A Moran coefficient-based mixed effects approach to investigate spatially varying relationships

Murakami, Daisuke; Yoshida, Takahiro; Seya, Hajime; Griffith, Daniel A.; Yamagata, Yoshiki

doi:10.1016/j.spasta.2016.12.001

Cited by 83 publications

(71 citation statements)

References 41 publications

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“…The fast RE‐ESF model also can be extended to models whose likelihood function is identical to equation . Such models include the RE‐ESF‐based spatially varying coefficients model (Murakami et al ), and the RE‐ESF with another random effects term, such as group effects. Bates () extends a linear mixed effects model, which is identical to our model, to non‐Gaussian/nonlinear (nonspatial) mixed effects models.…”

Section: Discussionmentioning

confidence: 99%

Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches

Murakami

Griffith

2018

Geographical Analysis

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Eigenvector spatial filtering (ESF) is a spatial modeling approach, which has been applied in urban and regional studies, ecological studies, and so on. However, it is computationally demanding, and may not be suitable for large data modeling. The objective of this study is developing fast ESF and random effects ESF (RE‐ESF), which are capable of handling very large samples. To achieve it, we accelerate eigen‐decomposition and parameter estimation, which make ESF and RE‐ESF slow. The former is accelerated by utilizing the Nyström extension, whereas the latter is by small matrix tricks. The resulting fast ESF and fast RE‐ESF are compared with nonapproximated ESF and RE‐ESF in Monte Carlo simulation experiments. The result shows that, while ESF and RE‐ESF are slow for several thousand samples, fast ESF and RE‐ESF require only several seconds for the samples. It is also suggested that the proposed approaches effectively remove positive spatial dependence in the residuals with very small approximation errors when the number of eigenvectors considered is 200 or more. Note that these approaches cannot deal with negative spatial dependence. The proposed approaches are implemented in an R package “spmoran.”

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Section: Discussionmentioning

confidence: 99%

Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches

Murakami

Griffith

2018

Geographical Analysis

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“…otherwise, where r is the maximum distance in the minimum tree that spans all points and does not have any nodes that link back to itself as in Murakami et al (2017).…”

Section: Is An Indicator Of Whether Times T U and T U ′ Both Fall In mentioning

confidence: 99%

Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic

Lorio¹,

Diawara²,

Waller³

2018

IJSP

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Moran's Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of the disease spread over time, steered by a common factor in the scale. The main consequence of our results is that our Moran statistic is calculated from an explicit algorithm in a Monte Carlo simulation setting. Results are compared to Geary's statistic and estimates of parameters under Poisson process are given.

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“…All three effects are subject to issues of scale, whether this concerns the effects of the scale (or support) of the observation units (e.g., Gotway and Young 2002;Zhang, Atkinson, and Goodchild 2014;Murakami and Tsutsumi 2015), or whether the modeling objective itself is to capture processes that operate across scales (e.g., Finley 2011;Harris, Dong, and Zhang 2013a;Dong and Harris 2014;Dong et al 2015;Osland, Thorsen, and Thorsen 2016;Bivand et al 2017;Fotheringham, Yang, and Kang forthcoming;Leong and Yue 2017;Murakami et al 2017;Lu et al forthcoming). Predictor variables also play a role.…”

Section: Introductionmentioning

confidence: 99%

“… This empirical result of autocorrelated predictors lends weight to the likewise predictor specifications used in the simulation experiment, and suggested consequences thereafter. Murakami et al () and Geniaux and Martinetti (forthcoming) also acknowledge the influence of autocorrelated predictors and the identification difficulties that may result. …”

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confidence: 99%

“…9 This empirical result of autocorrelated predictors lends weight to the likewise predictor specifications used in the simulation experiment, and suggested consequences thereafter. Murakami et al (2017) and Geniaux and Martinetti (forthcoming) also acknowledge the influence of autocorrelated predictors and the identification difficulties that may result. 10 In practice, it would be prudent to re-investigate with further Moran's I tests with different weights structures, together with more informative measures such as variograms.…”

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A Simulation Study on Specifying a Regression Model for Spatial Data: Choosing between Autocorrelation and Heterogeneity Effects

Harris

2018

Geographical Analysis

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In this simulation study, regressions specified with autocorrelation effects are compared against those with relationship heterogeneity effects, and in doing so, provides guidance on their use. Regressions investigated are: (1) multiple linear regression, (2) a simultaneous autoregressive error model, and (3) geographically weighted regression. The first is nonspatial and acts as a control, the second accounts for stationary spatial autocorrelation via the error term, while the third captures spatial heterogeneity through the modeling of nonstationary relationships between the response and predictor variables. The geostatistical‐based simulation experiment generates data and coefficients with known multivariate spatial properties, all within an area‐unit spatial setting. Spatial autocorrelation and spatial heterogeneity effects are varied and accounted for. On fitting the regressions, that each have different assumptions and objectives, to very different geographical processes, valuable insights to their likely performance are uncovered. Results objectively confirm an inherent interrelationship between autocorrelation and heterogeneity, that results in an identification problem when choosing one regression over another. Given this, recommendations on the use and implementation of these spatial regressions are suggested, where knowledge of the properties of real study data and the analytical questions being posed are paramount.

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A Moran coefficient-based mixed effects approach to investigate spatially varying relationships

Cited by 83 publications

References 41 publications

Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches

Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches

Density Estimation of Spatio-temporal Point Patterns Using Moran's Statistic

A Simulation Study on Specifying a Regression Model for Spatial Data: Choosing between Autocorrelation and Heterogeneity Effects

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