Evaluation of spatial data’s impact in mid-term room rent price through application of spatial econometrics and machine learning. Case study: Lisbon

i EVALUATION OF SPATIAL DATA’S IMPACT IN MID-TERM ROOM RENT PRICE THROUGH APPLICATION OF SPATIAL ECONOMETRICS AND MACHINE LEARNING Case S udy: Lisbon Mihail Pe ko ii EVALUATION OF SPATIAL DATA’S IMPACT IN MID-TERM ROOM RENT PRICE THROUGH APPLICATION OF SPATIAL ECONOMETRICS AND MACHINE LEARNING Case S udy: Lisbon Disse a ion supe ised by: P o esso Dou o Robe o And é Pe ei a Hen iques, PhD Ins i u o Supe io de Es a ís ica e Ges ão de In o mação, Uni e sidade NOVA de Lisboa Lisbon, Po ugal Joel Dinis Bap is a Fe ei a da Sil a, PhD Ins i u o Supe io de Es a ís ica e Ges ão de In o mação, Uni e sidade NOVA de Lisboa Lisbon, Po ugal P o esso Dou o Ca los G anell-Canu , PhD Ins i u e o New Imaging Technologies, Uni e si a Jaume I (UJI) Cas ellón de la Plana, Spain Feb ua y 28, 2020 iii DECLARATION OF ORIGINALITY I decla e ha he wo k desc ibed in his documen is my own and no om someone else. All he assis ance I ha e ecei ed om o he people is duly acknowledged and all he sou ces (published o no published) a e e e enced. This wo k has no been p e iously e alua ed o submi ed o NOVA In o ma ion Managemen School o elsewhe e. Lisbon, 28.02.2020 Mihail Pe ko i ACKNOWLEDGMENTS An idea abou making sense o economic phenomena h ough he lenses o geog aphical in o ma ion ha e always been a esea ch opic o in e es o me. Though esea ch and he esul s’ a e ma h a e o en imes unp edic able, he people ha guided me and suppo ed me h oughou his p ocess we e o una ely no . I wan o i s and o emos hank my main-supe iso P o esso D . Robe o Hen iques ha was open o hea ing my ideas and helping me cons uc hem in some hing p ac ical, o P o esso D . Joel Sil a who was always he e o sugges imp o emen s and guide me h ough new di ec ions and doo s when all I was seeing we e dead ends, o P o esso D . Ca los G anell o belie ing in me, and las , bu no leas , o P o esso D . Ma co Painho o keeping me le el-headed o push and p og ess un il I ha e eached he inish line. Addi ionally, my g ea es g a i ude goes o all colleagues om he Geospa ial Technologies Mas e as a whole, wi h special shou -ou s o my iend and la -ma e I za, o Damien, Ca los, B aund , Vicen e and Pablo. Las bu no leas , I would like o hank all my closes amily and iends in Macedonia. I am ex emely g a e ul o all he suppo , pa ience and encou agemen p o ided du ing he jou ney. EVALUATION OF SPATIAL DATA’S IMPACT IN MID-TERM ROOM RENT PRICE THROUGH APPLICATION OF SPATIAL ECONOMETRICS AND MACHINE LEARNING Case S udy: Lisbon ABSTRACT Household p e e ences is a opic whose ele ance can be ound o domina e he applied economics, bu whe eas u ban economies iew ci ies as p oduc ion cen e s, his hesis aims o gi e impo ance o he ole o consump ion. P o ision o PoIs migh gi e explana ion o wha indi iduals alue as an impo an asse o imp o emen o hei quali y o li e in a chosen ci y. As such, unde s anding sho - e m en als and eal es a e p ices ha e induced a ious esea ch o seek p oo o impac ing ac o s, bu analysis o mid- e m en has aced he challenge o being an o e looked ca ego y. This hesis consis s o an in eg a ed h ee-s eps app oach o analyze spa ial da a’s impac o e he mid- e m oom en , choosing Lisbon as i s case s udy. The p oposed me hodology cons i u es use o adi ional spa ial econome ic models and SVR, encompassing a la ge se o p oxies o ameni ies ha migh be ecognized o hold a possible impac o e en p ices. The analy ical amewo ks’ i s s ep is o c ea e a sui able HPM model ha cap u es he da a well, so signi ican a iables can be de ec ed and analyzed as a disc e e da ase . The second s ep applies subse s o he da ase in he c ea ion o SVR models, in hopes o iden i ying he SVs in luencing p ice a iances. Finally, SOM clus e s a e chosen o add ess whe he mo e na u al o de o da a di ision exis s. Resul s con i m he impac o p oximi y o a ious ca ego ies o ameni ies, bu he en ichmen o models wi h he p oposed p oxies o spa ial da a ailed o co obo a e a ainmen o model wi h a highe accu acy. (Nüs e al., 2018) p o ides a sel -assessmen o he ep oducibili y o esea ch, and acco ding o he c i e ia gi en, his disse a ion is e alua ed as: 0, 2, 1, 2, 2 (inpu da a, p ep ocessing, me hods, compu a ional en i onmen , esul s). i KEYWORDS P edic i e Modeling Ameni ies Suppo Vec o Reg ession Spa ial Econome ics Hedonic P ice Modelling Poin s o In e es Mid-Te m Ren ii ACRONYMS AIC – Akaike In o ma ion Re ie al ANN – A i icial Neu al Ne wo k API – Applica ion P og amming In e ace BGRI - Base Geog á ica de Re e enciação de In o mação BMU – Bes -Ma ching Uni CCDR – Comissão de Coo denação e Desen ol imen o Regional CML – Câma a Municipal de Lisboa CPI – Consume P ice Index DoF – Deg ees o F eedom DTM – Digi al Te ain Model GIS – Geog aphic In o ma ion Sys ems HPM – Hedonic P ice Modelling MAE – Mean Absolu e E o MD – Minimum Dis ance MLP – Mul i-Laye Pe cep on MMH – Maximum Ma gin Hype plane OSM – OpenS ee Map POI – Poin o In e es RMSE – Roo Mean Squa e E o SD – S anda d De ia ion SDEM – Spa ial Du bin E o Model SLX – Spa ially Lagged X SOM – Sel -O ganizing Map SQL – S anda dized Que y Language SVM – Suppo Vec o Machine SVR – Suppo Vec o Reg ession iii INDEX OF THE TEXT ACKNOWLEDGMENTS ....................................................................................................... IV ABSTRACT .............................................................................................................................. V KEYWORDS .......................................................................................................................... VI ACRONYMS ......................................................................................................................... VII INDEX OF TABLES ................................................................................................................ X INDEX OF FIGURES ............................................................................................................. XI 1. INTRODUCTION .................................................................................................................. 1 1.1 THE MARKET AND ITS FLUCTUATIONS ............................................................................. 1 1.2 FACTORS DRIVING A MARKET – PREDICTIVE MODELLING .............................................. 2 1.3 RESEARCH OBJECTIVES ..................................................................................................... 3 1.4 DISSERTATION STRUCTURE ............................................................................................... 3 2. THEORETICAL FRAMEWORK AND RELATED WORKS ............................................. 4 2.1 THEORETICAL BACKGROUND ............................................................................................ 4 2.1.1 A i icial In elligence and Machine Lea ning ........................................................... 4 2.1.2 Spa ial Econome ics ................................................................................................ 4 2.1.3 Suppo Vec o Reg ession ........................................................................................ 6 2.1.4 Sel -O ganizing Map and GeoSOM .......................................................................... 8 2.2 RELATED WORK ................................................................................................................ 9 2.2.1 Resea ch h ough Applica ion o Spa ial Econome ics ........................................... 9 2.2.2 Resea ch h ough Applica ions o SVR ....................................................................11 2.2.3 Resea ch h ough Usage o O he Algo i hms .........................................................11 3. DATA AND METHODOLOGY ..........................................................................................12 3.1 GEOGRAPHICAL CONTEXT ...............................................................................................12 3.2 PROPOSED ARCHITECTURE ...............................................................................................13 3.3 HARDWARE AND SOFTWARE ............................................................................................13 3.3.1 Pos g eSQL ..............................................................................................................13 3.3.2 R ...............................................................................................................................14 3.3.3 Py hon ......................................................................................................................14 3.4 DATA DESCRIPTION AND RESOURCES ..............................................................................15 3.4.1 Room Ren al Sou ces ...............................................................................................15 3.4.2 Zoma o API Res au an Da a Collec ion .................................................................15 3.4.3 Google Places API Da a Collec ion .........................................................................16 3.4.4 OpenS ee Map Da a ...............................................................................................16 3.4.5 Census Da a .............................................................................................................18 3.4.6 Ancilla y Da a ..........................................................................................................18 3.4.7 O he Va iables Impo ance – Access Limi a ions...................................................19 3.5 METHODOLOGY ................................................................................................................19 3.5.1 Va iables Con e sion ...............................................................................................20 3.5.2 Spa ial Da a En ichmen ..........................................................................................21 3.5.3 Da a P ep ocessing ..................................................................................................24 3.5.4 Spa ial Econome ics and Machine Lea ning ..........................................................27 ix 4. RESULTS AND DISCUSSION ...........................................................................................28 4.1 SPATIAL DEPENDENCE .....................................................................................................28 4.2 SPATIAL LAGGED X ..........................................................................................................29 4.3 SPATIAL DURBIN ERROR MODEL .....................................................................................33 4.4 SUPPORT VECTOR REGRESSION .......................................................................................38 4.5 NATURAL DATA CLUSTERS USING SOM AND GEOSOM .................................................43 4.6 OVERVIEW OF GIVEN ANALYSIS ......................................................................................46 5. CONCLUSIONS ...................................................................................................................47 6. BIBLIOGRAPHIC REFERENCES ......................................................................................49 7. ANNEX .................................................................................................................................56 5 O dina y Leas Squa es (OLS) is a simple HPM eg ession ha akes he o m o equa ion (1): 𝒚𝒚𝒊𝒊=𝛂𝛂+ 𝜷𝜷𝟏𝟏𝒙𝒙𝟏𝟏+𝜷𝜷𝟐𝟐𝒙𝒙𝟐𝟐+ 𝜺𝜺𝒊𝒊 (𝟏𝟏) Whe e yi would be he i h obse a ion o he dependen a iable, x is a ec o o all explana o y a iables, and α is an in e cep ha holds he alue o y when all explana o y a iables a e equal o 0. 𝛽𝛽 is he ec o o he co esponding coe icien s o he es ima es p edic o s and 𝜺𝜺 is he andom e o . When dealing wi h gi en da a, he OLS model has ce ain assump ions, whose iola ion would lead o an inapp op ia e model. One o he assump ions speci ies ha inding spa ial au oco ela ion in he esiduals o he p edic ions shows ha he e is a spa ial pa e n in he da a unde analysis and mo e app op ia e models exis ha can accoun o i . Spa ial Lagged X (SLX) po ays a spa ial eg ession model ha ex ends o include explana o y a iables obse ed on neighbo ing c oss-sec ional uni s e ms. In o de o imp o e he model, a spa ial exogenous au o eg essi e lag is in oduced (Elho s & Halleck Vega, 2017). The equa ion (2) would hen ake he o m o : 𝒚𝒚𝒊𝒊𝒊𝒊 =𝐖𝐖𝒙𝒙𝒊𝒊𝒊𝒊 +𝐗𝐗𝒊𝒊𝒊𝒊𝜷𝜷+𝜺𝜺𝒊𝒊𝒊𝒊 (𝟐𝟐) Then, 𝐗𝐗𝒊𝒊𝒊𝒊 ep esen s he au o eg essi e coe icien ha p oduces he global spa ial spillo e e ec . I his comes o be equal o ze o, he model simpli ies o a con en ional linea eg ession model (Lesage, 2008). Ne e heless, his app oach has i s d awbacks because assump ions a e made ha all he spa ial dependence among esiduals is caused by a iables one can measu e. Spa ial Du bin Model is an ex ension o SAR ha includes he a e age o he a iables om he neighbo ing houses, bu i ex ends o allow o global di usion o shocks o he model dis u bances. This means ha he spillo e can be el o e mul iple egions, bu he decay pa ame e λ con ols ha highe -o de neighbo s (indi ec ones) o ecei e less impac han he di ec ones (Lesage, 2014). Addi ionally he E o addi ion wi hin his model c ea es he SDEM model ha accoun s o spa ial dependence among he e o e ms and edis ibu es his e o among he sample. The equa ion in ec o o m akes he equa ion (3) (LeSage & Pace, 2009): 𝒚𝒚𝒊𝒊𝒊𝒊 =𝐃𝐃𝒊𝒊𝒊𝒊ծ+𝐖𝐖𝒚𝒚𝒊𝒊𝒊𝒊𝝆𝝆+𝐗𝐗𝒊𝒊𝒊𝒊𝜷𝜷+𝑾𝑾𝑾𝑾𝑾𝑾𝑾𝑾 (𝟑𝟑) 𝑾𝑾= 𝝀𝝀𝑾𝑾𝑾𝑾+𝝐𝝐 Dummy Va iables a e bina y a iables ha equal ‘1’ i he a ge a iable is desc ibed o ei he , con ain some hing (e.g. e ace wi h seaside iew), o i belongs somewhe e (e.g. an apa men belongs o he pa ish o Al ama). ‘0’ hen desc ibes he opposi e case. Each o he a iables can ha e a posi i e o a nega i e ela ionship wi h he p ice. In an ideal case, minimum dis ance o an ameni y makes a p ice ise. Ne e heless, he ma ke can beha e unp edic ably o in e ac wi h o he a iables o yield a nega i e ela ionship. Fo example, a en o oom in an apa men whe e he a io o numbe o 6 bed ooms di ided by numbe o ba h ooms is high migh yield a nega i e e ec . Addi ionally, ha ing a minimum dis ance o clubs below 20 me e s migh dissuade po en ial enan s away om a p ope y. Di ec e ec : Change o a pa icula en i y o a lis ing (e.g. eno a ion o apa men om 1979 o 2019) changes he p ice a ge a iable. Indi ec e ec : Measu es he impac on he p ice o a a ge a iable om changing an exogenous a iable in ano he da a poin . Weigh Ma ix - A ma ix W is a ma ix o o de n x n whe e n is he numbe o egions. Non-ze o elemen s in ow i and column j in he ma ix hen ep esen he elemen ni is a neighbo o elemen nj. Rook and Queen each e e o wo common ways o calcula e s a is ics o ocal cells, and hese a e known as Moo e’s and Neumann’s neighbo hoods. These spa ial weigh s a e calcula ed, such ha each elemen in a ma ix ep esen s a spa ial weigh be ween wo neighbo s. The spa ial weigh s Wij a e non-ze o when i and j a e neighbo s, o ze o o he wise. The di e ence be ween he wo ypes o neighbo hood is ha in Rook con igui y, common e ices do no make wo polygons - neighbo s. The use o queen neighbo hood was he chosen app oach in o de o e lec eal-li e phenomena whe e i wo neighbo hoods mee a a common co ne , hey would s ill cause in luence be ween one-ano he . Figu e 2.1 - Types o Weigh ed Neighbou hoods 2.1.3 Suppo Vec o Reg ession SVM o igina ed om an algo i hm implemen a ion om 1995 by Co es and Vapnick (Co es & Vapnik, 1995). The algo i hm had been i s in oduced in o de o sol e pa e n ecogni ion p oblems. SVM is desc ibed as an algo i hm ha makes use o a hype plane cons uc ed in a highe dimensional inpu space ha sepa a es he da a in his high dimensional space op imally (Suykens & Vandewalle, 1999). Ne e heless, wha began as a classi ica ion p oblem, ose o applica ion o sol ing unc ion es ima ion p oblems. These indings p oceeded o addi ional inclusion o op ional pa ame e s like epsilon’s loss unc ion and in oduc ion o di e en ypes o ke nel unc ions in which da a can be mo e easily di ided. This way, he e could be di e en solu ions p oduced wi h di e en complexi ies and di e en h esholds o e o s in o de o build he mos cos -e icien model ha could be deemed a good enough i o he pu pose i had been buil o . 7 The e a e in ini e possible ways o cons uc a hype plane, and in classi ica ion, he bes hype plane can be de e mined as he one ha holds he la ges dis ance be ween hype planes and he suppo ec o s. Subsequen ly, de ec ion o SVs and Lag ange Mul iplie s demons a e he eco ds impo an o building he model (Wi en, Pal, & Fou h, 2017). Epsilon wi hin SVR Wi h gi en aining da a {(x1, y1) …. (xe, ye)} whe e X ⊂ X × R, whe e X deno es he space o he inpu pa e ns, SVR is looking o a unc ion (x) ha would ha e a mos ε de ia ion om he ac ual a ge s o all aining da a, whils main aining he la ges la ness (Smola & Schölkop , 2004). A linea i o a eg ession unc ion is p esen ed in Figu e 2.2: Figu e 2.2 - Tube wi h adius ε (Schölkop , 2002) I all da a poin s i wi hin he ube p esen ed, he i ed model hen has an e o 0. In his way, a model can be buil wi h an in ini ely high alue ε. This would lead o no penal y gi en o any da a poin and an e o o 0, bu his would be a meaningless accu acy measu e. In a linea case he SVR unc ion akes he o m o Equa ion (4) 𝑋𝑋 = 𝑏𝑏 + ∑i α a(i)⋅a (𝟒𝟒) The do no ion can be subs i u ed by a ious ke nel unc ions i a non-linea p oblem is p esen ed. Mos common ke nels used a e: • Linea ke nel Xi – Equa ion (4) 𝐾𝐾(𝑥𝑥𝑖𝑖,𝑥𝑥)=𝑥𝑥𝑇𝑇𝑥𝑥𝑖𝑖 (𝟓𝟓) • Polynomial ke nel – Equa ion (5) 𝐾𝐾(𝑥𝑥𝑖𝑖,𝑥𝑥)= (𝑥𝑥𝑇𝑇𝑥𝑥𝑖𝑖+ 1)𝑑𝑑 (𝟔𝟔) 8 • Radial Basis Func ion ke nel – Equa ion (6) 𝐾𝐾(𝑥𝑥𝑖𝑖,𝑥𝑥)=exp �−𝛾𝛾�|𝑥𝑥𝑖𝑖−𝑥𝑥|�2�,𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝛾𝛾=1 2𝜎𝜎2 (𝟕𝟕) Only he suppo ec o s a e impo an o he model – he dele ion o all o he ows bea s a coe icien 0 and hence, does no change he ou come o he p edic i e model. Ano he a iable whose alue plays impo ance in building he model is he egula iza ion pa ame e C ha deno es he limi o he absolu e alue o he coe icien s αi, which gi es he limi o how much i is needed o a oid misclassi ying a aining example. The limi cases hen become he ollowing: I. he la ge C becomes, he close he unc ion can i he da a in he hype plane and smalle -ma gin hype plane will be needed II. an ε o 0 c ea es a leas -absolu e-e o eg ession wi h cons ain C III. A la ge alue o ε jus ou pu s he la es ube ha encloses all da a Gamma (𝛾𝛾) is a speci ic pa ame e o adial basis ke nel ha de ines how a an in luence o a single aining example eaches. A la ge gamma would co espond o mo e suppo ec o s ha ing in luence on he hype plane. 2.1.4 Sel -O ganizing Map and GeoSOM The Sel -O ganizing Maps a e a clus e ing algo i hm in oduced in he 1980s (Kohonen, 1982). The main idea is o map high-dimensional da a, in o dimensions om which he human eye can unde s and and ex ac pa e ns. The uni s by hemsel es can be loosely o closely connec ed o each o he , and he deciding clus e s a e decided by he use . SOM algo i hm can ha e di e en dis ance me ics, bu mos o en makes use o he Euclidean dis ance as a measu e o closeness be ween wo a bi a y uni s. Once a SOM has been ained wi h a gi en pa e n, all he uni s mo e owa ds he bes ma ching uni (BMU). A he end, pa e ns ha a e simila in he inpu space should also ca y his beha iou in he ou pu space. GeoSOM is an adap a ion o SOM o accoun o he speci ici y o spa ial da a. The sea ch o he BMU akes pa in wo cycles. Ins ead o sea ching o a BMU h oughou he whole da ase , i ies o ind a neighbou ing one ha is limi ed in he sea ch adius wi h he pa ame e k. The ou pu space in SOM usually akes he o m o a 2- dimensional space (Kohonen, 2001) as he easies one o isualize. 9 Figu e 2.3 - Sel -O ganizing Map - I/O space (Hen iques, Bação, & Lobo, 2009) The e a e a numbe o impo an pa ame e s ha need o be uned when aining a da ase wi h SOM. These include lea ning a e, adius, a numbe o i e a ions, and hey need o be chosen acco dingly o minimize a model’s opological e o . 2.2 Rela ed Wo k Th oughou his subsec ion, e e ences and links o s udies ega ding p ice p edic ion a e men ioned o gain a gene al o e iew o wha esea ch has been applied and he co esponden indings ollow. Fo a clea e s uc u e, he ela ed wo ks a e di ided in o h ee sec ions, one deno ing Spa ial Econome ics’ ela ed s udies, a second o SVR ela ed s udies, and a hi d o gi ing b ie ing o o he algo i hms’ usage. 2.2.1 Resea ch h ough Applica ion o Spa ial Econome ics Resea ch shows indispu able e idence o he impac o he cul u al he i age on he eal es a e p ices in he ci y. A case s udy o he ci y o Lisbon inds p oo ha a p o ec ed zone can p oduce a nega i e impac on he house alue bu i also p oduced indings ha when accoun ing o he he e ogenei y o he a eas unde ques ion, he e ec s had seemingly disappea ed (F anco, Macdonald, F anco, & Macdonald, 2016). Ano he s udy has e ealed ha o e all, his o ic ameni ies gene ally gi e ise o dwelling p ices in o de o 4.2%, bu once he adius b oadened, a high concen a ion o hese his o ical ameni ies s a ed o yield a sligh ly nega i e e ec o 0.1% (F anco & Macdonald, 2016). When analyzed, hese pape s b ing abou conclusions ha li ing in a p oximi y o an ameni y wi h some deg ee o cul u al impo ance gi es exposu e and iden i y o an apa men being in he cen e o a local clus e (a desi able esiden ial a ea). Li ing in close p oximi y o many o hese objec s on he o he hand had shown a co ela ion o 10 i being a highly ou is ic a ea, which in u n is alued as a e y desi able dwelling o one’s day- o-day li e. O he esea ch has also ound ax exemp ions o d i e posi i e spillo e s o nea by p ope ies ( an Duijn and Rouwendal 2012, Ahl eld , Holman, and Wendland 2012, Coulson and Lah 2005). Wha ’s mo e, using a HPM on eal es a e p ices ha e ound Lisbon’s ‘Me o S a ion P oxy’ a iable coe icien o gi e be ween 3.49% and 5.18% ise in p ices wi h a ed posi i e accessibili y o a single me o line, o be ween 4.62% and 6.17% o accessibili y o wo me o lines and e en la ge o he ail accessibili y (Ma ínez & Viegas, 2009). Addi ionally esea ch ha e also used addi i e hedonic eg ession models o accoun o he he e ogenei y in he en ma ke (B unaue , Lang, Wechselbe ge , & Biene , 2010) o eal es a e p ices in Vienna. This had led o conclusions abou disco e ies o subma ke s which ha e as a signi ican ac o a ‘Belonging’ o lis ings in he speci ic ci y’s dis ic s. O he sou ces (Mo o, Mayo , & Lyons, 2013) include a s udy o e he ci y o Dublin as a case s udy whe e he i age si es wi hin he ci y we e ca ego ized as ac o s using a limi ed numbe o ca ego ies. This s udy had gi en a small bu signi ican posi i e sco e o ce ain ypes o ca ego ies (his o ic buildings and memo ials) as a spillo e e ec o apa men s in he icini y, al hough o he ca ego ies (a cheological si es) had p oduced a nega i e one. The s udy had been made h ough p oducing dummy a iables as lags o whe he a ce ain ype o building was in a adius o a chosen ameni y. Va iables pe aining o me os and bus s op as means o public anspo had also been used and i had been no ed ha li ing wi hin 100 me e s o a me o s a ion esul ed in a posi i e co ela ion wi h a p ice inc ease o an apa men (F anco e al., 2016). (Poo , 2015) ha e mo eo e a gued ha he p esence o cul u al he i age a ac s highly educa ed households using hei case s udy o he Ne he lands. This ac o had also caused a spillo e o indus ies in he coun y in es ing and p e e ing o eside whe e he eli e households o he coun y eside (Ma le and Woe kens, 2005). Las , bu no leas , o he s udy indings include cul u al he i age si es i sel ca ying a mul iplie e ec o o he ameni ies including es au an s and shops ( an Duijn, 2013). This gi es an idea o linea dependencies be ween exogenous a iables could clu e o bias an analysis and make o an o e ly complex model. These s udies, o he mos pa , decons uc many spa ial a iables seg ega ed and analyzed sepa a ely (as objec i e o unde s anding single a iable’s impo ance) a he han i ing one model using many. The majo i y o hem use Euclidean dis ance o calcula e p oximi y, whe ein a PoI can eside anywhe e wi hin a p oposed adius h eshold o an ameni y in ques ion. 11 2.2.2 Resea ch h ough Applica ions o SVR Finding using he SVR include (Chen, 2010) ha discuss ha s a i ica ion o Shanghai’s ma ke in o mo e homogeneous subse s p o ides conside able bene i s as con as o aking he agg ega e o he whole Shanghai’s en ma ke . The app oach used a hedonic app aisal model as a p ep ocessing s ep o choosing he igh a iables be o e building he SVR. Ano he pape has buil a eal es a e o ecas ing model based on pa icle swa m op imiza ion (PSO) be o e applying he SVR (Wang, Wen, Zhang, & Wang, 2014). Op imiza ion h ough HPM seems o be a ecu ing heme when using SVR and SVM. In his way, he signi ican a iables need o be de ec ed i s be o e building he model so he ime complexi y also lowe s subs an ially, whils also making su e he model’s accu acy does no su e om he mul icolinea i y p oblem. 2.2.3 Resea ch h ough Usage o O he Algo i hms A ecen s udy o eal-es a e p ice e alua ion was done h ough he usage o bo h NN and HPM as a way o compa ing he wo algo i hms. Ne e heless, his esea ch was concen a ed on p oducing minimum MAE accu acy model o p edic ions and does no gi e u he in o abou he singula in luence o unique a iables in building he model (Sa ono , 2017). This is because o he “black box” na u e o ANN in which mul iple neu ons a e exchanging in o ma ion and a e upda ing hei weigh s, bu o he ou e wo ld no a lo o subs an ial in o ma ion is gi en h ough which he obse e can ge many conclusions. Ano he s udy was done using ANN on he island o Cabo Ve de using 1092 da a poin s wi h a yea ly empo al scale be ween 2009 and 2014. This s udy also came abou as a compa ison be ween using he algo i hm o ANN and Random Fo es and d aws conclusions o MLP p oducing highe e o s han he la e algo i hm (Es e & Ma ins, 2016). The mos impo an a iables he e we e ound wi h he model i , and among hem, he loca ion o he apa men and he squa e me e o he apa men seemed o cause bo h highes signi ican and posi i e in luence, wi h he closeness o public ins i u ions and an exis ing balcony in he apa men compu ed as ones wi h leas impo ance. ML s udies o en ha e a lo o esea ch concen a ed solely on inding he bes model wi h he leas e o (C is ina and Teixei a 2009, McCluskey e al. 2013, Limsombunchai e al. 2004) wi h using NN and MLP’s as ML s anda ds ha manage o build models ha cap u e he da a’s beha io he bes , p oducing he smalles e o . One can also no e usage and compa ison o Random Fo es in eal es a e p edic ions in Ljubljana (Kiliba da, 2018), whe e indings sugges in he s udy a ea unde e alua ion, i pe o med signi ican ly be e han o he ML algo i hms. These a e jus a ew small e e ences o he as usage o many di e en algo i hms wi hin he ML ield ha could be used o assess his ype o da a, al hough i mus be no ed ha e e y algo i hm a ies in he ou pu in o ma ion and hence, he ype o analysis i allows o . 12 3. DATA AND METHODOLOGY This chap e explains in de ail he unde aken s eps o p oduce his disse a ion. Fi s , a geog aphical con ex is gi en in Sec ion 3.1 whe ein gene al in o ma ion abou he encompassing s udy a ea is in oduced. In Sec ion 3.2 a b ie o e iew o he p oposed a chi ec u e. The chap e con inues wi h Sec ion 3.3 he eupon gi ing a synopsis o he so wa e and algo i hms ha a e impe a i e o p oducing new spa ially consis en da a. Sec ion 3.4 hen desc ibes he da a sou ces and a iables choices. The inal, Sec ion 3.5 po ays how he di e en unde aken pa s o he me hodology come oge he o encapsula e he analysis. 3.1 Geog aphical Con ex Lisbon is he capi al and la ges ci y o Po ugal, wi h a bounding box desc ibing a la i ude ange be ween -9.2379 and -9.0863 and a longi ude ange o 38.6800 and 38.7967. The adminis a i e a ea o he ci y co e s app oxima ely 100.05km2, and he ci y’s las census had eco ded 505,526 ci izens. A clea dis inc ion is made be ween Lisbon’s adminis a i e a ea and he u ban a ea ha ex ends a beyond hese limi s. The posi i e ele a ion goes om 0 a i s minimum up o 227 me e s o al i ude. The ci y has a ci cula physical con igu a ion co e ing app oxima ely 12 kilome e s bo h eas o wes and no h o sou h. O icial di isions di ide i in o 24 pa ishes, o in 3623 subsec ions a he lowes mapping le el. Maps o he pa ishes’ polygons and he le el 4 subsec ions a e shown in Figu e 3.1 below. Figu e 3.1 - S udy A ea Di isions: Pa ishes e sus Le el 4 Census Blocks 13 3.2 P oposed A chi ec u e The pu pose o he me hodology is o y o inco po a e many di e en sou ces, acco ding o he a ailabili y o he da a and he ca ego ies o da a poin s hey o e . The policy o anspa ency o he EU gi es space o use open da a eely which helps in he p ocess o ga he ing an abundance o da a ha could be in e -checked o eliabili y be ween he di e en sou ces and gi es he choice be ween using sou ces wi h he bigges quan i y, bigges quali y o in eg a ions. Ne e heless, his also b ings abou weigh and complexi y o compu a ions needed o eplica ing he analysis. Fo easie p ocesses, all da a is impo ed o a Pos g eSQL da abase, om whe e i could be easily expo ed and ead in bo h QGIS and RS udio. This in eg a ion o en i onmen s p o ides a obus b idge o easie da a con e sion, manipula ion and addi ional pa alleliza ion o compu a ional p ocesses. The p oposed a chi ec u e is ound in Figu e 3.2. The Figu e shows li le de ail o he R analysis, al hough he packages used a e o be men ioned in he ollowing sec ion. Figu e 3.2 – P oposed A chi ec u e 3.3 Ha dwa e and So wa e Conce ning ha dwa e, he esea ch used an In el Co e i7-7700HQ wi h 16 GB o RAM capaci y, unde a Windows 10 ope a ing sys em. Rega ding so wa e, he majo i y o he unde aken analysis was done wi hin Pos g eSQL and R. Addi ionally ancilla y so wa e was used o isualiza ion including QGIS, A cGIS P o, as well as mino checks and la iles o he da ase o e sioning his o y as excel iles. 3.3.1 Pos g eSQL This is a ee and open-sou ce ela ional da abase managemen sys em ha ex ends he SQL language whe e use s can sa ely s o e and scale complica ed da a wo kloads (The Pos g eSQL Global De elopmen G oup., 2014). When dealing wi h spa ial-da a, he 14 da abase capabili ies can be accompanied by addi ional add-ons. pgAdmin4 e sion is used, alongside he ollowing ex ensions: • Pos GIS: Allows o geog aphic loca ion que ies o be un in SQL (Pos g eSQL Global De elopmen G oup, 2020). • pgRou ing: Enables a oad ne wo k analysis o be pe o med; I is used o calcula e he sho es pa h o places h ough pg _d i ingDis ance unc ion (OSGeo Founda ion, 2018) 3.3.2 R R is a sys em o s a is ical compu a ion and g aphics. I p o ides, among o he hings, a p og amming language, high-le el g aphics, in e aces o o he languages and debugging acili ies (R Co e Team, 2019). The language is able o be execu ed on many ope a ing sys ems ee o cha ge. The RS udio, subsequen ly, ep esen s an in e ace o he execu ion o R code. Packages ha make he analysis possible a e lis ed as ollows: • s : Package ha allows o eading, w i ing, manipula ing and isualizing spa ial da a and geome ies, o and om R (Edze Pebesma, 2019) • RPos g eSQL: Da abase in e ace and ‘Pos g eSQL’ d i e o R (Conway e al., 2019). Wi h his package di ec connec ion o he Pos g eSQL da abase is made, and ables and que ies o he da abase can be di ec ly impo ed and sa ed as a iables wi hin he RS udio en i onmen • dply : A ool used o easie manipula ion o da a ames (Wickham, 2019) • mag i : Ope a o ha o wa ds a esul s o an exp ession o he nex unc ion ha comes a e (S e an Mil on Bache and Hadley Wickham, 2014) • ca e : A comp ehensi e amewo k o machine lea ning models (Kuhn, 2020) • e1071: A package used o in ui i e applica ion and analysis o he SVR algo i hm, one among many p obabilis ic clus e ing and eg ession models (Meye , 2019) • spa ial eg: A collec ion o es ima ion unc ions o spa ial c oss-sec ional models (Roge Bi and 2019). Lib a y used o applying HPM on he da a • spdep: A collec ion o unc ions o c ea e spa ial weigh s ma ix objec s om polygon ‘con igui ies’ by dis ance and essella ions (Roge Bi and 2019). This package is used o applying unc ions in he HPM spa ial eg ession analysis. 3.3.3 Py hon Py hon is an in e p e ed, high-le el, gene al-pu pose p og amming language. The language can be used o any compu a ional pu poses, al hough o he means o he disse a ion, i was used o inding speci ic-pu pose API W appe s. The API W appe hen p o ides an in e ace be ween an API and a p og amming language, so all p o ided API me hods o da a collec ion can be made h ough he desi ed p og amming language’s unc ion calls and w appings. 21 dummy a iables we e, in u n, no included. The mos equen wo ds a e shown in Figu e 3.5 abo e. 3.5.2 Spa ial Da a En ichmen Da a om many o he sou ces o e laps. The e o e, decisions o uni ica ion o hese da a in o one sou ce we e unde aken. The da a om Zoma o holds he la ges quan i y o es au an s, and con ains in o ma ion pe aining o e iews and he cos liness o he es au an s. Hence, i was decided o use i as he only sou ce o ood- ela ed PoIs. O he PoI ca ego ies om a single sou ce (CML) we e me ged depending on whe he he di e en ia ion be ween hem ailed o appea as a esponse in simila s udies o his ype (e.g. p i a e and public schools o i s , second deg ee and p e-cycle a e me ged). Medical p ac i ione s we e subsequen ly me ged wi h independen doc o s. Ne e heless, hospi als and medical cen es a e le as a sepa a e ca ego y. I wo used sou ces a e ound o hold a subs an ial amoun o di e en unique da a, A cGIS P o Analysis – “Gene a e Nea Fea u es” unc ion is used o de ec ion o all ea u es be ween he wo laye s ha a e wi hin 2 me e s one o he . These we e p esumed o ep esen he same da a poin and we e dele ed om he second sou ce be o e me ging. The ca ego ies o ameni ies chosen a e lis ed in Figu e 3.6 and Figu e 3.7 below. Figu e 3.6 - Coun s o Fea u es pe Ca ego y A Figu e 3.7 - Coun s o Fea u es pe Ca ego y B 22 Fi y- i e new a iables hus exis ; 54 o hem a e shown in he Figu es abo e, and he las one deno es ele a ion ex ac ed om a DTM (Lisboa - Digi al Te ain Model, 2010). The spa ial da a en ichmen hen makes use o he unc ion pg _d i ingDis ance() o de ec ion o eachable ameni ies om a eco d’s lis ing. pg _d i ingDis ance('SELECT id, sou ce_osm, a ge _osm, cos _s, FROM ways', s a ing_ e ices, dis ance, di ec ed := alse) To be able o execu e his command, a lis ing needs i s node o igin poin , and a des ina ion poin . In he case o he ooms, compu a ions gene a e he closes node o each oom as well as he closes nodes o each o he des ina ions. Figu e 3.8 below shows sample ables wi h gene a ed closes nodes’ ield using he ways able. Figu e 3.8 - O igin (Room), Des ina ion (PoI) and Edge Ne wo k DB Schema Fo less cos ly compu a ion, an addi ional in e media y able ca chmen _a ea is c ea ed, which desc ibes all po en ially eachable nodes om all o igin nodes o he ooms (gi en a desi ed me e s uppe h eshold). WITH nodes AS ( SELECT a ay_agg(node_id) AS nodes om ap _ oom.node_id) SELECT om_ as s a _node, node as end_node, agg_cos as cos om nodes, pg _d i ingdis ance( 'SELECT gid as id, sou ce as sou ce, a ge as a ge , cos _s as cos , di ec ed FROM public.ways':: ex , nodes, 2000, alse) This code, in u n, p oduced a able ha holds all he eachable nodes wi hin 2km. A isualiza ion o he eachable a ea om a sample poin is shown in Figu e 3.9 below. 23 Figu e 3.9 - Road Ne wo k Accessibili y om a Sample Room The p oxies o each ca ego y o PoI hen cons i u e o : • Minimum dis ance (in me e s) om he oom o he closes ameni y o a p ede ined ype • Coun pe ca ego y o PoIs wi hin a dis ance h eshold. Fi e dis inc h esholds a e p oposed as ollows: 2km, 1.5km, 1km, 0.5km, and 0.25km. Two a iables ha we e speci ic in hei seg ega ion p ocess we e he ‘Pa ks’, many o which ha e mul iple closes nodes as being 0 me e s away om i s en ance, and he ‘Res au an s’ ha ha e a e y high quan i y and densi y h oughou he whole s udy a ea. The e o e, a sepa a e able o pa ks was cons uc ed ha holds all nodes less han 10 me e s away om he pa k o in e es , as possible des ina ion nodes om an o igin poin . Unique p oxies a e cons uc ed o he es au an s acco ding o hei expensi eness (1-4 s a s), and addi ionally, acco ding o hei a e age e iew a e (s a ing om 0 as no- e iews, 1 as bad, up o 5 as excellen a e). Figu e 3.10 below, p esen s an example wi h an in e pola ed su ace o he minimum dis ance needed o walk om a sample oom o he i s egis e ed s a ue in he da ase . 24 Figu e 3.10 - Example: Minimum Dis ance o a Mall (in me e s) 3.5.3 Da a P ep ocessing The goal o his sec ion is o p o ide an o e iew o he desc ip i e da a s a is ics, as well as some p ep ocessing decisions o he in eg a ed da ase and he easoning behind hem. Ou lie de ec ion – A ecommended app oach when dealing wi h da ase s is o emo e ou lie s. These can ep esen e oneous da a and in his speci ic case, alse en ies can be pa o o e p iced o e s i a oom’s acancy is a in he u u e, o addi ional nego ia ions migh be p esen be ween cus ome -clien , which canno be accoun ed o . The s a is ics o he endogenous a iable a e shown in Table 3.4 below: S a is ic Value Mean 473 S anda d E o 3.72 Median 420 Mode 400 S anda d De ia ion 173 Range 900 Minimum 100 Maximum 1000 Coun 2149 Table 3.4 – Desc ip i e S a is ics o Dependen Va iable The in e qua ile ange inds all alues om 870 abo e as ou lie s and no ou lie s below he minimum alue, which amoun s o a o al o 105 ou lie s ou side o he 1.5 in e qua ile anges below he i s and abo e he hi d qua ile. Ne e heless, his da a 25 and scena io depic s a eal-li e Lisbon en ma ke a a speci ic empo al ins ance in Sep embe 2019. Hence, i is decided agains he emo al o hese ou lie s. The Clus e and Ou lie Analysis was un in o de o iden i y clus e s and spa ial ou lie s. False Disco e y Ra e Co ec ion (FDR) pa ame e is checked, o educe he c i ical p- alues o accoun o mul iple es ing and spa ial dependence. I is no iceable ha he e a e many clus e s adjoining high-p iced ooms wi h low-p iced ooms nea by, as well as low-p iced ooms wi h many high-p iced ooms nea by. The high-low p ice clus e s end o exhibi a pa e n om cen al o he no he n bo de s o he s udy a ea, whe eas he low p icings wi h many high-p iced ooms end o ha e a gene alized localiza ion nea he coas . Clus e Type Coun High-High 185 High-Low 64 Low-High 86 Low-Low 232 Non-Signi ican 542 To al 1109 Table 3.5 – Coun s o Signi ican Ho -Spo Analysis Clus e s Figu e 3.11 - Anselin Local Mo an’ I When i comes o numbe s o ooms a ailable pe Pa ish, mos o he a ailable ooms a e ound in pa ishes whe e he signi ican clus e s domina e. As such, A enidas No as, A eei o, Al alade, San a Ma ia Maio and Mise icó dia hold he la ges quan i ies. Addi ionally, a high coun o bed ooms p edomina es he cen al pa ishes o Lisbon, as 26 he bed ooms end o dec ease apidly owa ds he no h bo de s and dec ease ma ginally owa ds he sou hwes and sou heas bo de s. Following his app oach, a ew bina y a iables we e pu unde inqui y and esul s o a Ho Spo Analysis a e subsequen ly shown in Table 3.6. Va iable Pa ish – Ho spo Pa ish – Coldspo Male Landlo d Lumia , San a Cla a, Ben ica, Al alade, Bea o, Penha de F ança, Belém San o An ónio, A oios Female Landlo d Ca nide, Al alade, Lumia , San a Cla a, Pa que das Nações São Domingos de Ben ica, A eei o No Landlo d A enidas No as, Campolide, A oios, San o An ónio Al alade, Lumia , Ben ica Has Ou doo A ea Ajuda, Ma ila, Oli ais, Es ela, Campo de Ou ique A enidas No as No Ou doo A ea Alcán a a, San a Ma ia Maio , Ma ila, Mise icó dia, São Vicen e, A eei o Lumia , Al alade, Oli ais, São Domingos de Ben ica Ou doo A ea N/A Campolide, Ca nide, Lumia , Al alade, A enidas No as Oli ais, Ma ila, Belém Table 3.6 – Ho -Spo s and Cold-Spo s o Pa ishes These ho spo s can indi ec ly in oke knowledge abou he pa e n – and i can be seen ha mos ooms ha a e en ed in an apa men wi h a hos appea in all pa ishes bu he cen al ones. This signi ies he a ea in ques ion is likely o be comp ised o s uden - domina ed apa men s and i includes he pa ishes o Al alade, A eei o, A enidas No as and San o An ônio. ‘Male Landlo d’ ho -spo s a e ound bo h in he Pa ishes in he no h and on he i e coas , bu ‘Female Landlo ds’ do no appea as ho spo s on any coas al pa ish. An exis ing ‘Ou doo A ea’ ho -spo s appea equen ly in Ajuda and Alcán a a, bu ho -spo s o apa men wi hou i appea equen ly in all pa ishes alongside he coas (in which Ajuda and Alcán a a also belong). Rooms belonging in apa men wi h ‘Non-speci ied Ou doo A ea’ also show a ew ho spo s in he mos cen al pa ishes. Iden i ica ion o Co ela ed P edic o s and Linea Dependencies - The da ase con ains many a iables, and a pai wise check is done o emo e a iables ha migh bias he eg ession. All p edic o s ha a e co ela ed wi h abo e 85% a e hus emo ed. Da a No maliza ion – The da ase la gely con ains da a in e y di e en me ics (me e s, quan i ies and bina y a iables) – he min-max ange is applied so he e exis s a common scale ha would no lead o any dis o ing di e ences in he ange o alues. Da a Agg ega ion – As he spa ial applica ion o hedonic p ice modelling h ough he ‘spa ial eg’ R package equi ed polygons neighbou s o calcula ing he lagged in luence o he exogenous a iables, di e en da ase is c ea ed o applying HPM. A spa ial join is pe o med using he laye o he Census Blocks a he 4 h le el wi h he laye o ooms and i s ea u es. Fo each polygon, he a e ages s a is ics o he lis ings belonging in he mapping uni is calcula ed. The esul ing shape ile hen con ains 987 polygons ha deno e only census blocks o which he e a e lis ings p esen . 27 Coun o Dwellings pe Block # o Census Blocks To al Rooms 1 503 503 2 218 436 3 113 339 4 63 252 5 36 180 6 15 90 7 12 84 8 11 88 9 7 63 11 3 33 14 2 28 10 1 10 12 1 12 13 1 13 18 1 18 987 2149 Table 3.7 – Coun o Agg ega ed Dwellings in Blocks T aining and Tes ing Spli – The HPM is o be buil o measu e how well he da a can i accoun ing o he e o o he esiduals h ough he spa ial-speci ic chosen models, and he whole da ase is used, as he knowledge o he neighbou polygons a iables is needed. The SVR model, on he o he hand, needs o be i s ained o be able o es he pe o mance on a di e en unseen se . In o de o a oid he o e i ing p oblem (Zang, Be a di, & Rei e mano á, 2010), a sepa a e es ing da ase is alloca ed o check whe he he algo i hm pe o ms well only because i has memo ized he pa e ns on he aining se oo well. The p ocess o o e i ing can also be waned by K-Fold c oss- alida ion, which can be in oked as a con ibu ing pa ame e wi hin he ‘e1071’ lib a y wi h which he SVR model is buil . The choice o k is usually 5 o 10, al hough a o mal bes - alue o K does no exis . In gene al, as k ge s la ge , he di e ence in size be ween he aining se and he esampling subse s ge s smalle . As his di e ence dec eases, he bias o he echnique becomes smalle (Kuhn & Johnson, 2013). 3.5.4 Spa ial Econome ics and Machine Lea ning As a las s ep in he me hodology, di e en subse s o he clean da ase a e o be es ed o compa isons o a iables’ in luence, and he assessmen will be done wi h he da ase s con aining: • All a iables (applied o HPM and SVR) • Only non-spa ial a iables (applied o HPM, SVR, SOM) • Only spa ial a iables (applied o HPM and SVR) • All signi ican a iables om HPM (applied o SVR and SOM) 28 4. RESULTS AND DISCUSSION Fo compa ison o he di e en eg ession models applied, Adjus ed R2 and Akaike In o ma ion C i e ion (AICs) me ics a e used. 4.1 Spa ial Dependence OLS was pe o med on he da ase , and on ha model, he Global Mo an I s a is ic was compu ed o e he esiduals. The null hypo hesis assumes no spa ial dependence, and he esul s show he ollowing: • S anda d de ia ion = 1.751 • p- alue = 0.03583 Al e na i e hypo hesis: GREATER Sample Es ima es: Obse ed Mo an Index Expec ed Index Va iance -0.0624 -0.1157 0.0008 Table 4.1 - Local Mo an’s I The p- alue below 0.01 p esen s a s a is ically signi ican ejec ion o he ini ial null hypo hesis. The da a unde analysis leads o spa ial esiduals, and spa ial models a e deemed app op ia e in o de o make he e ec s o spa ially dependen e o s disappea . The LaG ange Mul iplie es diagnos ics addi ionally gi es di ec ions o whe he he e is a signi ican imp o emen o he model i i spa ial models we e applied. Resul s can be seen in Table 4.2 below: Model p- alue SAR 0.9457 SDEM 0.0042 SARMA 0.0166 Table 4.2 – Models Imp o emen The p- alue sugges s ei he Spa ial Du bin E o Model (SDEM) o Spa ial Au o eg essi e Mo ing A e age (SARMA) can b ing a signi ican imp o emen , al hough SAR is deemed un i (insigni ican p- alue). Acco ding o Luc Anselin, he bes app oach is o con inue wi h he one wi h he lowes p- alue, which in his case was he SDEM (Anselin, Be a, Flo ax, & Yoon, 1996). Ano he model in oduced is SLX, in o de o be able o compa e models ei he wi h local (SLX) o global (SDEM) spillo e s in he dis u bances. 29 4.2 Spa ial Lagged X When applying an HPM eg ession, he con ibu ing in luence o indi idual a iables is compu ed. The numbe o s a s assigned nex o a a iable indica es i s signi icance. Coun s o how many o each signi icance ype is ound o he model ha includes all a ailable a iables is shown in Table 4.3. Code P obabili y (> |) Coun o Va iables *** >0.001 3 ** >0.01 6 * >0.05 38 X >0.1 41 Table 4.3 – Signi icance Pe cen age The esul s ha e a esidual s anda d e o o 114.7€ which amoun s o a MAPE o 15% on p edic ing a oom p ice wi hin census blocks ha has agg ega e desc ip i e s a is ics o maximum p ice o 950€ and a minimum o 200€ among hem. The a iables ha a e deno ed as impo an excluding he X in e cep amoun o 97 a iables. The mos signi ican di ec e ec ones (abo e 95% signi icance) a e p esen in Table 4.4 below: Va iable Es ima e SE - alue P (>| |) Sig. C. o Bed ooms -199.908 54.823 -3.646 0.00001 *** Male Landlo d -135.44 20.312 -6.668 0.00031 *** MD o Club 20.344 7.799 -2.609 0.00958 ** MD o Viewpoin 89.951 33.764 2.664 0.00817 ** MD o Thea e 51.507 18.864 2.73 0.00672 ** Lag Cen alHea _F -271.162 97.123 -2792 0.00560 ** Lag C. o Bed ooms -126.196 46.517 -2.713 0.00708 ** Lag Ele a o N/A 350.502 159.086 2.203 0.00283 ** Table 4.4 – Signi ican Va iables – Model using All Va iables F om hese a iables, i is in e ed ha he exis ence o a male landlo d li ing inside he apa men makes he p ice o he oom be a subjec o nega i e in luence. This may esul om he ac ha he ooms a e mos ly used be ween 6 mon hs and 1 yea , and as such a e pe ec o ei he s uden s o people ha ha e ecen ly s a ed wo king. In his sense, o eigne s ha wan o expe ience Lisbon may end o ei he g a i a e owa ds an apa men ha he e is no landlo d li ing in, o expe ience mo e eedom du ing hei s ay – o hey s a is ically alue a emale pe son li ing o aking ca e o an apa men much mo e han a male pe son. S ill, on a e age ooms wi hou landlo ds a e p iced highe . This signi icance can be ein o ced by s udies ha con i m ha young adul hood has become a dis inc new li e phase (Be houd, Ge shuny, & B i ish Household Panel Su ey., 2000). Du ing his phase, people alue and choose o li e in pee -sha ed households and quasi-communes wi h people likely o be hei own age, a he han li ing wi h a landlo d (Hea h, 2004). 30 Howe e , simila s udies ha measu e a hos ’s gende signi icance in he p ices o sho - e m s ays applied on an Ai bnb da ase co obo a e no impac on i , as opposed o de ec ion o signi ican acial disc imina ion (Kaka , Voelz, & Wu, 2017). The numbe o bed ooms a iable impac in decline o p ice comes also as gene ally, apa men s end o ha e one ki chen o use and hus, he spaces would be subjec o sha ed use among people ha a e no necessa ily amilia wi h each o he . F om he spa ial ones, he mos signi ican ones deno e he minimum dis ance om a iewpoin as a posi i e coe icien . This means apa men s close o a iewpoin would be lowe -p iced. This migh be a esul as hese iewpoin s a e o en o -g id o whe e mos daily ac i i ies happen, and li ing close o a iewpoin can be o en connec ed o an upwa d slope when looking a he oom as a des ina ion. Coun s o uni e si ies wi hin 500 me e s and ams wi hin 1km also all yield posi i ely in luencing a iables (T oy & G o e, 2008). The anspo a ions’ e ec s a e no unique o mid- e m en als as i has been p o en hey a e ound in esiden ial p ope y alue indices wi hin he same s udy a ea, and u he hey can be used o o ecas possible upwa d p ice changes i an a ea is a subjec o new anspo a ion in es men s (Ma ínez and Viegas, 2009). A lag o he dummy a iable signi ying he exis ence o an ele a o wi hin he buildings o he apa men s lis ed wi hin a census a ea close o he one being en ed would seem a e ched o ha e an in luence in p edic ing p ice – bu i migh be ha he i s ule o nea by hings being mo e simila han a ones comes o play he e – and buildings wi h no ele a o s migh beha e in a clus e ed way. Howe e , he in luencing s eep coe icien o 350 aises a ques ionable impac . F om he a iables wi h less signi icance, he ollowing coun s a e p esen : Type o a iable Signi icance “*” Signi icance “X” Spa ial 14 13 Spa ial Lagged 8 19 Census 5 2 Census Lagged 3 3 Non-Spa ial 2 1 Non-Spa ial Lagged 3 2 To al 35 39 Table 4.5 - Coun o Signi ican Va iables in SLX Adding each o he a iables’ e ec combined wi h i s lagged coun e pa ’s indi ec e ec yields he o al signi icance o a iable. In his way, a s a is ically insigni ican a iable wi h i s s a is ically insigni ican lagged coun e pa migh yield a s a is ically signi ican a iable o he model. The di e ences be ween he wo models include a diminishing amoun o a iables being signi ican , bu spa ial ones ha appea o be impo an in he model include a uni e si y wi hin 0.5km, a ou is ou (coun s wi hin bo h 1km and 0.5km), and a non-spa ial posi i e one deno ing ha he hos has disclosed whe he he apa men has cen al hea ing. This, howe e , migh lead o di e en knowledge – apa men s wi h mo e missing da a migh be less desi able o en . When subse s o he a iables a e applied he esul s di e ma ginally, bu he AIC’s me ic does no imp o e. I can be no ed ha he a iables signi ican wi h con idence abo e 95% s ay he same in bo h he non-spa ial model and he spa ially en iched one. 37 o eseeable u u e, and la e e ise he oom o a less expensi e p ice when he e is less ime o ind a sui able enan o he p oposed loca ion. This is a s a egy ha is commonly used in sho - e m en als by mo e expe ienced hos s ha manage mo e lis ings as i helps in maximizing p o i s (Gibbs, Gu en ag, G e zel, Yao, & Mo on, 2018). These dynamics could be o e come i he e is a mul i- empo al egis e ing on p ice modi ica ions o e he s udy a ea aken h oughou di e en mon hs wi hin he yea . Figu e 4.7 - Boxplo s o 4 Highly Signi ican P oxies - SDEM Addi ionally, boxplo s o signi ican a iables a e shown in Figu e 4.7 abo e. These boxplo s ep esen agg ega ions o anges o he p ice on he X-axis , and a signi ican a iable o choice on he Y-axis, wi h he ed line deno ing he 10 h and 90 h pe cen ile o i s alues wi hin he gi en p ice ange. F om he boxplo s, i can be no ed ha coun o uni e si ies wi hin 1km ha e a sligh endency o co ela e o a aise in a lis ing’s p ice. As is, his is a desi able geog aphic loca ion o a s uden . As la e indings sugges he housing ma ke in Lisbon is exhibi ing an accommoda ion sho age and housing c isis (Cocola-Gan and Gago, 2018), he hos s migh eel he highe p ice will no impede hem om inding a enan . This inding ollows and ea i ms s uden i ica ion li e a u e claims ha s ess p oximi y o campuses as a main d i ing o ce in choice p ocesses o s uden clus e s wi hin a ci y (Sage, Smi h, & Hubba d, 2012). 38 F om he o he a iables, i is ound ha cheape ooms ha e e y ew, i a all, cul u al acili ies a ound hem. The minimum dis ance o a hea e also eco ds a sligh downwa d spi al wi h he lis ings wi h highes p ices esiding closes o his ameni y. Ano he a iable ha ollows a simila s uc u e is he coun o elec onic s o es wi hin 1km. Ne e heless, wi h 427 elec onics s o es h oughou he s udy a ea, i is likely ha mos o hem ha e clus e ed ho spo s in cen al pa ishes whe e his in luence s ems om. The coun o elec onic s o es wi hin 1 km o he lis ing dis ibu ed among he pa ishes o he s udy a ea a e shown on a cho ople h map in Figu e 4.8 below and ha assump ion can be empi ically con i med. Figu e 4.8 – Elec onic S o es pe Pa ish To con inue he analysis, a da ase con aining only he signi ican a iables as deno ed by SDEM is ex ac ed and u he applied o c ea ing an SVR model. 4.4 Suppo Vec o Reg ession Be o e applying SVR, he da ase s a e di ided in o a aining (85%) and es ing da ase (15%) wi h andomized ows aken as aining samples. The ou pu s models’ e o s ange be ween 80 and 150, al hough a MAE ha di e s a lo be ween a aining and es ing se poin s o an o e i ed model, so esul s need o be analysed ca e ully and pa ame e choices subsequen ly uned. In Table 4.11, a g id sea ch o he hype pa ame e op imiza ion is shown. The minimal alue o he accu acy me ic o RMSE as gi en by e1071 inds he model ha bes i s he da a. 39 Pa ame e Sea ch G id Values Coun C 0.001,0.01,0.1,1,5,10,50,250,500 9 ε 0.001, 0.01, 0.1, 0.3, 0.5, 1.5 6 𝜸𝜸 .0001,.001,.01,.1,1, 2 6 Models Tes ed 324 Table 4.11 – Hype pa ame e Op imiza ion Va Inclusion C ε 𝜸𝜸 SV SV% RMSE (€) RBF All (M1) 10 0.3 0.001 1109 65% 133 RBF Spa ial (M2) 1 0.5 0.01 909 52% 147 RBF Non-Spa (M3) 5 0.3 0.01ssd 1079 62% 130 RBF Sign (M4) 5 0.5 0.1 888 67% 143 Lin All (M5) 0.1 0.5 / 907 52% 155 Lin Spa ial (M6) 0.001 0.5 / 906 52% 157 Lin Non-Spa (M7) 0.1 0.5 / 905 52% 146 Lin Sign (M8) 0.01 0.5 / 888 52% 141 Table 4.12 – Bes Pe o ming Models F om he p oposed hype pa ame e op imiza ion used on he SVR models (Table 4.11) and he esul ing RMSE and SVs (Table 4.12), i can be no ed ha all models equi e a subs an ial amoun o eco ds o be used (upwa d o 50%) o de ine he ma gins o he hype planes. This is a con ibu ing p oo he e is no much egula i y in he da ase . Mo eo e , a small sample o 2149 da a poin s o e 312 a iables migh be deemed as oo li le aining da a o disce n a meaning ul hype plane. The bes pe o ming model s ill shows he non-spa ial inclusi e as he one ha bes i s he da a. Ne e heless, he usage o spa ial a iables in addi ion seems o p oduce a model wi h a compa able beha io in bo h he coun s o suppo ec o s and RMSE. Mo eo e , he linea ke nel pe o ms compa a i ely wo se o all he da a subse choices. In Table 4.13, he MAE me ic o he bes models is shown (see Table 4.12 o model names). In model M1, i can be no ed ha he ain and es pe o mance di e subs an ially. Addi ional g id sea ch o e he same da ase wi h a lowe alue o he pa ame e C (0.1) was done, and a new app op ia e model is calcula ed. In Table 4.13, his model is deno ed as M9: Model MAE T ain (€) MAE – Tes (€) R2 – T ain R2 - Tes M1 60.78 102.93 0.80 0.44 M2 84.95 114.46 0.66 0.32 M3 83.96 98.96 0.55 0.37 M4 104.78 110.15 0.42 0.26 M9 115.08 114.35 0.33 0.23 Table 4.13 – MAE on Bes RBF Ke nel Models 40 The new aining and es ing e o s in model M9 a e much mo e compa able al hough hey p oduce a much wo se i . The a iabili y o he da a is no cap u ed well, no in he aining, no in he es ing se . Model M3 using only he non-spa ial a iables is s ill he bes p edic o and a di e ence o 16 eu os be ween aining and es ing da a p o ides p oo ha his model does no o e i he da a. The la ges a iables’ con ibu ion owa ds models M3 and M4 a e shown in Table 4.14 below. M3 Va iable Impo ance Con ibu ion (%) Numbe o bed ooms 18.9 Numbe o ba h ooms 17.3 No P e e ed Gende 5.50 Double Bed - Dummy 5.20 No speci ied - Ele a o 4.90 Cen al Hea ing – T ue 4.90 Ou doo A ea – T ue 4.40 Single Bed- Dummy 4.30 Male Landlo d 3.50 Female Landlo d 2.40 Table 4.14 – Va iables Con ibu ions; Model M3 and M4 M4 – Va iable Impo ance Con ibu ion (%) Numbe o bed ooms 6.45 Bed oom - Single 3.26 Pa k Coun s – 250m 2.34 Room Squa ed – No Speci ied 2.17 Ele a ion 1.95 MD - Lodging 1.94 Tou is Tou Coun s – 500m 1.91 Viewpoin Coun s – 500m 1.80 MD – Real Es a e 1.79 Supe ma ke – 250m 1.74 Resul s sugges ha Model M3 gi es li le in luence o unique a iables, al hough i uses a la ge ange o hem. Ne e heless, when he a iables a e sepa a ed in o spa ial, and non-spa ial, i is compu ed ha he models gains con ibu ions cons i u e only 25% om he non-spa ial ela ed a iables, and 75% impo ance om a iables ha a e pe aining o he su oundings o he a ea. As he spa ial a iables a e only supposed o be e he p edic ion o close he e o gap enough o jus i y hei use, i seems his model has lea n o sepa a e he da a using hem as he p ima y exogenous a iables. Ex ac ion o he Lag ange Mul iplie ’s coe icien s o he SV o he models did no bene i he s udy as coun s o 852 and 601 SV’s coe icien s in model M3 and M4 acco dingly a e gi en he maximum mul iplie ’s alue as he o ce equi ed o en o ce he cons ain s o he models. 41 Figu e 4.9 – SVM Reg ession – Residual E o s abo e SD Th eshold F om mapping he high esiduals in Figu e 4.9, he wo models demons a e a di e en e o beha io , whe ein model M3 in cen al Lisbon and ollow a high esidual pa e n owa ds he sou h-wes bo de s o he a ea, whe eas M4 seems o ha e i s e o s sp ead h oughou mos pa ishes. Mo eo e , he model pe o ms qui e well in ce ain eguesias in he no h-eas e n egions o he case s udy whe ein no da a poin s wi h la ge e o s a e ound. Howe e , he cen al a eas expe ience e sa ile p ices o which a ma gin canno be ound – he spa ial a iables a e hus no help ul, bu hey a e c ea ing close clus e s in he mos cen al pa ishes whe ein la ge coun s o many ameni ies a e si ua ed. To ha e a be e o e iew o he aul s o each model, he wo models a e compa ed h ough sca e plo s in Figu e 4.10 and Figu e 4.11 below: Figu e 4.10 – Model Compa ison in Residual E o 42 Figu e 4.11 – Compa ison o E o s h ough B eaks’ Agg ega ions Model M3 has a mo e s abilized e o beha io h oughou he anges when compa ed o M4, acco ding o he b akes gi en. Model M4, on he o he hand, has a e y la ge absolu e di e ence be ween he p edic ed p ice and he ac ual p ice o he oom o en in he b eaks deno ing he highe anges. Howe e , bo h models ail o ind easoning o p ices ising owa ds he uppe ange in gene al (and his is whe e he la ges esiduals a e p oduced). The maximum absolu e e o s a e egis e ed in model M3 on he posi i e scale (o e es ima ion o 395€) on an a e age p iced oom (450€), and M1 wi h -426€ unde es ima ion on a high p iced lis ing o 900€. Figu e 4.12 – Residual E o Compa ison 43 4.5 Na u al Da a Clus e s using SOM and GeoSOM Bo h SOM and GeoSOM clus e ing o he da ase s we e applied on Models M3 and M4, o check whe he he s uc u e o he a iables would make simila -p iced ooms join oge he , o i would jus o ce he o de o na u al geog aphic coo dina es o o e ule he non-spa ial a iables impac . Di e en sizes o neu ons a e e i ied as ollows: 10x1, 15x1 and15x10. Manual sepa a ion o clus e s a e elec ed isually using he GeoSOM so wa e, wi h an icipa ions o clea e sepa a ion o he da a whils also main aining a small opological e o . F om he desc ip i e s a is ics o each clus e , unde s andings o a a iable’s agg ega e beha io is o be ou lined. The SOM algo i hm clus e s o M4 we e chosen wi h a opological e o a a alue o 0.01 and 14 numbe o clus e s. The clus e s show a e y spa se beha io h oughou he s udy a ea. E en hough Clus e 3 neu ons on he U- Ma ix showed a simila i y be ween hese eco ds, e y li le spa ial pa e n was de ec ed when di iding hem be ween he pa ishes. Figu e 4.13 – SOM Clus e s – Model M4 When i comes o he p ice a iable, he chosen clus e s’ minimum p ices anged om a minimum a e age o 398€ in Clus e 2, up o a maximum a e age p ice o 607€ in Clus e 10. Bo h o hese clus e s a e ound pa ially in he majo i y o he pa ishes. When GeoSOM is used, mo e na u al o de o geog aphic clus e s appea , as imposed by he limi ing adius pa ame e . In Figu e 4.14 below, he bina y a iables om he GeoSOM clus e o M3 a e p esen ed on pa allel coo dina e plo s. 44 Figu e 4.14 – GeoSOM – M3 Bina y Va iables Va iable/Clus e 1 2 3 4 5 C. o Bed ooms 3.08 4.55 2.78 3.36 3.07 C. o Ba h ooms 1.27 1.58 1.21 1.26 1.29 Minimum S ay 43.01 75.48 21.55 75.45 43.59 A e age P ice 506 454 403 434 420 Minimum P ice 110 200 200 225 100 Maximum P ice 1000 940 890 900 920 Table 4.15 – Clus e S a is ics o Nume ic Va iables in GeoSOM M3 Figu e 4.15 – GeoSOM – Model M3 45 Lis ings in Clus e 3 a e ela i ely indisce nible wi h hose om Clus e 4 in he no h- eas bounda ies as shown in Figu e 4.15, and hey also blend wi h Clus e 2 in he cen al a ea. A huge disc epancy can be no ed in he ‘Minimum-S ay’ a iable, wi h a subs an ially low alue in Clus e 3 deno ing ha he e is no minimum-s ay ule o hese lis ings. This clus e also desc ibes a high chance o a landlo d li ing in he icini y o he apa men , co ela es wi h a smalle numbe o bed ooms, and missing in o ma ion abou he exis ence o cen al hea ing. Al hough geog aphically hese ooms ie in oge he wi h he wo o he clus e s, his clus e deno es an a ea whe e i is mo e likely he owne is suble ing a oom o hei own li ing space o inc ease hei li ing income. Unsu p isingly, he oom p ice he e is he lowes , al hough he la ges di e ence be ween he minimum a e aged oom p ice Clus e and he maximum is only 103 eu os (12% o he p ice ange). Clus e 2 desc ibes ooms which a e no gende - assigned, and con ain he la ges numbe o bed ooms wi hin one apa men . Clus e 1 acqui es he coas al pa ishes geog aphically, bu non-spa ial a iable wise he a e age o he a iables a e mo e compa able o Clus e 2 wi h a sligh ly smalle pe cen age o lis ings wi hou landlo ds, and a smalle a e age o ooms wi hin he apa men . Clus e 4 seems o ha e a high p obabili y o double beds wi hin he oom, and abou an equal p obabili y o a landlo d possibly li ing in he lis ing. Clus e 5 is he one wi h he second-lowes p ice a e age and a la ge lack o in o ma ion abou he ype o bed. This a iable can p esumably be co ec ed by image p ocessing/analysis o exis ing images o he oom, o de ec he bed size – an a ea ha could be u he explo ed. Figu e 4.16 – SOM, Model M4 A he end, a SOM di ision using he SDEM signi ican a iables is made, wi h a choice o 14 Clus e s o easie compa ison wi h Model M3. Al hough he e is a la ge pe cen age o some clus e s being cons i u ed o one pa ish i is s ill ha d o pe cei e a g ea di ision, as many clus e s ha e a he e ogenei y ha sp eads h oughou he whole s udy a ea (e.g Clus e 2 and Clus e 7). The Mise icó dia a ea is he pu es pa ish desc ibed by only 2 Clus e s (8 and 12), ollowed by San a Ma ia Maio wi h 3 Clus e s (8 and 11 wi h mul iple lis ings and 1 lis ing in Clus e 5). Clus e 11 and 12 desc ibe 46 he mos expensi e lis ings om wo coas al pa ishes: San a Ma ia Maio and Mise icó dia, wi h a e ages o 685€ and 721€ espec i ely. Clus e 8 con ains cheape lis ings om he wo pa ishes mixed oge he . Clus e 9 desc ibes he cheapes lis ings (a e aged), comple ely exclusi e o lis ings om he pa ishes o A oios and San o An onio. These pa ishes by hemsel es, howe e a e no cheap, as lis ings wi h a wide a ie y o p ices om he wo pa ishes can be ound in 7 and 8 clus e s o he p oposed 14, acco dingly. 4.6 O e iew o Gi en Analysis The da ase was analyzed using spa ial econome ics, and wo ypes o HPM models we e es ed (SDEM and SLX) as judged by he mos signi ican p- alue om he Lag ange Mul iplie es diagnos ics. The spa ial speci ica ions o he models made use o da a agg ega ion wi h 987 esul ing polygons desc ibing a e ages p ices wi hin he blocks o he s udy a ea ha con ain a leas one lis ing. The mos signi ican a iable in bo h SDEM and SLX, and u he in SVR was he coun o bed ooms – and i bea s a nega i e coe icien . The dummy a iable ‘Male Landlo d’ also le eled a con idence o abo e 99% bea ing a nega i e coe icien . The SDEM model ound 118 a iables o bea signi icance opposed o 44 om he SLX model. Va iables deno ing minimum dis ance and coun s o ameni ies up o 250m ha e a high equency in he mo e signi ican le els. 500m and 1km sha e lowe , bu also simila equencies be ween one ano he . The impo ance o a iables deno ing a p oximi y o ameni y abo e 1000m a e a ely a case o in e es , and only appea a signi icance le els ‘X’ and ‘*’. The da a a iabili y wi hin he bes SDEM model was cap u ed wi h an R Squa ed o 0.92 deno ing 35.7€ e o . This p esen s 8% imp o emen o e he non-spa ially en iched model. Usage o a high amoun o a iables aised ques ion o model’s da a o e i ing. Sensi i i y analysis illus a ed as changes wi hin he coe icien s adjoined o he a iables, hough he a iables signi icance yielded ma ginal di e ences. Hype pa ame iza ion o he SVR pa ame e s allowed o c ea ion o a model ha i s he o iginal da a poin s wi h an a e aged pe cen age e o o 11% o he p ice ange. The spa ially en iched model esul ed in wo se pe o mance wi h a 12% mean absolu e e o . All SVR models needed mo e han 50% o he da a as SVs, and he maximum Lag ange Mul iplie coe icien was gi en o he majo i y o he SVs. The bigges aul s in building his p edic i e model we e he bigge p iced lis ings which a e ound o be as ly unde es ima ed. The models hus ail o ind a disce nable pa e n o wha allows a highe p ice ag in a eco d. A SOM model wi h all he signi ican a iables (as deno ed by SDEM) demons a ed some geog aphically unde s andable clus e s – as wo ooms belonging o he same node (o one e y close) would sha e e y simila p oxies s a is ics. 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ANNEX • Sample Que y – C ea ion o all eachable nodes om he lis ings wi hin 5KM o hei icini y using he OSM Ne wo k and pgRou ing • Sample Que y - Gene a ing Closes Nodes o Pa ks 57 • Sample Que y – C ea ion o Va iable: Coun s o T ams wi hin 2KM 58 • Sample Que y – C ea ion o Va iable: Minimum Dis ance o T ams 59 EVALUATION OF SPATIAL DATA’S IMPACT IN MID-TERM ROOM RENT PRICE THROUGH APPLICATION OF SPATIAL ECONOMETRICS AND MACHINE LEARNING 2020 Case S udy: Lisbon Guia pa a a o ma ação de eses Ve são 4.0 Janei o 2006