A Comparison of Multivariate Log Gaussian Cox Process and Saturated
Pairwise Interaction Gibbs Point Process
Abstract
The study of the spatial point patterns in ecology, such as the records
of the observed locations of trees, shrubs, nests, burrows, or
documented animal presence, relies on multivariate point process models.
This study aims to compare the efficacy and applicability of two
prominent multivariate point process models, the multivariate log
Gaussian Cox process (MLGCP) and the Saturated Pairwise Interaction
Gibbs Point Process model (SPIGPP) , highlighting their respective
strengths and weaknesses in various scenarios. Using synthetic and real
datasets, we assessed both models based on their predictive accuracy of
the empirical K function (can we say this?). Our analysis revealed that
both MLGCP and SPIGPP effectively identify and capture mild to moderate
attractions and regulations. MLGCP struggles to capture repulsive
associations as they intensify. In contrast, SPIGPP can well estimates
both the direction and magnitude of interactions even when the model is
miss-specified. Both models present unique advantages: MLGCP is
particularly effective when there is a need to account for complex,
unobserved heterogeneities that vary across space, while SPIGPP is
suitable when interactions between points are the primary focus. The
choice between these models should be guided by the specific needs of
the research question and data characteristics.