1998. 地価の推計手法 kriging Cressie, 1993 kriging kriging 9kriging Kriging kriging 1 z = Xβ+ ε ε~ N(, C ) 1 z N 1X N K ε N 1 N 1 C N N β K 1 ε E[ ε ] = i Co
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1 GIS Theory and Applications of GIS, 14, Vol., No., pp.1-11 我が国の三大都市圏を対象とした住宅地価分布図の作成堤盛人 * 村上大輔 ** 嶋田章 *** Creation of Residential Land Price Maps for the Three Metropolitan Areas in Japan Morito Tsutsumi*, Daisuke Murakami**, Akira Shimada*** Abstract: The spatial distribution of land price is indicative of the urban structure of a region. However, since most information on land price is in the form of point data and not surface data, a certain process must be established for the creation of a land price map. The final objective of the current study is to create accurate land price maps of three metropolitan areas in Japan: Tokyo, Nagoya and Kyoto-Osaka-Kobe metropolitan areas. This study uses the officially assessed land prices provided by the Japanese government and data from the land price surveys conducted by prefectural governments. First, the study presents empirical analysis of land price function of each metropolitan area by employing trans-gaussian kriging, which enables us to consider both spatial dependence and difference of price elasticity by price ranges. Then, the study creates land price maps. Finally, we compare the created land price maps and discuss the nature of the differences in detail. Keywords: land price residential landmetropolitan area spatial statistics visualization 1. はじめに km Luo and Wei 4 Basu and Thibodeau * University of Tsukuba tsutsumi@sk.tsukuba.ac.jp ** National Institute for Environmental Studies *** Ministry of the Environment 69 1
2 1998. 地価の推計手法 kriging Cressie, 1993 kriging kriging 9kriging Kriging kriging 1 z = Xβ+ ε ε~ N(, C ) 1 z N 1X N K ε N 1 N 1 C N N β K 1 ε E[ ε ] = i Cov( εi, ε i ) = c( dii, ) 3 i i'ε i ε i' d i,i' c(d i,i' ) 4 c(d i,i' ) dii, τ exp cd ( ii, ) = r σ + τ if d ii, otherwise 4 σ τ r 95% r 3effective range Cressie, 1993 kriging z 5 ẑ t z = x β + ε 5 t x K 1 ε ẑ E[( z ˆ z)] 6 Ez [ ] = Ez [ ˆ ] 7 t z ˆ = az 8 an 1 a t 1 1 t 1 aˆ = C c+ C XXC ( X) ( x XC c ) 9 c N 1 â 8 1 t 1 ˆ t zˆ ˆ = xβ+ cc ( z Xβ ) 1 ˆ t 1 1 t 1 β= ( XC X) XC z kriging z kriging Cressie 1993 Trans-Gaussian Kriging Rosen, 1974 Ekeland et al., 4 Kostov, 9 trans-gaussian kriging Cressie,
3 trans-gaussian kriging φ( ) y i z i z i kriging ẑ ẑ y i ŷ ŷ E[ ŷ ] φ ( µ ) Ey [ ˆ] φ ( µ ) + E[( zˆ µ )] 11 μ 5 x t β '' φ( ) 1 φ( ) y φ ( µ ) E[ y] φ ( µ ) + E[( z µ )] t φ ( μ) φ( β, τ, σ, r) = { E[( z μ) ] E[( zˆ μ) ] 13 } trans-gaussian kriging φ( ) Box-Cox Box and Cox, 1964 trans-gaussian kriging z i λ yi 1 = λ log( yi ) if λ otherwise 14 λ Box-Cox trans-gaussian kriging 15 z( λ ) = Xβ+ ε ε~ N(, C ) 15 z(λ) z i (λ) N 1 y { } { ˆ } 1/ λˆ ˆ ˆ ˆ t ( ) 1 (, ˆ, ˆ, ˆ, ˆ) ˆ λz λ + + φ β τ σ rλ if λ yˆ = 16 ˆ t exp z ( λ) + φ( β, τˆ, σˆ, rˆ, λˆ) otherwise ˆ ( ˆ z λ) z ( λ) ˆ t φ( β, τˆ, σˆ, rˆ, λˆ ) z z (λ) 13 Box-Coxkriging McGrath et al. 4 Eom et al. 6 Box-Cox trans-gaussian kriging R gstat geor Zhang et al., 8; Pebesma et al., 11 trans- Gaussian kriging Box-Cox trans-gaussian kriging R ver. 3..1ArcGIS ver. 1. trans-gaussian kriging De Oliveira et al.1997; Kazianka and Pilz, 11 i ii 3.1. i 1 i
4 準地と重複している地点及び 6 年から新たに都 道府県地価調査の基準地となった地点のデータは除 外している 各大都市圏の地価の基本統計量は表 に示すとおりである 説明変数は表 3 に示すとおりである 各変数は 誰もが容易に入手可能であり なおかつ対象範囲を ほぼ同一精度でカバーするという条件の下で選ん だ ここで 説明変数の一つである都心鉄道距離は 東京大都市圏 最寄り駅から主要駅 東京大都市圏では東京 新宿 池袋 渋谷 品川の各駅 中京大都市圏では名古屋 栄の両駅 京阪神大都市圏では大阪 京都 三ノ宮 梅田の各駅で定義する までの鉄道ネットワーク距 離の最小値で定義する 一方 都心鉄道時間は 最 寄り駅から同様の主要駅までの所要時間 Yahoo! 路 線情報より算出 の最小値で定義する 都心鉄道時 中京大都市圏 間は快速列車や乗り換えの待ち時間等を反映する 都心鉄道時間データの作成には 膨大な作業時間が 必要となるため 時間に代えてデータの作成が容易 な直線距離を用いることの妥当性も関心事である 以降 都心への交通利便性を表わす変数として都心 表3 京阪神大都市圏 図1 変数名 三大都市圏の地価データの空間分布 表1 対象地域の面積と人口 東京 中京 京阪神 面積 km 16,65 6,99 11,74 人口 千人 36,95 8,93 18,768 表 平均値 中央値 標準偏差 最大値 最小値 評価地点数 うち公示地価 うち都道府県地価調査 1 中京 84,7 8,9 41, 3, 3,,555 1, 京阪神 1,995 18, 7,63 533, 3,155 5,136 3,517 1,864 1 公示地価標準地との重複により分析では除外した地点を含む総地点数 の単価であり 評価の時点が半年ずれているため 調査地価については 5 年と 6 年での単純平 均により時点修正を行った ただし 地価公示の標 データ元と作成方法 最寄駅 距離 m 最寄りの鉄道駅 出典 国土数値情報 ま での直線距離 各土地利用 の面積 m/km 国土数値情報の土地利用3次メッシュ データの 11 の土地利用種別 田 その他農 用地 森林 荒地 建物用地 幹線交通用 地 その他の用地 河川及び湖沼 海浜 海水域 ゴルフ場 のうち 建物用地以外 の種別の 1km メッシュあたりの面積 用途地域 ダミー 国土数値情報の用途地域データの 11 用途 地域ダミー 第 1 種住居地域 第 1 種中高 層住居専用地域 第 1 種低層住居専用地 域 第 種住居地域 第 種中高層住居専 用地域 準住居地域 商業地域 近隣商 業地域 工業地域 準工業地域 市街化区域 ダミー 国土数値情報の都市地域データをもとに 市街化区域内の地点には 1 それ以外の地 点には を付与 地価 円 / m の基本統計量 東京 176,63 149, 155,839,5, 3,6 9,45 6,53 3,116 本研究で使用する説明変数 最寄り鉄道駅 出典 国土数値情報 か 都心鉄道 1 ら各大都市圏の主要駅までの鉄道ネット 距離 km ワークに沿った距離 Yahoo! 路線情報により算出した 最寄り 都心鉄道 1 の鉄道駅から各大都市圏の主要駅までの 時間 分 鉄道による所要距離 1 各モデルでは都心鉄道距離または都心鉄道時間のいずれかを使用 7 4
5 m / km 三大都市圏の地価分布図 4 VIF Variance Inflation Factor1997 1% 1 1% 51 (=17 3) km 3 4 t t m m /km m /km m /km m /km. 1 7 m /km m /km m /km m /km m /km m /km km 4. 1 λ *** 9. *** 7.79 *** 5.65 *** 5.76 *** *** ** 14.3 *** 13.8 *** 1.5 *** 13.9 *** 16. *** 1.67 * 3.9 ***.98 ***.91 *** 3.9 *** 9.4 *** 4.78 *** *** 9.4 *** 7.63 *** 5.65 *** 5.75 *** * *** * 14.1 *** 13.7 *** 1.5 *** 13.9 *** 15.9 *** 1.67 * 3.4 ***.99 ***.9 *** 3.11 *** 9.4 *** 8.93 *** AIC 7,534 7,479 1 ***, **, * 1%, 5%, 1%
6 6km fold cross-validation 5-fold cross-validation yˆi y i = 17 y 9,45 1.1% 1.1% 1 3km 1 1 VIF 5 1% 1 1% i 5 t t m m /km m /km m /km m /km m /km m /km m /km m /km m /km m /km km.13 1/3 14 km 15. *** 8.9 *** 9.98 *** 5.36 *** 7.37 *** 1.77 * ***.14 **. ** 1.89 * 9.68 *** 11.1 *** 11.1 *** 1. *** 8.83 ***.69 *** 4.96 *** 3.71 *** *** 3.5 *** *** 9.7 *** 9.9 *** 5.4 *** 7.9 *** ***.14 **.15 ** 1.71 * 9.61 *** 11. *** 11.1 *** 1.3 *** 8.74 ***.58 *** 4.98 *** 3.7 *** *** *** λ AIC 54,81 54,79 1 *** ** * 1% 5% 1% /m 1 /m 3 /m 74 6
7 1 VIF 1 6 1% 1 1% 4km 各大都市圏の分析結果の比較 1% 6 t t m m /km m /km m /km m /km m /km m /km m /km m /km m /km m /km km x ˆ 15.8 *** 14.3 *** 11.9 *** 4.37 *** 11. *** * 5.37 *** ***.53 *** 7.1 *** 14.1 *** 6.17 *** 6.1 *** *** 4.8 ***.7 *** *** 14.4 *** 11.9 *** 4.35 *** 11.1 *** * 5.33 *** ***.57 *** 7.14 *** 14.1 *** 6.15 *** 5.99 *** *** 4.9 *** *** λ AIC 114, ,384 1 *** ** * 1% 5% 1% λ y x 1 ˆ ˆ 1 = β + β1x1 18 λˆ x 1 km 15km 1km18 y x1 1 ˆβ ˆβ 1 y x1 x 1 = y x
8 y x km 35km 5km Box-Cox /m ~3 /m 45~6 /m 3 19RMSE Root Mean Square Error N RMSE = ( yˆ i yi) / N 19 i= 1 y i yˆi 5-fold crossvalidation RMSE7 RMSE RMSE RMSE trans-gaussian kriging RMSE kriging RMSE 7 trans- Gaussian kriging RMSE kriging trang-gaussian kriging trans- Gaussian kriging RMSE 7 RMSE /m trans-gaussian kriging kriging 34,7 34,674 34,887 34,83 1,345 1,346 1,661 1,65 16,78 16,76 16,
9 3.% 5. おわりに trans- Gaussian kriging trans-gaussian kriging Fotheringham et al., kriging 謝辞 参考文献 GIS
10 7 kriging CD-ROM 1 E 1 Basu, S., and Thibodeau, T. G. (1998) Analysis of spatial autocorrelation in house prices. Journal of Real Estate Finance and Economics, 17 (1), Box, G. E. P. and Cox, D. R. (1964) An analysis of transformation. Journal of Royal Statistical Society: Series B, 6 (), Cressie, N. (1993) Statistics for Spatial Data, Revised Edition. New York: John Wiley & Sons. De Oliveira, V., Kedem, B. and Short. D. (1997) Bayesian prediction of transformed Gaussian random fields. Journal of the American Statistical Association, 9 (44), Ekeland, I., Heckman, J. and Nesheim, L. (4) Identification and estimation of hedonic models. Journal of Political Economy, 11 (1), S6 S19. Eom, J. K., Park, M. S., Heo, T. Y. and Hunsinger, L. F. (6) Improving the prediction of annual average daily traffic for nonfreeway facilities by applying a spatial statistical method. Transportation Research Board, 1968, 9. Fotheringham, A.S., Brunsdon, C. and Charlton, M. () Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. John Wiley & Sons. Kazianka, H. and Pilz, J. (11) Bayesian spatial modeling and interpolation using copulas. Computers & Geosciences, 37 (3), Kostov, P. (9) A spatial quantile regression hedonic model of agricultural land prices. Spatial Economic Analysis, 4 (1), Luo, J. and Wei, Y. H. D. (4) A geostatistical modeling of urban land values in Milwaukee, Wisconsin. Geographic Information Sciences, 1 (1), McGrath, D., Zhang, C. and Carton, O. T. (4) Geostatistical analyses and hazard assessment on soil lead in Silvermines area, Ireland. Environmental Pollution, 17 (), Pebesma, E., Cornford, D., Dubois, G., Heuvelink, G., Hristopoulos, D., Pilz, J., Stoehlker, U., Morin, G. and Skoien, J. (11) INTAMAP: the Design and Implementation of an Interoperable Automated Interpolation Web Service. Computers & Geoscience, 37 (3), Rosen, S. (1974) Hedonic markets and implicit prices: product differentiation and pure competition. Journal of Political Economy, 8 (1), Zhang, C., Fay, D., McGrath, D., Grennan, E. and Carton, O. T. (8) Use of trans-gaussian kriging for national soil geochemical mapping in Ireland. Geochemistry: Exploration, Environment, Analysis, 8 (3-4),
11 図 平成 18 年 地価分布図 の地価水準と町丁目界 図6 図3 都心距離モデルの推計結果 東京大都市圏 図4 都心時間モデルの推計結果 東京大都市圏 図 5 平成 18 年 地価分布図 東急不動産作成 をもとに 筆者らが色づけしたもの 都心距離モデルの推計結果 中京大都市圏 図7 都心時間モデルの推計結果 中京大都市圏 図8 都心距離モデルの推計結果 京阪神大都市圏 図9 都心時間モデルの推計結果 京阪神大都市圏 79 11
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土木学会論文集 D3( 土木計画学 ), Vol. 71, No. 2, 31-43,
1 2 1 305 8506 16 2 E-mail: murakami.daisuke@nies.go.jp 2 305 8573 1 1 1 E-mail: tsutsumi@sk.tsukuba.ac.jp Key Words: sampling design, geostatistics, officially assessed land price, prefectural land price
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2010 年度 S-PLUS 学生研究奨励賞 発表内容 我が国の三大都市圏における 地価分布の推計 筑波大学大学院 システム情報工学研究科博士前期課程 1 年 嶋田章 地価の分布をみる意義 地価は都市構造を反映 地形, 人口, 交通網など様々な要素と関係 都市にまつわる研究では古くから注目されている指標 地價は都市の言語である 石川栄耀 (1931) 地価の面的な分布は都市構造の把握や政策立案の資料になりうる
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