user_registered":"2024-03-06 19:22:54","user_description":"Josiah Parry is a Senior Product Engineer in Spatial Analytics and Data Science and helps lead the R-ArcGIS Bridge project.","user_avatar":""}],"short_description":"Address spatial confounding with Create Spatial Component Explanatory Variables in ArcGIS Pro 3.4","flexible_content":[{"acf_fc_layout":"content","content":"

In ArcGIS Pro 3.4, we released a new tool Create Spatial Component Explanatory Variables<\/strong><\/a> which can create variables that effectively account for the confounding nature of spatial data in machine learning.<\/p>\n

Creating Spatial Components<\/h2>\n

In many cases, there are unmeasured spatial processes that can wreak havoc in our predictive models!<\/p>\n

The Create Spatial Component Explanatory Variables<\/strong><\/a> tool can help create variables that account for the unmeasured spatial patterns that may be present in your dataset. It does so by creating spatial components<\/strong> based solely on the arrangement of the geometry in your dataset. The tool selects the subset of spatial components that best predict a numeric variable.<\/p>\n

To illustrate, we will use the famous Ames housing dataset (De Cock, 2011) to illustrate how this tool works. We want to predict the price of houses being sold in Ames, Iowa.<\/p>\n

 <\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647332,"id":2647332,"title":"Ames housing data set","filename":"sale-price.png","filesize":221656,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/sale-price","alt":"Screenshot of ArcGIS Pro showing a map of house sale prices in Ames, Iowa with a histogram of prices displayed in a chart below","author":"354322","description":"","caption":"Ames, Iowa housing dataset","name":"sale-price","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:00:32","modified":"2025-01-09 02:01:27","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":1487,"height":933,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","medium-width":416,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","medium_large-width":768,"medium_large-height":482,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","large-width":1487,"large-height":933,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","1536x1536-width":1487,"1536x1536-height":933,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","2048x2048-width":1487,"2048x2048-height":933,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price-741x465.png","card_image-width":741,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/sale-price.png","wide_image-width":1487,"wide_image-height":933}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

The average sale price in the dataset is just around $180,000. However, there is a very long tail where the 95th percentile of house sales are priced at $335,000. Looking at the variable we can see a fair amount of spatial clustering in housing price which traditional machine learning models may not be able to handle very well.<\/p>\n

Predicting housing prices with Boosted Regression<\/h2>\n

We will create a baseline model that uses the Forest-based and Boosted Classification and Regression<\/a> tool from the Spatial Statistics toolbox. This baseline model will predict the sale price based on the type of building that is sold as well as the year that the property was built.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647352,"id":2647352,"title":"Housing Building Type and Year Built","filename":"building-type-year-built.png","filesize":565114,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/building-type-year-built","alt":"Screenshot of ArcGIS Pro displaying 2 maps. The left side colors points based on their building type. Below it is a bar chart of the building types. Duplex has a value of 104, OneFam has 2425, Twnhs has 101, TwnhsE has 233, and TwoFmCon has 62. On the right displays the points colored by the year they were built. A lot of recently build properties in center. Below is a histogram that displays a long left tail with most houses being built in the early 2000s.","author":"354322","description":"","caption":"Ames housing building types and years built","name":"building-type-year-built","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:03:47","modified":"2025-01-09 02:07:12","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":1916,"height":932,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","medium-width":464,"medium-height":226,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","medium_large-width":768,"medium_large-height":374,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","large-width":1916,"large-height":932,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built-1536x747.png","1536x1536-width":1536,"1536x1536-height":747,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","2048x2048-width":1916,"2048x2048-height":932,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built-826x402.png","card_image-width":826,"card_image-height":402,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/building-type-year-built.png","wide_image-width":1916,"wide_image-height":932}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

Open the Forest-based and Boosted Classification and Regression<\/strong> tool. We will pass in the Ames dataset and choose the sale_price<\/code> as our dependent variable and the year_built<\/code> and bldg_type<\/code> as our independent variables. Additionally, we will use Gradient Boosted as our Model type.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647362,"id":2647362,"title":"Create a Boosted Regression Tree","filename":"fbcr-no-components.png","filesize":45198,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-no-components","alt":"Forest Based Classification and Regression Geoprocessing Dialog","author":"354322","description":"","caption":"Build a base model based on the year built and building type","name":"fbcr-no-components","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:09:25","modified":"2025-01-09 02:10:41","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":547,"height":904,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","medium-width":158,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","medium_large-width":547,"medium_large-height":904,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","large-width":547,"large-height":904,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","1536x1536-width":547,"1536x1536-height":904,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","2048x2048-width":547,"2048x2048-height":904,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-281x465.png","card_image-width":281,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components.png","wide_image-width":547,"wide_image-height":904}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

After the model has trained, we can review the geoprocessing messages to assess the baseline model\u2019s overall performance.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647382,"id":2647382,"title":"Base Model Diagnostics","filename":"fbcr-no-components-validation.png","filesize":22658,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-no-components-validation","alt":"Validation Data: Regression diagnostics.","author":"354322","description":"Boosted regression tree diagnostics","caption":"","name":"fbcr-no-components-validation","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:12:49","modified":"2025-01-09 02:13:41","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":764,"height":346,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","medium-width":464,"medium-height":210,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","medium_large-width":764,"medium_large-height":346,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","large-width":764,"large-height":346,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","1536x1536-width":764,"1536x1536-height":346,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","2048x2048-width":764,"2048x2048-height":346,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","card_image-width":764,"card_image-height":346,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-validation.png","wide_image-width":764,"wide_image-height":346}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

The validation diagnostics shows how our baseline model performs on out of sample data. The results are not the most impressive with an R-squared of only 0.39<\/strong> and a mean absolute error of almost $45,000 dollars.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647402,"id":2647402,"title":"Base Model Variable Importance","filename":"fbcr-no-components-variable-imp.png","filesize":13645,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-no-components-variable-imp","alt":"Variable importance for year_built and bldg_type with 79% and 21% respectively","author":"354322","description":"","caption":"","name":"fbcr-no-components-variable-imp","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:14:37","modified":"2025-01-09 02:15:15","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":769,"height":180,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp-213x180.png","thumbnail-width":213,"thumbnail-height":180,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","medium-width":464,"medium-height":109,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","medium_large-width":768,"medium_large-height":180,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","large-width":769,"large-height":180,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","1536x1536-width":769,"1536x1536-height":180,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","2048x2048-width":769,"2048x2048-height":180,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","card_image-width":769,"card_image-height":180,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-variable-imp.png","wide_image-width":769,"wide_image-height":180}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

What is also quite interesting is that the bldg_type<\/code> variable has a large weight importance meaning it is used a lot to help make branching decisions in our model.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647422,"id":2647422,"title":"Base Model Standardized Residuals","filename":"fbcr-no-components-resid.png","filesize":804161,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-no-components-resid","alt":"Screenshot of ArcGIS Pro illustrating standardized residuals from the base boosted tree regression model.","author":"354322","description":"","caption":"","name":"fbcr-no-components-resid","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:18:19","modified":"2025-01-09 02:18:45","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":1377,"height":933,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","medium-width":385,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","medium_large-width":768,"medium_large-height":520,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","large-width":1377,"large-height":933,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","1536x1536-width":1377,"1536x1536-height":933,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","2048x2048-width":1377,"2048x2048-height":933,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid-686x465.png","card_image-width":686,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-no-components-resid.png","wide_image-width":1377,"wide_image-height":933}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

We can also see that there are quite extreme pockets of residuals throughout the corners of the map. Perhaps spatial heterogeneity is at play here and we need to better account for it.<\/p>\n

Creating spatial components<\/h2>\n

To improve the quality of this model, we will create spatial components that are most predictive of sale_price<\/code>. To do so, open the Create Spatial Component Explanatory Variables tool and use ames<\/code> as the Input Features and the sale_price<\/code> as the Input Fields.<\/p>\n

 <\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647452,"id":2647452,"title":"Create Spatial Component Explanatory Variable Geoprocessing Tool","filename":"creating-components-gp-ui.png","filesize":23391,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/creating-components-gp-ui","alt":"Geoprocessing dialog for the Create Spatial Component Explanatory Variables tool.","author":"354322","description":"","caption":"","name":"creating-components-gp-ui","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:20:26","modified":"2025-01-09 02:20:56","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":545,"height":428,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","medium-width":332,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","medium_large-width":545,"medium_large-height":428,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","large-width":545,"large-height":428,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","1536x1536-width":545,"1536x1536-height":428,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","2048x2048-width":545,"2048x2048-height":428,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","card_image-width":545,"card_image-height":428,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/creating-components-gp-ui.png","wide_image-width":545,"wide_image-height":428}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

This tool will run through 28 possible spatial weights matrix configurations to identify the spatial weights matrix and combination of spatial components that are most predictive (using linear regression) of the sale_price<\/code> variable. The output shows the first spatial component that was selected.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647242,"id":2647242,"title":"ames_spatial_components","filename":"ames_spatial_components.png","filesize":373551,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/ames_spatial_components","alt":"Screenshot of ArcGIS Pro illustrating the output of the first component. There are two strong clusters. One in the east with low values colored blue. Another north colored dark red. The rest, spread to the west, are generally yellow.","author":"354322","description":"","caption":"Output from Create Spatial Explanatory Variables","name":"ames_spatial_components","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 01:39:37","modified":"2025-01-09 02:22:55","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":728,"height":496,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","medium-width":383,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","medium_large-width":728,"medium_large-height":496,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","large-width":728,"large-height":496,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","1536x1536-width":728,"1536x1536-height":496,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","2048x2048-width":728,"2048x2048-height":496,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components-683x465.png","card_image-width":683,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/ames_spatial_components.png","wide_image-width":728,"wide_image-height":496}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

Incorporating space into our boosted tree-based model<\/h2>\n

We can use these newly created components in our regression tree model to try and improve the performance. In the Explanatory Training Variables, include the first 10 components in addition to the original explanatory variables and run the tool again to train a new model.<\/p>\n

We can now review the performance of the new model which incorporates these spatial components. The validation R-squared has shot up by almost 0.4, almost doubling the variance explained by the regression model. This is a massive increase in model performance. Additionally, the mean absolute error (MAE) has been decreased from $45,000 to just under $30,000. That means that on average, the model\u2019s predictions are almost $15,000 closer to the true value\u2014that\u2019s no small amount to laugh at<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647482,"id":2647482,"title":"Boosted Regression Model with Spatial Components","filename":"fbcr-w-comp.png","filesize":47296,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-w-comp","alt":"Forest-based and Boosted Classification and Regression geoprocessing dialog. The variable to predict is sale_price and the explanatory training variables are bldg_type, year_built, and spatial components 1 through 9","author":"354322","description":"","caption":"","name":"fbcr-w-comp","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:24:22","modified":"2025-01-09 02:25:36","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":551,"height":821,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","medium-width":175,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","medium_large-width":551,"medium_large-height":821,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","large-width":551,"large-height":821,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","1536x1536-width":551,"1536x1536-height":821,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","2048x2048-width":551,"2048x2048-height":821,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-312x465.png","card_image-width":312,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp.png","wide_image-width":551,"wide_image-height":821}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

When looking at the importance of each of these variables, we can see that the year_built<\/code> variable is still very important in calculating the the sale_price<\/code> of a house. Now, though, the building type variable is arguably the least useful variable in the model!<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647492,"id":2647492,"title":"Diagnostics of Model with Spatial Components","filename":"fbcr-w-comp-diagnostics.png","filesize":29460,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-w-comp-diagnostics","alt":"Boosted regression tree model with spatial components included model diagnostics. Shows an R-squared of 0.778.","author":"354322","description":"","caption":"","name":"fbcr-w-comp-diagnostics","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:27:01","modified":"2025-01-09 02:28:22","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":765,"height":338,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","medium-width":464,"medium-height":205,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","medium_large-width":765,"medium_large-height":338,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","large-width":765,"large-height":338,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","1536x1536-width":765,"1536x1536-height":338,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","2048x2048-width":765,"2048x2048-height":338,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","card_image-width":765,"card_image-height":338,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-diagnostics.png","wide_image-width":765,"wide_image-height":338}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"image","image":{"ID":2647502,"id":2647502,"title":"Variable Importance","filename":"fbcr-w-comp-vip.png","filesize":50069,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-w-comp-vip","alt":"Boosted regression tree with spatial components variable importance. The most important variable is spatial component 1 followed by year_built then more spatial components.","author":"354322","description":"","caption":"","name":"fbcr-w-comp-vip","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:29:06","modified":"2025-01-09 02:29:59","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":761,"height":577,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","medium-width":344,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","medium_large-width":761,"medium_large-height":577,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","large-width":761,"large-height":577,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","1536x1536-width":761,"1536x1536-height":577,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","2048x2048-width":761,"2048x2048-height":577,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip-613x465.png","card_image-width":613,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-vip.png","wide_image-width":761,"wide_image-height":577}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

Lastly, when reviewing the model\u2019s residuals, the residuals no longer appear to be spatially clustered. Rather, instead, they appear to be quite randomly distributed around the city itself.<\/p>\n"},{"acf_fc_layout":"image","image":{"ID":2647552,"id":2647552,"title":"Standardized Residuals of Boosted Regression Tree Model with Spatial Components","filename":"fbcr-w-comp-std-resid.png","filesize":830660,"url":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","link":"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\/fbcr-w-comp-std-resid","alt":"Screenshot of ArcGIS Pro showing the standardized residuals of the Boosted Regression Tree model with spatial components.","author":"354322","description":"","caption":"Standardized residuals of boosted regression tree using spatial components ","name":"fbcr-w-comp-std-resid","status":"inherit","uploaded_to":2614512,"date":"2025-01-09 02:34:46","modified":"2025-01-09 02:37:33","menu_order":0,"mime_type":"image\/png","type":"image","subtype":"png","icon":"https:\/\/www.esri.com\/arcgis-blog\/wp-includes\/images\/media\/default.png","width":1373,"height":939,"sizes":{"thumbnail":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid-213x200.png","thumbnail-width":213,"thumbnail-height":200,"medium":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","medium-width":382,"medium-height":261,"medium_large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","medium_large-width":768,"medium_large-height":525,"large":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","large-width":1373,"large-height":939,"1536x1536":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","1536x1536-width":1373,"1536x1536-height":939,"2048x2048":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","2048x2048-width":1373,"2048x2048-height":939,"card_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid-680x465.png","card_image-width":680,"card_image-height":465,"wide_image":"https:\/\/www.esri.com\/arcgis-blog\/app\/uploads\/2025\/01\/fbcr-w-comp-std-resid.png","wide_image-width":1373,"wide_image-height":939}},"image_position":"center","orientation":"horizontal","hyperlink":""},{"acf_fc_layout":"content","content":"

Careful Considerations<\/h2>\n

By including spatial components into our model, we were able to greatly improve its predictive power. However, that doesn\u2019t mean that they should be preferred. In fact, these spatial components are likely indicative of omitted variable bias (OVB).<\/p>\n

When spatial components are useful in model predictions it is likely that there is some other real world phenomenon that the model is not taking into account. You can use these components to supplement your well measured variables, or even help you identify additional measures that you may need.<\/p>\n

 <\/p>\n

Citations<\/h2>\n

Tobler, W. R. 1970. \u201cA Computer Movie Simulating Urban Growth in the Detroit Region.\u201d Economic Geography 46: 234\u201340. https:\/\/doi.org\/10.2307\/143141.<\/p>\n

Pebesma, E.; Bivand, R. (2023). Spatial Data Science: With Applications in R (1st ed.). 314 pages. Chapman and Hall\/CRC, Boca Raton. https:\/\/doi.org\/10.1201\/9780429459016<\/p>\n

De Cock, D. (2011) Ames, Iowa: Alternative to the Boston Housing Data as an End of Semester Regression Project. Journal of Statistics Education, 19, Published Online. https:\/\/doi.org\/10.1080\/10691898.2011.11889627<\/p>\n"}],"related_articles":[{"ID":2594792,"post_author":"71281","post_date":"2024-11-20 10:37:50","post_date_gmt":"2024-11-20 18:37:50","post_content":"","post_title":"What\u2019s New in Spatial Statistics: Filter Spatial Autocorrelation From Field","post_excerpt":"","post_status":"publish","comment_status":"closed","ping_status":"closed","post_password":"","post_name":"whats-new-in-spatial-statistics-filter-spatial-autocorrelation-from-field","to_ping":"","pinged":"","post_modified":"2025-01-10 16:21:22","post_modified_gmt":"2025-01-11 00:21:22","post_content_filtered":"","post_parent":0,"guid":"https:\/\/www.esri.com\/arcgis-blog\/?post_type=blog&p=2594792","menu_order":0,"post_type":"blog","post_mime_type":"","comment_count":"0","filter":"raw"}],"show_article_image":false,"card_image":false,"wide_image":false},"yoast_head":"\nMachine Learning & Spatial Components in ArcGIS Pro<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Machine Learning & Spatial Components in ArcGIS Pro\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.esri.com\/arcgis-blog\/products\/arcgis-pro\/analytics\/machine-learning-spatial-components-in-arcgis-pro\" \/>\n<meta property=\"og:site_name\" content=\"ArcGIS Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/esrigis\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-01-11T00:25:55+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@ESRI\" 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