空間的自己相関の存在するデータが回帰分析に及ぼす影響に関する研究

DOI Web Site 被引用文献5件
  • 樋口 洋一郎
    東京工業大学大学院情報理工学研究科情報環境学専攻
  • 高塚 創
    東京工業大学大学院理工学研究科社会工学専攻

書誌事項

タイトル別名
  • A Study of Effects of Spatially Autocorrelated Data on Regression Analysis
  • クウカンテキ ジコ ソウカン ノ ソンザイスル データ ガ カイキ ブンセキ

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抄録

Recently, social and economic data collected at various regional levels have been used for statistical regional analyses in planning. In these analyses, the regression analysis using Ordinary Least Squares (OLS) method has been most popular. It assumes that error-terms have zero-means, common variances and independent normal distributions. However, the assumption is often not adequate for spatial data. In fact, residuals in regression are often spatially autocorrelated, as indicated in this study from prefectural data.<br>Martin (1974) and Dow et al. (1982) investigated OLS estimators for parameters when error-terms are spatially autocorrelated. As they pointed out, the OLS estimators are unbiased, but the variances of estimeters and t-values are biased. However, they did not concretely indicate the magnitude of biases in t-values, which was more important for regional analysis.<br>This study finds the range of the biases in simple regression, by means of simulation, with the prefectures in Japan as objective areas and the “inverse of distances” matrix as the weighting matrix in which elements means proximity between each area. The results indicate that t-value is over-estimated if spatial autocorrelations of both error-terms and explanatory variables are of the same sign. On the other hand, t-value is under-estimated if they are of the opposite sign. This corresponds to Martin's result. More specifically, when both error-terms and explanatory variables are positively autocorrelated, the rate of over-estimation of t-value is approximately 1.4 at the maximum.<br>We also explain other factors, namely, sample size, configuration of areas and weighting matrix, in relation to the biases of t-value. Particularly, the setting of weighting matrix has a great influence on the biases. In the case of a 3×16 mesh, the maximum bias of using “contiguous” matrix is 1.7 times as large as using “inverse of distances” matrix.<br>There are many studies in which the autocorrelation parameters are estimated. However, the method to directly estimate the weighting matrix has not been developed yet. It is therefore necessary to develop a general procedure of estimating the weighting matrix from spatial and time-series data.

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