Leverage and influence diagnostics for Gibbs spatial point processes

Adrian Baddeley, Ege Rubak, Rolf Turner

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

For point process models fitted to spatial point pattern data, we describe diagnostic quantities analogous to the classical regression diagnostics of leverage and influence. We develop a simple and accessible approach to these diagnostics, and use it to extend previous results for Poisson point process models to the vastly larger class of Gibbs point processes. Explicit expressions, and efficient calculation formulae, are obtained for models fitted by maximum pseudolikelihood, maximum logistic composite likelihood, and regularised composite likelihoods. For practical applications we introduce new graphical tools, and a new diagnostic analogous to the effect measure DFFIT in regression.
Original languageEnglish
JournalSpatial Statistics
Volume29
Pages (from-to)15-48
Number of pages34
ISSN2211-6753
DOIs
Publication statusPublished - Mar 2019

Fingerprint

Influence Diagnostics
Spatial Point Process
Composite Likelihood
Leverage
Diagnostics
Point Process
Process Model
Spatial Point Pattern
Regression Diagnostics
Pseudo-likelihood
Poisson Point Process
Composite materials
Logistics
logistics
Regression
Model

Keywords

  • Composite likelihood
  • Conditional intensity
  • DFBETA
  • DFFIT
  • Model validation
  • Pseudolikelihood

Cite this

Baddeley, Adrian ; Rubak, Ege ; Turner, Rolf. / Leverage and influence diagnostics for Gibbs spatial point processes. In: Spatial Statistics. 2019 ; Vol. 29. pp. 15-48.
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Leverage and influence diagnostics for Gibbs spatial point processes. / Baddeley, Adrian; Rubak, Ege; Turner, Rolf.

In: Spatial Statistics, Vol. 29, 03.2019, p. 15-48.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Rubak, Ege

AU - Turner, Rolf

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AB - For point process models fitted to spatial point pattern data, we describe diagnostic quantities analogous to the classical regression diagnostics of leverage and influence. We develop a simple and accessible approach to these diagnostics, and use it to extend previous results for Poisson point process models to the vastly larger class of Gibbs point processes. Explicit expressions, and efficient calculation formulae, are obtained for models fitted by maximum pseudolikelihood, maximum logistic composite likelihood, and regularised composite likelihoods. For practical applications we introduce new graphical tools, and a new diagnostic analogous to the effect measure DFFIT in regression.

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KW - Conditional intensity

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