Spatial Probit Model Research Articles

A method for measuring spatial effects on socioeconomic inequalities using the concentration index

BackgroundAlthough spatial effects contribute to inequalities in health care service utilisation and other health outcomes in low and middle income countries, there have been no attempts to incorporate the impact of neighbourhood effects into equity analyses based on concentration indices. This study aimed to decompose and estimate the contribution of spatial effects on inequalities in uptake of HIV tests in Malawi.MethodsWe developed a new method of reflecting spatial effects within the concentration index using a spatial weight matrix. Spatial autocorrelation is presented using a spatial lag model. We use data from the Malawi Demographic Health Survey (n = 24,562) to illustrate the new methodology. Need variables such as ‘Any STI last 12 month’, ‘Genital sore/ulcer’, ‘Genital discharge’ and non need variables such as Education, Literacy, Wealth, Marriage, and education were used in the concentration index. Using our modified concentration index that incorporates spatial effects, we estimate inequalities in uptake of HIV testing amongst both women and men living in Malawi in 2015–2016, controlling for need and non-need variables.ResultsFor women, inequalities due to need variables were estimated at − 0.001 and − 0.0009 (pro-poor) using the probit and new spatial probit estimators, respectively, whereas inequalities due to non-need variables were estimated at 0.01 and 0.0068 (pro-rich) using the probit and new spatial probit estimators. The results suggest that spatial effects increase estimated inequalities in HIV uptake amongst women. Horizontal inequity was almost identical (0.0103 vs 0.0102) after applying the spatial lag model. For men, inequalities due to need variables were estimated at − 0.0002 using both the probit and new spatial probit estimators; however, inequalities due to non-need variables were estimated at − 0.006 and − 0.0074 for the probit and new spatial probit models. Horizontal inequity was the same for both models (− 0.0057).ConclusionOur findings suggest that men from lower socioeconomic groups are more likely to receive an HIV test after adjustment for spatial effects. This study develops a novel methodological approach that incorporates estimation of spatial effects into a common approach to equity analysis. We find that a significant component of inequalities in HIV uptake in Malawi driven by non-need factors can be explained by spatial effects. When the spatial model was applied, the inequality due to non need in Lilongwe for men and horizontal inequity in Salima for women changed the sign.This approach can be used to explore inequalities in other contexts and settings to better understand the impact of spatial effects on health service use or other health outcomes, impacting on recommendations for service delivery.

Partial ML estimation for spatial autoregressive nonlinear probit models with autoregressive disturbances

In this paper, we propose a Partial MLE (PMLE) for a general spatial nonlinear probit model, i.e., SARAR(1,1) probit, defined through a SARAR(1,1) latent linear model. This model encompasses both the SAE(1) probit and the more interesting SAR(1) probit models, already considered in the literature. We provide a complete asymptotic analysis of our PMLE as well as appropriate definitions of the marginal effects. Moreover, we address the issue of the choice of the groups (couples, in our case) by proposing an algorithm based on a minimum KL divergence problem. Finite sample properties of the PMLE are studied through extensive Monte Carlo simulations. In particular, we consider both sparse and dense matrices for the true spatial model specifications, and cases of model misspecification given wrong assumed weighting matrices. In a real data example, we finally also compare our estimator with different MLE–based estimators and with the Bayesian approach.

Modeling spatial dependence and economic hotspots in landowners’ willingness to supply bioenergy crops in the northeastern United States

AbstractThis paper investigates the spatial heterogeneity of landowners’ willingness to supply three bioenergy crops: switchgrass, Miscanthus, and willow, in the northeastern United States. Spatial heterogeneity might arise for several reasons. For example, landowners closer to bioenergy processing plants might be more likely to be willing to supply bioenergy crops, and landowners who are more willing to supply bioenergy crops may be spatially clustered because they share similar land attributes, demographics, experiences, and/or values. Using high‐resolution GIS data related to the location of pellet plants utilizing bioenergy crops and survey data related to landowners’ characteristics including spatial location, we estimate a spatial probit model to explain the variation in individual‐specific reservation prices (RPs)—the feedstock price at which landowners become willing to supply a bioenergy crop. We find that respondents’ RP is lower the closer they live to their nearest pellet plant and spatial dependency is only present for switchgrass supply. We also identify three economic hotspots (areas with high potential supply and low RPs) for each bioenergy crop. We believe that bioenergy supply chains could be developed around these hotspots.

Exploring network effects of point-to-point networks: An investigation of the spatial patterns of Southwest Airlines’ network

This paper explores network effects in Point-to-Point airline networks by examining the spatial patterns of Southwest airlines' route network during Southwest's major network expansionary period for completing continental US geographic coverage between 1990 and 2006. Estimation results from a spatial probit model reveal clear spatial dependence in profitability across different routes served by the carrier. Detailed investigation suggests two main sources of network effects, namely: (1) airport and regional presence, and (2) substitutability between airport-pair markets. Findings of the paper suggest also that the network effects embedded in Southwest's Point-to-Point network have many distinguishing features as compared to those identified in a typical Hub-and-Spoke network. The results of this study on Southwest's network expansionary period help us to predict how emerging LCC networks in other large aviation market, such as China, are likely to be developed over time if regulators give carriers reasonable freedom to develop their service network efficiently.

Spatial Cumulative Probit Model: An Application to Poverty Classification and Mapping

Previous studies on household poverty classification have commonly dichotomized the dependent variable into non-poor or poor, and used binary models. This way, the most extreme categories of poverty, which are usually the main targets of interventions, are not identified. Moreover, expenditure data used to describe poverty is typically collected at several locations over large geographical domains. Local disturbances introduce spatial correlation, implying that global parameters (obtained via independence assumptions of standard statistical methods) cannot adequately describe site-specific conditions of the data. The objective, therefore, is to describe an appropriate method for ordered categorical data collected at geo-referenced locations over large geographical space. To achieve this, a model named Spatial Cumulative Probit Model (SCPM) was proposed. This model classified household poverty in an ordinal spatial framework. Bayesian inference was performed on data sampled by Markov Chain Monte Carlo (MCMC) algorithms. A test of model adequacy show that the SCPM is unbiased and attains a lower misclassification rate of 14.43% than the simple Cumulative Probit (CP) model with misclassification rate of 16.5% that ignores spatial dependence in the data. Overall, ‘savannah ecological zone’, ‘polygamous marriage’ and ‘rural location’ were the most powerful predictors of extreme poverty in Ghana. The prediction map, created by this study, identified positive correlation with respect to ‘poor’ and ‘extremely poor’ categories. Results of the model in this study can be considered a category and site-specific report that identifies all levels and sites of poverty for easy targeting, thus, avoiding the blanket approach that prefers the one-fits-it-all solution to the problem of poverty. Analysis was based on the Ghana Living Standards Survey (GLSS 6) dataset.

Patterns and correlates of urban trail use: Evidence from the Cincinnati metropolitan area

Transportation, parks, and health organizations are collaborating to develop multiuse trail networks that meet the needs of metropolitan residents for utilitarian travel, recreation, and fitness. This paper describes how trails are used and explores correlates of trail use in the Greater Cincinnati region. Drawing on a systematic survey of users, we use ordinary probit and spatial models to explore the effects of socio-demographics, trip characteristics, attitudes, and the built environment, on recreational and utilitarian use. Most (89%) respondents report using trails for recreation; just 8.8% say they use trails for utilitarian purposes. Ordinary probit models show that users reporting recreational use are significantly more likely to be female, have incomes greater than $120,000, and travel longer distances on trails, but less likely to bike or walk to access trails. Transit connectivity is negatively correlated with recreational use. Trail users reporting utilitarian purposes are disproportionately male, significantly less likely to have incomes greater than $120,000, and more likely to take short trips on trails and to access trails by cycling or walking. They say they would commute more by cycling if connectivity were improved. Spatial probit model indicates negative spatial relationships among recreational users, implying the absence of a spatially-based common culture of trail use. Trail planners in this region can use these findings to strengthen the planning and design of trail networks and to meet the needs of different users. Given the finding most trail use is for recreational purposes, additional studies of the needs of utilitarian users are warranted.

Bayesian Spatial Ordinal Models for Regional Household Poverty-Severity

The use of discrete spatial-statistical methods for poverty analyses is important, especially in light of the fact that living standards surveys are generally dominated by categorical observations made at several locations. The proximity of these observations imposes geographical structure on the data. This study presents ordinal geo-statistical models for household poverty analyses that recognize the ordinal nature of poverty severity. For all models, Bayesian inference via Markov Chain Monte Carlo (MCMC) was used. Precision of the models, understood in terms of ease of implementation and accuracy of estimation, is compared. The objective was to quantify spatial associations, given some household features, and produce a map of poverty-severity for Ghana. The Clipped Gaussian Spatial Ordinal Probit (CG-SOP) Model was identified as best for describing spatial poverty. Positive correlation with respect to the distribution of extreme poverty was observed. We see evidence of this in the map of predictions. Significant variables include household size, education, and residency of household head. This approach to poverty analysis is relevant for policy design and the implementation of cost-effective programmes to reduce (category and site)-specific poverty, and monitoring changes in both category and geographical trends thereof. Analysis was based on the Ghana living standards survey (GLSS) 2012 data.

Bringing space into the equation: Modelling the social and spatial interdependence of neighborhood effects on educational outcomes

While there is an ever-growing body of research on neighborhood effects on various forms of life chances, the suggested social mechanisms still refer to rather ambiguous theoretical concepts. Furthermore, previous research seldom adequately models the suggested social interdependence at the individual level. Instead, researchers largely rely on contextual regression models. This paper addresses both problems by using spatial econometrics to reconstruct neighborhood effects in terms of interdependent social action. To this end, a rational action model of neighborhood effects on educational outcomes is elaborated as a theoretical alternative. Furthermore, using data on the transition to secondary school in Switzerland as an illustration, spatial probit models are estimated to directly test neighborhood effects at the individual level. It can be shown how the interdependence of parental educational motivation within neighborhoods crucially shapes students’ transition to the more advantageous school track, thereby revealing an additional path by which educational inequalities are reproduced.

The varying driving forces of urban expansion in China: Insights from a spatial-temporal analysis

Identifying the driving mechanisms and forces of urban expansion is an important step toward better understanding of the spatial pattern, process, and consequences of urban expansion, which is essential for making effective urban growth planning and policies. Despite many previous studies devoted to investigating urban expansion patterns and mechanisms, the spatial-temporal dynamics of driving forces and their regional differences have not been well-documented. This study examines drivers of urban expansion and their effects across different regions in China in different periods. A spatial Probit model is employed, with data selected based on a national-level sampling strategy, to model urban expansion probability from a spatially explicit perspective. Results indicate that multiple factors including socioeconomic, physical, proximity, accessibility, and neighborhood factors have driven urban expansion in China. Driving factors for urban expansion vary between national and regional levels, suggesting that analyses on different spatial scales are necessary. The dynamics and driving forces of urban expansion in China have been spatial heterogeneous. Furthermore, driving forces have trended toward more diversity over time, and the constraining effects of natural conditions on urban expansion have gradually decayed. These findings aid in gaining a better understanding of the urban expansion process in China, which will in turn benefit urban planning and management across different regions. Lastly, important policy implications are inferred.

Spatial concentration of foreign owned entities in Poland

Foreign direct investment plays a crucial role in global capital and trade flows. The FDI’s influence on national, regional and local economies is often the subject of public political and economic discussion, as well as numerous incentives to acquire foreign capital. The aim of this article is to identify the spatial concentration of firms with foreign capital (FOEs) in Poland at the municipality/gmina level (LAU 2) between 1995 and 2017 as well as the determinants of their location. With the use of I Moran’s statistics and spatial probit models, the intensity of the FDI location as well as their location determinants were verified. The authors also indicate the areas of spatial concentration and potential areas of positive externalities resulting from FOEs agglomeration.

"Birds of a Feather" Fail Together: Exploring the Nature of Dependency in SME Defaults.

This article studies the effects of incorporating the interdependence among London small business defaults into a risk analysis framework using the data just before the financial crisis. We propose an extension from standard scoring models to take into account the spatial dimensions and the demographic characteristics of small and medium-sized enterprises (SMEs), such as legal form, industry sector, and number of employees. We estimate spatial probit models using different distance matrices based only on the spatial location or on an interaction between spatial locations and demographic characteristics. We find that the interdependence or contagion component defined on spatial and demographic characteristics is significant and that it improves the ability to predict defaults of non-start-ups in London. Furthermore, including contagion effects among SMEs alters the parameter estimates of risk determinants. The approach can be extended to other risk analysis applications where spatial risk may incorporate correlation based on other aspects.

Do neighboring municipalities matter in industrial location decisions? Empirical evidence from Spain

This paper focuses on industrial location, assuming that entrepreneurs not only consider the advantages associated with a certain municipality, but also those coming from nearby areas. Exploratory analysis reflects the existence of spatial patterns in the creation of manufacturing establishments and sheds light on the geographical scope on which agglomeration economies operate in industrial location. Spatial Probit models and standard Probit models with spatially lagged explanatory variables are estimated to test whether neighboring municipalities’ location decisions and characteristics, including agglomeration economies, matter in industrial location choices. Results show that neighboring municipalities location decisions and characteristics help to explain location decisions of new establishments for 11 manufacturing industries in Spanish municipalities (NUTS V) over the period 1991–1995.

Urban segregation and unemployment: A case study of the urban area of Marseille – Aix-en-Provence (France)

In this paper, we study the effects of the spatial organization of the urban area of Marseille – Aix-en-Provence on unemployment there. More specifically, differences in the characteristics of the residential population induce urban stratification with the result that urban structure may affect the probability of employment. In order to evaluate the effects of spatial structure on unemployment, we implement a spatial probit model to reveal the employment probabilities of young adults still living with their parents. Our results support the hypothesis that living in or near a deprived neighborhood decreases the probability of employment.

Effectiveness of conservation easements in agricultural regions.

Conservation easements are a standard technique for preventing habitat loss, particularly in agricultural regions with extensive cropland cultivation, yet little is known about their effectiveness. I developed a spatial econometric approach to propensity-score matching and used the approach to estimate the amount of habitat loss prevented by a grassland conservation easement program of the U.S. federal government. I used a spatial autoregressive probit model to predict tract enrollment in the easement program as of 2001 based on tract agricultural suitability, habitat quality, and spatial interactions among neighboring tracts. Using the predicted values from the model, I matched enrolled tracts with similar unenrolled tracts to form a treatment group and a control group. To measure the program's impact on subsequent grassland loss, I estimated cropland cultivation rates for both groups in 2014 with a second spatial probit model. Between 2001 and 2014, approximately 14.9% of control tracts were cultivated and 0.3% of treated tracts were cultivated. Therefore, approximately 14.6% of the protected land would have been cultivated in the absence of the program. My results demonstrate that conservation easements can significantly reduce habitat loss in agricultural regions; however, the enrollment of tracts with low cropland suitability may constrain the amount of habitat loss they prevent. My results also show that spatial econometric models can improve the validity of control groups and thereby strengthen causal inferences about program effectiveness in situations when spatial interactions influence conservation decisions.

Approximate likelihood estimation of spatial probit models

A new estimation method for spatial binary probit models is presented. Both spatial auto-regressive (SAR) and spatial error (SEM) models are considered. The proposed estimator relies on the approximation of the likelihood function, that follows a multivariate normal distribution which parameters depend on the spatial structure of the observations. The approximation is inspired by the univariate conditioning procedure proposed by Mendell and Elston, with some modifications to improve accuracy and speed. Very accurate parameter estimations have been achieved in reasonable time for simulated data samples with as much as one million observations. The lessons learned in the Monte Carlo experiment have been applied to a case study on urban sprawl over more than forty thousands plots in Southern France.

Composite marginal likelihood estimation of spatial autoregressive probit models feasible in very large samples

Composite Marginal Likelihood (CML) has become a popular approach for estimating spatial probit models. However, for spatial autoregressive specifications the existing brute-force implementations are infeasible in large samples as they rely on inverting the high-dimensional precision matrix of the latent state variable. The contribution of this paper is to provide a CML implementation that circumvents inversion of that matrix and therefore can also be applied to very large sample sizes.

The complex interplay of social networks, geography and HIV risk among Malaysian Drug Injectors: Results from respondent-driven sampling

BackgroundHIV is primarily concentrated among people who inject drugs (PWID) in Malaysia, where currently HIV prevention and treatment coverage is inadequate. To improve the targeting of interventions, we examined HIV clustering and the role that social networks and geographical distance play in influencing HIV transmission among PWID. MethodsData were derived from a respondent-driven survey sample (RDS) collected during 2010 of 460 PWID in greater Kuala Lumpur. Analysis focused on socio-demographic, clinical, behavioural, and network information. Spatial probit models were developed based on a distinction between the influence of peers (individuals nominated through a recruitment network) and neighbours (residing a close distance to the individual). The models were expanded to account for the potential influence of the network formation. ResultsRecruitment patterns of HIV-infected PWID clustered both spatially and across the recruitment networks. In addition, HIV-infected PWID were more likely to have peers and neighbours who inject with clean needles were HIV-infected and lived nearby (<5km), more likely to have been previously incarcerated, less likely to use clean needles (26.8% vs 53.0% of the reported injections, p<0.01), and have fewer recent injection partners (2.4 vs 5.4, p<0.01). The association between the HIV status of peers and neighbours remained significantly correlated even after controlling for unobserved variation related to network formation and sero-sorting. ConclusionThe relationship between HIV status across networks and space in Kuala Lumpur underscores the importance of these factors for surveillance and prevention strategies, and this needs to be more closely integrated. RDS can be applied to identify injection network structures, and this provides an important mechanism for improving public health surveillance, accessing high-risk populations, and implementing risk-reduction interventions to slow HIV transmission.

Composite Marginal Likelihood Estimation of Spatial Autoregressive Probit Models Feasible in Very Large Samples

Composite Marginal Likelihood (CML) has become a popular approach for estimating spatial probit models. However, for spatial autoregressive specifications the existing brute-force implementations are infeasible in large samples as they rely on inverting the high-dimensional precision matrix of the latent state variable. The contribution of this paper is to provide a CML implementation that circumvents inversion of that matrix and therefore can also be applied to very large sample sizes.

Assessing Geographic Variation in Strabismus Diagnosis among Children Enrolled in Medicaid

To determine how strabismus diagnosis varies within a given community and across communities among children with Medicaid health insurance. Retrospective cohort analysis. Children aged ≤10 years enrolled in Medicaid in Michigan or North Carolina during2009. Children who met the study inclusion criteria were identified from the Medicaid Analytic Extract database, which includes claims data for all children enrolled in Medicaid throughout the United States. Residential location was determined by the last known 5-digit ZIP code for each child, which was linked to the centroid of a ZIP Code Tabulation Area (ZCTA) for geo-referencing and spatial analyses. International Classification of Diseases, 9th Revision, Clinical Modification billing codes were used to identify children diagnosed with strabismus (code 378.xx). Bayesian hierarchical intrinsic conditional autoregressive spatial probit models were used to determine the risk of a child receiving a strabismus diagnosis in communities throughout Michigan and North Carolina. Maps display communities (ZCTAs) where the 95% credible intervals for the spatial random effects estimates do not cross zero, allowing for identification of locations with increased and decreased strabismus diagnosis risk relative to other communities in the states. Likelihood of receiving a diagnosis of strabismus. In 2009, among 519 212 eligible children in Michigan, 7535 (1.5%) received ≥1 strabismus diagnosis, and in North Carolina, 5827 of 523 886 eligible children (1.1%) were diagnosed with strabismus. In both states, the proportion receiving a strabismus diagnosis among black (0.9% in Michigan; 0.7% in North Carolina) and Hispanic (1.1% in Michigan; 0.8% in North Carolina) children was lower than the proportion for white children (1.8% in Michigan; 1.6% in North Carolina). Children living in poorer communities in both states were less likely to be diagnosed with strabismus independent of their race/ethnicity. A child's likelihood of being diagnosed with strabismus is associated with characteristics of the residential community where he or she resides. The findings of this study highlight the importance of ensuring that children who live in less affluent communities have access to the necessary services and eye care professionals to properly diagnose and treat them for this condition.

Use and interpretation of spatial autoregressive probit models

Applications of spatial probit regression models that have appeared in the literature have incorrectly interpreted estimates from these models. Spatially dependent choices frequently arise in various modeling scenarios, including situations involving analysis of regional voting behavior, decisions by states or cities to change tax rates relative to neighboring jurisdictions, decisions by households to move or stay in a particular location. We use county-level voting results from the 2004 presidential election as an illustrative example of some issues that arise when drawing inferences from spatial probit model estimates. Although the voting example holds particular intuitive appeal that allows us to focus on interpretive issues, there are numerous other situations where these same considerations come into play. Past work regarding Bayesian Markov Chain Monte Carlo estimation of spatial probit models from LeSage and Pace (Introduction to spatial econometrics. Taylor and Francis, New York, 2009) is used, as well as derivations from LeSage et al. (J R Stat Soc Ser A Stat Soc 174(4):1007–1027, 2011) regarding proper interpretation of the partial derivative impacts from changes in the explanatory variables on the probability of voting for a candidate. As in the case of conventional probit models, the effects arising from changes in the explanatory variables depend in a nonlinear way on the levels of these variables. In non-spatial probit regressions, a common way to explore the nonlinearity in this relationship is to calculate “marginal effects” estimates using particular values of the explanatory variables (e.g., mean values or quintile intervals). The motivation for this practice is consideration of how the impact of changing explanatory variable values varies across the range of values encompassed by the sample data. Given the nonlinear nature of the normal cumulative density function transform on which the (non-spatial) probit model relies, we know that changes in explanatory variable values near the mean may have a very different impact on decision probabilities than changes in very low or high values. For spatial probit regression models, the effects or impacts from changes in the explanatory variables are more highly nonlinear. In addition, since spatial models rely on observations that each represent a location or region located on a map, the levels of the explanatory variables can be viewed as varying over space. We discuss important implications of this for proper interpretation of spatial probit regression models in the context of our election application.