Pub Date : 2025-11-07DOI: 10.1016/j.spasta.2025.100943
Christian Caamaño-Carrillo , Moreno Bevilacqua , Diego I. Gallardo
We propose a novel spatial survival model based on a Weibull random field, designed to overcome the limitations of existing copula-based approaches; particularly those relying on the Farlie–Gumbel–Morgenstern (FGM) copula. Although the FGM model only captures weak dependence and enforces reflection symmetry and a forced nugget effect, our model allows for stronger spatial dependence, reflection asymmetry, and mean-square continuity. These properties provide a more flexible and realistic framework for analyzing spatially correlated time-to-event data. The model unifies the proportional hazards (PH), the accelerated failure time (AFT), and the mean parameterizations of the Weibull distribution, allowing a clear interpretation of the effects of the covariates. Due to the analytical intractability of the full likelihood, parameter estimation is performed using a weighted pairwise composite likelihood method based on nearest neighbors. This method offers computational efficiency and robustness to right-censored data. Simulation studies confirm the effectiveness of the proposed model, and an application to real housing data illustrates its practical value.
{"title":"Spatial survival models based on Weibull random fields","authors":"Christian Caamaño-Carrillo , Moreno Bevilacqua , Diego I. Gallardo","doi":"10.1016/j.spasta.2025.100943","DOIUrl":"10.1016/j.spasta.2025.100943","url":null,"abstract":"<div><div>We propose a novel spatial survival model based on a Weibull random field, designed to overcome the limitations of existing copula-based approaches; particularly those relying on the Farlie–Gumbel–Morgenstern (FGM) copula. Although the FGM model only captures weak dependence and enforces reflection symmetry and a forced nugget effect, our model allows for stronger spatial dependence, reflection asymmetry, and mean-square continuity. These properties provide a more flexible and realistic framework for analyzing spatially correlated time-to-event data. The model unifies the proportional hazards (PH), the accelerated failure time (AFT), and the mean parameterizations of the Weibull distribution, allowing a clear interpretation of the effects of the covariates. Due to the analytical intractability of the full likelihood, parameter estimation is performed using a weighted pairwise composite likelihood method based on nearest neighbors. This method offers computational efficiency and robustness to right-censored data. Simulation studies confirm the effectiveness of the proposed model, and an application to real housing data illustrates its practical value.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100943"},"PeriodicalIF":2.5,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Small area estimation (SAE) addresses the estimation of parameters for population subsets when the sample itself is too small to produce reliable direct estimates. The standard method, empirical best linear unbiased prediction, uses a predictor under a linear mixed model that assumes normality of the variable of interest and independence among small areas. However, in practical studies, the distribution of the variable of interest tends to be positively skewed and there exists spatial dependence among the small areas. To address both of these, a previous study had proposed a spatial synthetic (SYNT) predictor that predicts non-sampled values of the variable of interest using its unconditional mean. The SYNT predictor is derived based on a unit-level spatial lognormal mixed model. Herein, we propose spatial empirical best predictor (SEBP) to improve the SYNT predictor by using its conditional mean to predict the non-sampled values of the variable of interest. We perform simulation studies to evaluate the performance of SEBP and compare them with those of the SYNT predictor and other existing methods. Our results reveal that the SEBP performs better in terms of the average relative bias and average relative root mean square error when the spatial correlation among small areas is small, medium or large. In an SAE application on the average monthly household per-capita expenditure for sub-districts in Bogor, Indonesia, the proposed SEBP provides better estimates than other established methods.
{"title":"Spatial empirical best predictor of small area linear parameter for positively skewed outcomes","authors":"Dian Handayani , Khairil Anwar Notodiputro , Asep Saefuddin , I Wayan Mangku , Anang Kurnia","doi":"10.1016/j.spasta.2025.100941","DOIUrl":"10.1016/j.spasta.2025.100941","url":null,"abstract":"<div><div>Small area estimation (SAE) addresses the estimation of parameters for population subsets when the sample itself is too small to produce reliable direct estimates. The standard method, empirical best linear unbiased prediction, uses a predictor under a linear mixed model that assumes normality of the variable of interest and independence among small areas. However, in practical studies, the distribution of the variable of interest tends to be positively skewed and there exists spatial dependence among the small areas. To address both of these, a previous study had proposed a spatial synthetic (SYNT) predictor that predicts non-sampled values of the variable of interest using its unconditional mean. The SYNT predictor is derived based on a unit-level spatial lognormal mixed model. Herein, we propose spatial empirical best predictor (SEBP) to improve the SYNT predictor by using its conditional mean to predict the non-sampled values of the variable of interest. We perform simulation studies to evaluate the performance of SEBP and compare them with those of the SYNT predictor and other existing methods. Our results reveal that the SEBP performs better in terms of the average relative bias and average relative root mean square error when the spatial correlation among small areas is small, medium or large. In an SAE application on the average monthly household per-capita expenditure for sub-districts in Bogor, Indonesia, the proposed SEBP provides better estimates than other established methods.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100941"},"PeriodicalIF":2.5,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.spasta.2025.100939
Anna Gloria Billé , Roberto Benedetti , Paolo Postiglione
Spatial heterogeneity in terms of spatially-varying coefficients is often not properly considered in modeling economic data. This neglect might cause serious problems in the estimation of the parameters of a model specification when group-wise heterogeneity is at work. In this paper we propose a two-step algorithm for the identification of endogenous (data-driven) spatial regimes by using an iterative procedure that is based on weighting functions updated dynamically over time. In the first step, clusters of spatial units (i.e. spatial regimes) are defined using both space and time information. In the second step, a spatial panel data model with random effects is estimated with the spatial regimes identified in the previous step. The additional random effects assumption on the model specification ensures the possibility of controlling also for individual effects as well as group-wise slope coefficients. The proposed method is applied to two real data sets to illustrate our procedure.
{"title":"Dynamic spatial regimes for spatial panel data","authors":"Anna Gloria Billé , Roberto Benedetti , Paolo Postiglione","doi":"10.1016/j.spasta.2025.100939","DOIUrl":"10.1016/j.spasta.2025.100939","url":null,"abstract":"<div><div>Spatial heterogeneity in terms of spatially-varying coefficients is often not properly considered in modeling economic data. This neglect might cause serious problems in the estimation of the parameters of a model specification when group-wise heterogeneity is at work. In this paper we propose a two-step algorithm for the identification of endogenous (data-driven) spatial regimes by using an iterative procedure that is based on weighting functions updated dynamically over time. In the first step, clusters of spatial units (i.e. spatial regimes) are defined using both space and time information. In the second step, a spatial panel data model with random effects is estimated with the spatial regimes identified in the previous step. The additional random effects assumption on the model specification ensures the possibility of controlling also for individual effects as well as group-wise slope coefficients. The proposed method is applied to two real data sets to illustrate our procedure.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100939"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145473635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-01DOI: 10.1016/j.spasta.2025.100938
Denis Allard
This paper illustrates how progress in spatial statistics is fueled by scientific questions arising from applications in agriculture and environment. The unifying theme is the work that has been carried out at BioSP, a statistics and mathematics research unit mainly affiliated to the “Mathematics and Digital Technologies” division at INRAE, the French National Research Institute for Agriculture, Food and Environment. Starting from the 20 contributions that BioSP members have published in Spatial Statistics since its creation in 2012, almost fifteen years of advances are reviewed, spanning point processes, (multivariate) spatio-temporal Gaussian processes, compositional data, stochastic weather generators and extreme value theory. Most of the content is focused on theoretical and methodological developments, with examples being limited due to length constraints for the article. Attention is given to how these advances have been inspired by problems arising in other research domains. In return, it will be shown how they have opened new research questions in spatial statistics and how they had impact in the scientific fields they originated from. In conclusion, some perspectives and outlooks are discussed, in particular in relation to the AI revolution.
{"title":"Growth of spatial statistics for agriculture and environment: The example of BioSP at INRAE","authors":"Denis Allard","doi":"10.1016/j.spasta.2025.100938","DOIUrl":"10.1016/j.spasta.2025.100938","url":null,"abstract":"<div><div>This paper illustrates how progress in spatial statistics is fueled by scientific questions arising from applications in agriculture and environment. The unifying theme is the work that has been carried out at BioSP, a statistics and mathematics research unit mainly affiliated to the “Mathematics and Digital Technologies” division at INRAE, the French National Research Institute for Agriculture, Food and Environment. Starting from the 20 contributions that BioSP members have published in <em>Spatial Statistics</em> since its creation in 2012, almost fifteen years of advances are reviewed, spanning point processes, (multivariate) spatio-temporal Gaussian processes, compositional data, stochastic weather generators and extreme value theory. Most of the content is focused on theoretical and methodological developments, with examples being limited due to length constraints for the article. Attention is given to how these advances have been inspired by problems arising in other research domains. In return, it will be shown how they have opened new research questions in spatial statistics and how they had impact in the scientific fields they originated from. In conclusion, some perspectives and outlooks are discussed, in particular in relation to the AI revolution.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100938"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-27DOI: 10.1016/j.spasta.2025.100936
Ronny Vallejos , Clemente Ferrer , Jorge Mateu
This paper introduces a novel coefficient for measuring agreement between two lattice sequences observed in the same areal units, motivated by the analysis of different methodologies for measuring poverty rates in Chile. Building on the multivariate concordance coefficient framework, our approach accounts for dependencies in the multivariate lattice process using a non-negative definite matrix of weights, assuming a Multivariate Conditionally Autoregressive (GMCAR) process. We adopt a Bayesian perspective for inference, using summaries from Bayesian estimates. The methodology is illustrated through an analysis of poverty rates in the Metropolitan and Valparaíso regions of Chile, with High Posterior Density (HPD) intervals provided for the poverty rates. This work addresses a methodological gap in the understanding of agreement coefficients and enhances the usability of these measures in the context of social variables typically assessed in areal units.
{"title":"A concordance coefficient for lattice data: An application to poverty indices in Chile","authors":"Ronny Vallejos , Clemente Ferrer , Jorge Mateu","doi":"10.1016/j.spasta.2025.100936","DOIUrl":"10.1016/j.spasta.2025.100936","url":null,"abstract":"<div><div>This paper introduces a novel coefficient for measuring agreement between two lattice sequences observed in the same areal units, motivated by the analysis of different methodologies for measuring poverty rates in Chile. Building on the multivariate concordance coefficient framework, our approach accounts for dependencies in the multivariate lattice process using a non-negative definite matrix of weights, assuming a Multivariate Conditionally Autoregressive (GMCAR) process. We adopt a Bayesian perspective for inference, using summaries from Bayesian estimates. The methodology is illustrated through an analysis of poverty rates in the Metropolitan and Valparaíso regions of Chile, with High Posterior Density (HPD) intervals provided for the poverty rates. This work addresses a methodological gap in the understanding of agreement coefficients and enhances the usability of these measures in the context of social variables typically assessed in areal units.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100936"},"PeriodicalIF":2.5,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-26DOI: 10.1016/j.spasta.2025.100937
André Victor Ribeiro Amaral , Adam M. Sykulski , Sophie Fielding , Emma Cavan
Antarctic krill (Euphausia superba) are among the most abundant species on our planet and serve as a vital food source for many marine predators in the Southern Ocean. In this paper, we utilise statistical spatio-temporal methods to combine data from various sources and resolutions, aiming to model krill abundance. Our focus lies in fitting the model to a dataset comprising acoustic measurements of krill biomass. To achieve this, we integrate climate covariates obtained from satellite imagery and from drifting surface buoys (also known as drifters). Additionally, we use sparsely collected krill biomass data obtained from net fishing efforts (KRILLBASE) for validation. However, integrating these multiple heterogeneous data sources presents significant modelling challenges, including spatio-temporal misalignment and inflated zeros in the observed data. To address these challenges, we fit a Hurdle-Gamma model to jointly describe the occurrence of zeros and the krill biomass for the non-zero observations, while also accounting for misaligned and heterogeneous data sources, including drifters. Therefore, our work presents a comprehensive framework for analysing and predicting krill abundance in the Southern Ocean, leveraging information from various sources and formats. This is crucial due to the impact of krill fishing, as understanding their distribution is essential for informed management decisions and fishing regulations aimed at protecting the species.
{"title":"Navigating challenges in spatio-temporal modelling of Antarctic krill abundance: Addressing zero-inflated data and misaligned covariates","authors":"André Victor Ribeiro Amaral , Adam M. Sykulski , Sophie Fielding , Emma Cavan","doi":"10.1016/j.spasta.2025.100937","DOIUrl":"10.1016/j.spasta.2025.100937","url":null,"abstract":"<div><div>Antarctic krill (<em>Euphausia superba</em>) are among the most abundant species on our planet and serve as a vital food source for many marine predators in the Southern Ocean. In this paper, we utilise statistical spatio-temporal methods to combine data from various sources and resolutions, aiming to model krill abundance. Our focus lies in fitting the model to a dataset comprising acoustic measurements of krill biomass. To achieve this, we integrate climate covariates obtained from satellite imagery and from drifting surface buoys (also known as drifters). Additionally, we use sparsely collected krill biomass data obtained from net fishing efforts (KRILLBASE) for validation. However, integrating these multiple heterogeneous data sources presents significant modelling challenges, including spatio-temporal misalignment and inflated zeros in the observed data. To address these challenges, we fit a Hurdle-Gamma model to jointly describe the occurrence of zeros and the krill biomass for the non-zero observations, while also accounting for misaligned and heterogeneous data sources, including drifters. Therefore, our work presents a comprehensive framework for analysing and predicting krill abundance in the Southern Ocean, leveraging information from various sources and formats. This is crucial due to the impact of krill fishing, as understanding their distribution is essential for informed management decisions and fishing regulations aimed at protecting the species.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100937"},"PeriodicalIF":2.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-25DOI: 10.1016/j.spasta.2025.100935
Kabelo Mahloromela, Inger Fabris-Rotelli
A point pattern is typically analysed to understand the first- and second-order properties of the underlying point process. These properties are usually inferred using estimation procedures that depend on interpoint distance and are thus sensitive to the choice of distance metric. Euclidean distance is conventionally used to quantify proximity between points, but it does not accurately reflect spatial relationships when points are constrained within irregular, nonconvex spatial domains. Herein, we propose a strategy to embed visibility graph distances into Euclidean metric space using multidimensional scaling. The aim is to simplify analyses, leverage well-developed methods based on Euclidean distance, and retain, as far as possible, the true proximity relationships on a nonconvex spatial domain. The kernel smoothed intensity estimate and the -function are computed in this new spatial context and used to validate the effectiveness of the embedding strategy.
{"title":"A framework for analysing point patterns on nonconvex domains using visibility graphs and multidimensional scaling","authors":"Kabelo Mahloromela, Inger Fabris-Rotelli","doi":"10.1016/j.spasta.2025.100935","DOIUrl":"10.1016/j.spasta.2025.100935","url":null,"abstract":"<div><div>A point pattern is typically analysed to understand the first- and second-order properties of the underlying point process. These properties are usually inferred using estimation procedures that depend on interpoint distance and are thus sensitive to the choice of distance metric. Euclidean distance is conventionally used to quantify proximity between points, but it does not accurately reflect spatial relationships when points are constrained within irregular, nonconvex spatial domains. Herein, we propose a strategy to embed visibility graph distances into Euclidean metric space using multidimensional scaling. The aim is to simplify analyses, leverage well-developed methods based on Euclidean distance, and retain, as far as possible, the true proximity relationships on a nonconvex spatial domain. The kernel smoothed intensity estimate and the <span><math><mi>K</mi></math></span>-function are computed in this new spatial context and used to validate the effectiveness of the embedding strategy.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100935"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-25DOI: 10.1016/j.spasta.2025.100928
Yangha Chung , Ji Meng Loh , Woncheol Jang
We introduce a doubly-smoothed bandwidth selection method to obtain bandwidth matrices for estimating the intensity function of a spatial point process. The doubly-smoothed bootstrap involves taking bootstrap samples by adding random noise and using Dirichlet rather than multinomial weights. The mean integrated squared error (MISE) and asymptotic mean integrated squared error (AMISE) as a function of can then be computed numerically using the bootstrap samples, with optimal obtained by minimizing the MISE or AMISE with respect to We present simulation results comparing the doubly-smoothed bandwidth selection method with other methods for a number of intensity functions. We also apply our methods to a data set of police pedestrian stops in New York City.
{"title":"Bandwidth selection for the intensity in spatial point processes","authors":"Yangha Chung , Ji Meng Loh , Woncheol Jang","doi":"10.1016/j.spasta.2025.100928","DOIUrl":"10.1016/j.spasta.2025.100928","url":null,"abstract":"<div><div>We introduce a doubly-smoothed bandwidth selection method to obtain bandwidth matrices <span><math><mi>H</mi></math></span> for estimating the intensity function of a spatial point process. The doubly-smoothed bootstrap involves taking bootstrap samples by adding random noise and using Dirichlet rather than multinomial weights. The mean integrated squared error (MISE) and asymptotic mean integrated squared error (AMISE) as a function of <span><math><mi>H</mi></math></span> can then be computed numerically using the bootstrap samples, with optimal <span><math><mi>H</mi></math></span> obtained by minimizing the MISE or AMISE with respect to <span><math><mrow><mi>H</mi><mo>.</mo></mrow></math></span> We present simulation results comparing the doubly-smoothed bandwidth selection method with other methods for a number of intensity functions. We also apply our methods to a data set of police pedestrian stops in New York City.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100928"},"PeriodicalIF":2.5,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-24DOI: 10.1016/j.spasta.2025.100933
Maria E. Kamenetsky , Jun Zhu , Ronald E. Gangnon
Patterns in disease across space and time are important to epidemiologists and health professionals because they may indicate underlying elevated disease risk. In some cases, elevated risk may be driven by environmental exposures, infectious diseases or other factors where timely public health interventions are important. The spatial and spatio-temporal scan statistics identify a single most likely cluster or equivalently select a single correct model. We instead consider an ensemble of single cluster models. We use stacking, a model-averaging technique, to combine relative risk estimates from all of the single cluster models into a sequence of meta-models indexed by the effective number of parameters/clusters. The number of parameters/spatio-temporal clusters is chosen using information criteria. A simulation study is conducted to demonstrate the statistical properties of the stacking method. The method is illustrated using a dataset of female breast cancer incidence data at the municipality level in Japan.
{"title":"Spatial and spatio-temporal cluster detection using stacking","authors":"Maria E. Kamenetsky , Jun Zhu , Ronald E. Gangnon","doi":"10.1016/j.spasta.2025.100933","DOIUrl":"10.1016/j.spasta.2025.100933","url":null,"abstract":"<div><div>Patterns in disease across space and time are important to epidemiologists and health professionals because they may indicate underlying elevated disease risk. In some cases, elevated risk may be driven by environmental exposures, infectious diseases or other factors where timely public health interventions are important. The spatial and spatio-temporal scan statistics identify a single most likely cluster or equivalently select a single correct model. We instead consider an ensemble of single cluster models. We use stacking, a model-averaging technique, to combine relative risk estimates from all of the single cluster models into a sequence of meta-models indexed by the effective number of parameters/clusters. The number of parameters/spatio-temporal clusters is chosen using information criteria. A simulation study is conducted to demonstrate the statistical properties of the stacking method. The method is illustrated using a dataset of female breast cancer incidence data at the municipality level in Japan.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100933"},"PeriodicalIF":2.5,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-23DOI: 10.1016/j.spasta.2025.100934
Giovanni Millo
We address the issue of specifying a spatial lag vs. spatial error process in spatial panel models. The popular locally robust Lagrange multiplier (RLM) tests for spatial lag vs. error are compared to optimal alternatives based on maximum likelihood estimation: Wald and likelihood ratio (LR) tests requiring estimation of the full encompassing model, and conditional Lagrange multiplier (CLM) tests drawing on the reduced specification. Monte Carlo simulations are performed in a typical spatial panel context. Individual effects are successfully eliminated through the forward orthogonal deviations transformation, making the RLM suitable for panel data. Nevertheless, the statistical properties of Wald and LR are superior to those of the RLM. The CLM also dominates the RLM, as long as the sample is at least of moderate size. The RLM are computationally very convenient, but ML-based tests are feasible in most usage cases on mainstream hardware.
{"title":"Specifying spatial effects in panel data: Locally robust vs. conditional tests","authors":"Giovanni Millo","doi":"10.1016/j.spasta.2025.100934","DOIUrl":"10.1016/j.spasta.2025.100934","url":null,"abstract":"<div><div>We address the issue of specifying a spatial lag vs. spatial error process in spatial panel models. The popular locally robust Lagrange multiplier (RLM) tests for spatial lag vs. error are compared to optimal alternatives based on maximum likelihood estimation: Wald and likelihood ratio (LR) tests requiring estimation of the full encompassing model, and conditional Lagrange multiplier (CLM) tests drawing on the reduced specification. Monte Carlo simulations are performed in a typical spatial panel context. Individual effects are successfully eliminated through the forward orthogonal deviations transformation, making the RLM suitable for panel data. Nevertheless, the statistical properties of Wald and LR are superior to those of the RLM. The CLM also dominates the RLM, as long as the sample is at least of moderate size. The RLM are computationally very convenient, but ML-based tests are feasible in most usage cases on mainstream hardware.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"70 ","pages":"Article 100934"},"PeriodicalIF":2.5,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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