### Abstract

The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.

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

Pages (from-to) | 331-343 |

Number of pages | 13 |

Journal | Advances in Applied Probability |

Volume | 32 |

Issue number | 2 |

State | Published - Jun 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Advances in Applied Probability*,

*32*(2), 331-343.

**Comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns.** / Diggle, Peter J.; Mateu, Jorge; Clough, Helen E.

Research output: Contribution to journal › Article

*Advances in Applied Probability*, vol. 32, no. 2, pp. 331-343.

}

TY - JOUR

T1 - Comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns

AU - Diggle, Peter J.

AU - Mateu, Jorge

AU - Clough, Helen E.

PY - 2000/6

Y1 - 2000/6

N2 - The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.

AB - The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.

UR - http://www.scopus.com/inward/record.url?scp=0034206290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034206290&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 331

EP - 343

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 2

ER -