1# RECORD 1daf1d20ba429ff68e39043313dece9a679c8c5d2# TITLE: A spatial semiparametric M-quantile regression for hedonic price modelling3# YEAR: 2023.0 VENUE: AStA Advances in Statistical Analysis DOI: 10.1007/s10182-023-00476-w4# AUTHORS: Francesco Schirripa Spagnolo; R. Borgoni; A. Carcagnì; A. Michelangeli; N. Salvati5# PAGES: 25 CANDIDATE TABLE PAGES (1-based): [16]6# ABSTRACT: This paper proposes an M-quantile regression approach to address the heterogeneity of the housing market in a modern European city. We show how M-quantile modelling is a rich and flexible tool for empirical market price data analysis, allowing us to obtain a robust estimation of the hedonic price function whilst accounting for different sources of heterogeneity in market prices. The suggested methodology can generally be used to analyse nonlinear interactions between prices and predictors. In particular, we develop a spatial semiparametric M-quantile model to capture both the potential nonlinear effects of the cultural environment on pricing and spatial trends. In both cases, nonlinearity is introduced into the model using appropriate bases functions. We show how the implicit price associated with the variable that measures cultural amenities can be determined in this semiparametric framework. Our findings show that the effect of several housing attributes and urban amenities differs significantly across the response distribution, suggesting that buyers of lower-priced properties behave differently than buyers of higher-priced properties.789===== PAGE 1 (score 5, numeric-paren 0, table-words 0, var-words 5) =====1011Vol.:(0123456789)12AStA Advances in Statistical Analysis (2024) 108:159–18313https://doi.org/10.1007/s10182-023-00476-w141 315ORIGINAL PAPER16A spatial semiparametric M‑quantile regression for hedonic 17price modelling18Francesco Schirripa Spagnolo1 · Riccardo Borgoni2 · Antonella Carcagnì2 · 19Alessandra Michelangeli2 · Nicola Salvati120Received: 11 July 2022 / Accepted: 11 March 2023 / Published online: 30 March 2023 21© The Author(s) 202322Abstract23This paper proposes an M-quantile regression approach to address the heterogeneity 24of the housing market in a modern European city. We show how M-quantile mod-25elling is a rich and flexible tool for empirical market price data analysis, allowing 26us to obtain a robust estimation of the hedonic price function whilst accounting for 27different sources of heterogeneity in market prices. The suggested methodology can 28generally be used to analyse nonlinear interactions between prices and predictors. In 29particular, we develop a spatial semiparametric M-quantile model to capture both 30the potential nonlinear effects of the cultural environment on pricing and spatial 31trends. In both cases, nonlinearity is introduced into the model using appropriate 32bases functions. We show how the implicit price associated with the variable that 33measures cultural amenities can be determined in this semiparametric framework. 34Our findings show that the effect of several housing attributes and urban amenities 35differs significantly across the response distribution, suggesting that buyers of lower-36priced properties behave differently than buyers of higher-priced properties.37Keywords Robust method · Hedonic regression · Penalised splines · Spatial data38 * Francesco Schirripa Spagnolo 39 40francesco.schirripa@unipi.it41 42Riccardo Borgoni 43 44riccardo.borgoni@unimib.it45 46Antonella Carcagnì 47 48antonella.carcagni@unimib.it49 50Alessandra Michelangeli 51 52alessandra.michelangeli@unimib.it53 54Nicola Salvati 55 56nicola.salvati@unipi.it571 58Università di Pisa, Pisa, Italy592 60Università Degli Studi di Milano-Bicocca, Milan, Italy616263===== PAGE 16 (score 148, numeric-paren 133, table-words 2, var-words 11) =====646517466 67F. Schirripa Spagnolo et al.681 369for penalised regression splines once a certain minimum value is reached (Pratesi 70et al. 2009; Ruppert et al. 2003).71All covariates act in an a priori predictable manner. Most of them are statistically 72significant and are valued differently at different points of the conditional distribu-73tion of house prices. This is also clearly displayed in Fig. 4, which shows the effect 74Table 3 Results of SSPMQ ( q = 0.10, 0.25, 0.50, 0.75, 0.90 ) estimated using 20 knots for f1q and 40 75knots for f2q - 훿= 3†76† Point estimates with standard errors in parentheses and the associated p-value: ∗∗∗p < 0.01 ; ∗∗p < 0.05 ; 77∗p < 0.178Variable79훽0.1080훽0.2581훽0.5082훽0.7583훽0.9084Housing-specific characteristics85Intercept863755.36***874712.36***885951.43***896987.73***907475.13***91(582.01)92(435.49)93(418.10)94(553.04)95(773.76)96Floor low97− 282.06*98− 278.25***99− 245.67**100− 181.39101− 59.53102(148.31)103(103.94)104(100.43)105(139.40)106(273.26)107Floor high108− 218.79109− 258.78***110− 227.98***111− 101.96112124.35113(145.36)114(102.90)115(100.03)116(139.94)117(276.12)118Lift119562.95***120579.63***121532.38***122575.58***123862.57***124(170.38)125(119.65)126(114.56)127(156.44)128(302.79)129Heating System130125.97131184.53132− 1.57133− 25.19134− 567.16135(195.78)136(135.17)137(30.98)138(181.81)139(345.35)140Parking area1411227.97*1421940.22***1432325.26***1441913.61***1451508.37146(721.31)147(462.08)148(441.55)149(602.36)150(1103.27)151Bathroom152841.78***153924.98***154896.58***155742.37***156824.39**157(178.24)158(126.16)159(123.13)160(174.75)161(355.76)162Housing Area16313793.34***1642229.88165− 18234.58***166− 38649.82***167− 59740.72***168(3749.06)169(2575.02 )170(2402.27)171(3718.76)172(7237.17)173Housing Area217426441.33**17588902.99***176201195.88***177312160.71***178450974.91***179(12661.30)180(8845.19)181(8073.78)182(13545.17)183(25960.66)184Housing Area318559418.29***18621609.05***187− 70502.26***188− 146289.17***189− 281400.47***190(11060.53)191(7778.60)192(6841.90)193(13132.12)194(24340.79)195Age196385.45**197467.61***198536.03***199662.14***2001622.88***201(162.86)202(115.82)203(112.99)204(159.36)205(316.73)206Urban amenities207Abandoned area208− 191.62209− 356.68***210− 506.70***211− 667.02***212− 1056.59***213(184.95)214(132.17)215(127.00)216(174.07)217(325.83)218University219808.94***220896.77***221927.38***222763.42***223513.88*224(146.14)225(107.38)226(106.50)227(154.85 )228(297.03 )229Metro230140.45231− 39.91232− 242.94**233− 402.89***234− 304.77235(143.41)236(103.14)237(101.00 )238(141.32)239(275.28)240Year241− 440.49***242− 428.92***243− 377.85***244− 356.10***245− 283.69246(130.27 )247(92.56 )248(89.97 )249(125.08 )250(246.91 )251252253===== PAGE 17 (score 14, numeric-paren 0, table-words 1, var-words 12) =====2542551752561 3257A spatial semiparametric M‑quantile regression for hedonic…258of each variable at different M-quantiles. Grey bands represent the 95% confidence 259interval of the parameter of interest. We have also added a blue line to each graph to 260represent the regression coefficients obtained by fitting the standard semiparamet-261ric additive model on the mean specified in Equation (1). This allows us to assess 262whether and for which variables there is a heterogeneous effect on the distribution of 263response.264Some housing-specific attributes have a different impact at different levels of the 265price distribution, suggesting that their value is different at different points of the 266housing price distribution. The floor at which the house is located has been found 267to be statistically significant only for very low and medium-value houses. A non-268constant effect of floor level along the price distribution has also been found by 269Fig. 4 Plot of regression coefficients with their confidence intervals of all the covariates included in the 270SSPMQ model: Intercept (a), Floor low (b), Floor high (c), Lift (d), Heating system (e), Parking Area 271(f), Bathroom (g), Building’s age (h), Abandoned area (i), University (j), Metro (k) and Year (l). The 272plots are drawn using the estimates obtained for the five M-quantiles considered in table 3 and interpolate 273them linearly. The blue lines represent the regression coefficients obtained fitted a standard semiparamet-274ric linear model on the mean275