### Abstract

Spatial nonstationarity is a condition in which a simple 'global' model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 UK census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.

Original language | English (US) |
---|---|

Pages (from-to) | 281-298 |

Number of pages | 18 |

Journal | Geographical Analysis |

Volume | 28 |

Issue number | 4 |

State | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geography, Planning and Development

### Cite this

*Geographical Analysis*,

*28*(4), 281-298.

**Geographically weighted regression : a method for exploring spatial nonstationarity.** / Brunsdon, C.; Fotheringham, Stewart; Charlton, M. E.

Research output: Contribution to journal › Article

*Geographical Analysis*, vol. 28, no. 4, pp. 281-298.

}

TY - JOUR

T1 - Geographically weighted regression

T2 - a method for exploring spatial nonstationarity

AU - Brunsdon, C.

AU - Fotheringham, Stewart

AU - Charlton, M. E.

PY - 1996

Y1 - 1996

N2 - Spatial nonstationarity is a condition in which a simple 'global' model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 UK census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.

AB - Spatial nonstationarity is a condition in which a simple 'global' model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 UK census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.

UR - http://www.scopus.com/inward/record.url?scp=0030432956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030432956&partnerID=8YFLogxK

M3 - Article

VL - 28

SP - 281

EP - 298

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

IS - 4

ER -