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空間データのための回帰分析       @t2gtnd    HiRoshima.R #1
空間データって?• 地理情報システムGIS (Geographic Information System) の進  化にともない,位置情報を付加された空間データが入手可能  になってきた.これにより,・・・・要するに・・・観測地点の位置が分かっ...
空間データの例)コロンバス市の犯罪データ• オハイオ州コロンバス市49  地区における1980年の地区  別犯罪発生数と経済指標  (収入・家価格)のデータ –   crime : 千世帯辺りの犯罪数 –   income : 世帯収入(×$1...
重回帰分析• 位置情報を無視すれば、普通の重回帰分析   crime  0  1  income  2  housing                                     経済指標と犯罪数の関       ...
地理的加重回帰(GWR)• 位置によって回帰係数が変わると考えると…crime  0 ( x, y)  1 ( x, y)  income  2 ( x, y)  housing                        地...
GWRの適用結果            GWRの結果   重回帰分析の結果位置の数だけ回帰係数を推定するので、推定値の五数要約値を出力
akimaパッケージを用いて回帰 係数の等値線地図を作成0 ( x, y)1 ( x, y) 2 ( x, y)
重回帰と地理的加重回帰のどっちがいい?• グローバル検定 LMZ.F3GWR.test  残差分散を比較することで,帰無仮説:重回  帰,対立仮説:地理的加重回帰の検定を行うコロンバス市の犯罪データでは,重回帰(回帰係数は位置によらず一定)で十分!
GWRはESRI社のArcGISにも実装
補足)地理的加重一般化線形モデル• 目的変数が離散値の場合  → 地理的加重一般化線形モデル  (2値:ロジスティック回帰,計数値:ポアソン回帰)• spgwrパッケージに用意されている関数 – バンド幅の最適化 → ggwr.sel – 地理...
主な参考文献spgwrの他にもsp, spdep,   地理的加重回帰の提案者maptoolsなど空間データを      たちの本扱うパッケージを紹介
おしまい
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空間データのための回帰分析

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空間データのための回帰分析

  1. 1. 空間データのための回帰分析 @t2gtnd HiRoshima.R #1
  2. 2. 空間データって?• 地理情報システムGIS (Geographic Information System) の進 化にともない,位置情報を付加された空間データが入手可能 になってきた.これにより,・・・・要するに・・・観測地点の位置が分かっているデータ
  3. 3. 空間データの例)コロンバス市の犯罪データ• オハイオ州コロンバス市49 地区における1980年の地区 別犯罪発生数と経済指標 (収入・家価格)のデータ – crime : 千世帯辺りの犯罪数 – income : 世帯収入(×$1,000) – housing : 家価格(×$1,000) – (x,y) : 地区所在地の座標• 知りたいこと 経済指標と犯罪発生数の関係
  4. 4. 重回帰分析• 位置情報を無視すれば、普通の重回帰分析 crime  0  1  income  2  housing 経済指標と犯罪数の関 係(回帰係数)は位置に よらず一定(と仮定)
  5. 5. 地理的加重回帰(GWR)• 位置によって回帰係数が変わると考えると…crime  0 ( x, y)  1 ( x, y)  income  2 ( x, y)  housing 地域によって変わる 地域によって変わる 収入と犯罪数の関係 家価格と犯罪数の関係 i ( x, y) の推定方法 固定した位置(x,y)の周辺データに対して 各観測値に距離に基づく重みを設定し, カーネル平滑化の要領で局所的な重み つき重回帰分析を繰り返す. バンド幅の最適化 → gwr.sel 地理的加重回帰の推定 → gwr
  6. 6. GWRの適用結果 GWRの結果 重回帰分析の結果位置の数だけ回帰係数を推定するので、推定値の五数要約値を出力
  7. 7. akimaパッケージを用いて回帰 係数の等値線地図を作成0 ( x, y)1 ( x, y) 2 ( x, y)
  8. 8. 重回帰と地理的加重回帰のどっちがいい?• グローバル検定 LMZ.F3GWR.test 残差分散を比較することで,帰無仮説:重回 帰,対立仮説:地理的加重回帰の検定を行うコロンバス市の犯罪データでは,重回帰(回帰係数は位置によらず一定)で十分!
  9. 9. GWRはESRI社のArcGISにも実装
  10. 10. 補足)地理的加重一般化線形モデル• 目的変数が離散値の場合 → 地理的加重一般化線形モデル (2値:ロジスティック回帰,計数値:ポアソン回帰)• spgwrパッケージに用意されている関数 – バンド幅の最適化 → ggwr.sel – 地理的加重一般化線形モデルの推定 → ggwr – グローバル検定 → (理論的にも)未実装 たぶん
  11. 11. 主な参考文献spgwrの他にもsp, spdep, 地理的加重回帰の提案者maptoolsなど空間データを たちの本扱うパッケージを紹介
  12. 12. おしまい

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