[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120926-en":3,"doc-seo-120926-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120926,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","A Comparative Analysis of Machine Learning Methods and Spatial Statistical Methods for Areal Unit Scottish Property Price Data - MSc(R) Thesis","Spatial areal unit data consist of contiguous, non-overlapping areas, such as Scotland’s Data Zones, and exhibit spatial correlation where nearby zones show more similar values and structures than distant zones. The thesis contrasts classical spatial statistical modelling—especially the conditional autoregressive (CAR) approach—with non-linear machine learning methods for property price prediction. It also evaluates whether combining spatial and ML methods improves performance, using training/test splits and prediction metrics.","MacBride, Cara Margaret (2024) A comparative analysis of machine learning methods and spatial statistical methods for areal unit Scottish property price data. MSc(R) thesis.  \n[https://theses.gla.ac.uk/84170/](https://theses.gla.ac.uk/84170/)  \nCopyright and moral rights for this work are retained by the author  \nA copy can be downloaded for personal non-commercial research or study, without prior permission or charge  \nThis work cannot be reproduced or quoted extensively from without first obtaining permission from the author  \nThe content must not be changed in any way or sold commercially in any format or medium without the formal permission of the author  \nWhen referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given  \nEnlighten: Theses  \n[https://theses.gla.ac.uk/](https://theses.gla.ac.uk/)  \n[research-enlighten@glasgow.ac.uk](research-enlighten@glasgow.ac.uk)  \nA Comparative Analysis of Machine Learning Methods and Spatial Statistical Methods for Areal Unit Scottish Property Price Data  \nCara Margaret MacBride  \nSchool of Mathematics and Statistics University of Glasgow  \nA thesis submitted for the degree of Master of Statistics by Research September 2023  \nAbstract  \nSpatial areal unit data are a type of spatial data which consist of a set of contiguous non-overlapping areal units in space, one example being Data Zones (DZ) in Scotland. A special feature about these data is that they are spatially correlated. This means that pairs of areal units that are close to each other in space have more similar data values and structure to one another than areal units that are further apart. In general, spatial data are modelled using classical spatial statistical methods that account for spatial correlation within the data. One widely established spatial method being the conditional autoregressive (CAR) model where spatial correlation is modelled through a set of random effects. However, in recent years, the application of machine learning (ML) methods to spatial data in order to generate predictions has risen in popularity. Unlike spatial methods, machine learning methods can account for non-linear effects. This results in two important questions of interest: (i) Are classical spatial statistical methods or a-spatial machine learning methods best for prediction of spatial areal unit data? and (ii) Can machine learning methods and spatial methods be combined as one to improve predictive performance compared to using the two methods in isolation? By partitioning the data into training and test sets and evaluating predictions using prediction metrics, this MSc addresses these questions in the context of property prices at the Data Zone level in Scotland. In general, I found that there was little difference between spatial methods and machine learning methods in terms of prediction and the combination of both also had a very similar predictive performance.  \nContents  \nContents ii  \nList of Tables v List of Figures vii  \n1 Introduction 1  \n1.1 Aims and Objectives ............................. 3  \n1.2 Thesis Structure ................................ 3  \n2 Data and exploratory analysis 5  \n2.1 Study Region ................................. 5  \n2.2 Property Price ................................. 6  \n2.3 Covariates ................................... 12  \n2.3.1 Property Type Characteristics .................... 13  \n2.3.2 Physical Geography .......................... 14  \n2.3.3 Characteristics of Data Zones .................... 15  \n2.3.4 Data Splitting ............................. 18  \n2.4 Normal Linear Model ............................. 21  \n2.4.1 Variable Selection ........................... 23  \n2.5 Discussion ................................... 24  \n3 Property price predictions using spatial conditional autoregressive models 26  \n3.1 Introduction .................................. 26  \n3.2 Exploratory Analysis ............................. 26  \n3","cbCaitCNm8dCj8ku","https://ap.wps.com/l/cbCaitCNm8dCj8ku","pdf",7775246,1,91,"English","en",105,"# Introduction\n## Aims and Objectives\n## Thesis Structure\n# Data and exploratory analysis\n## Study Region\n## Property Price\n## Covariates\n### Property Type Characteristics\n### Physical Geography\n### Characteristics of Data Zones\n### Data Splitting\n## Normal Linear Model\n### Variable Selection\n## Discussion\n# Property price predictions using spatial conditional autoregressive models\n## Exploratory Analysis\n### KNN Method\n### Border Sharing Method\n### Assessing the presence of spatial autocorrelation\n## Spatial modelling of areal unit data\n### Prior distributions\n### Spatial prediction\n### Parameter estimation\n## Choosing the number of neighbours k to construct W\n### Validation strategy\n### Test Set Predictions\n## Discussion\n# Property price predictions using classical machine learning methods\n## Decision Trees\n### Partitioning\n### Creating an optimal tree\n### Prediction using decision trees\n## Bagging\n## Random Forests\n### Structure\n### Tuning Parameters\n### Choosing the tuning parameter combination\n### Test Set Predictions\n## Gradient Boosting\n### Structure\n### Tuning Parameters\n### Choosing the tuning parameter combination\n### Test Set Predictions\n## Discussion\n# Property price prediction by combining spatial and machine learning methods\n## Geographically Weighted Random Forests\n### Structure","[{\"question\":\"What makes areal unit data different for modelling and prediction?\",\"answer\":\"Areal unit data are spatially structured: units are contiguous and non-overlapping, and values are spatially correlated, so nearer areas tend to be more similar than farther ones.\"},{\"question\":\"Which modelling approaches are compared in the thesis?\",\"answer\":\"The thesis compares classical spatial statistical methods, particularly the conditional autoregressive (CAR) model, with machine learning methods that can capture non-linear effects.\"},{\"question\":\"Does combining spatial and machine learning methods improve property price prediction?\",\"answer\":\"Results show little difference between spatial methods and machine learning methods, and combining them produces a very similar predictive performance to using either approach alone.\"}]","A Comparative Analysis of Machine Learning Methods and Spatial Statistical Methods for Areal Unit Scottish Property Price Data - MSc(R) Thesis | PDF",1785732736,229,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-comparative-analysis-of-machine-learning-methods-and-spatial-statistical-methods-for-areal-unit-scottish-property-price-data-mscr-thesis","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/a-comparative-analysis-of-machine-learning-methods-and-spatial-statistical-methods-for-areal-unit-scottish-property-price-data-mscr-thesis/120926/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What makes areal unit data different for modelling and prediction?","Question",{"text":75,"@type":76},"Areal unit data are spatially structured: units are contiguous and non-overlapping, and values are spatially correlated, so nearer areas tend to be more similar than farther ones.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which modelling approaches are compared in the thesis?",{"text":80,"@type":76},"The thesis compares classical spatial statistical methods, particularly the conditional autoregressive (CAR) model, with machine learning methods that can capture non-linear effects.",{"name":82,"@type":73,"acceptedAnswer":83},"Does combining spatial and machine learning methods improve property price prediction?",{"text":84,"@type":76},"Results show little difference between spatial methods and machine learning methods, and combining them produces a very similar predictive performance to using either approach alone.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]