Probit in a Spatial Context: A Monte Carlo Analysis

Beron, Kurt J.; Vijverberg, Wim P. M.

doi:10.1007/978-3-662-05617-2_8

Cited by 107 publications

(133 citation statements)

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“…The two dominant techniques, both based on simulation methods, for the estimation of the spatial lag model are the frequentist recursive importance sampling (RIS) estimator (which is a generalization of the more familiar GewekeHajivassiliou-Keane or GHK simulator; see Beron et al, 2003 andVijverberg, 2004) and The next section presents the model formulation for both the spatial lag and spatial error structures, while Section 3.2 discusses model estimation.…”

Section: The Modelmentioning

confidence: 99%

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

Castro

Paleti

Bhat

2012

Transportation Research Part B: Methodological

130

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This paper proposes a reformulation of count models as a special case of generalized orderedresponse models in which a single latent continuous variable is partitioned into mutually exclusive intervals. Using this equivalent latent variable-based generalized ordered response framework for count data models, we are then able to gainfully and efficiently introduce temporal and spatial dependencies through the latent continuous variables. Our formulation also allows handling excess zeros in correlated count data, a phenomenon that is commonly found in

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Section: The Modelmentioning

confidence: 99%

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

Castro

Paleti

Bhat

2012

Transportation Research Part B: Methodological

130

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“…The recursive importance sampling algorithm was applied to calculate the n -dimensional integral in the likelihood function and thus estimate the parameters in the spatial probit model. This method uses random draws of truncated normal distributions (Beron and Vijverberg 2004). This simulator is one of the most efficient techniques for estimating the likelihood function (Pace and LeSage 2011).…”

Section: Spatial Probit Regressionmentioning

confidence: 99%

Applying spatial regression to evaluate risk factors for microbiological contamination of urban groundwater sources in Juba, South Sudan

2016

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This study developed methodology for statistically assessing groundwater contamination mechanisms. It focused on microbial water pollution in low-income regions. Risk factors for faecal contamination of groundwater-fed drinking-water sources were evaluated in a case study in Juba, South Sudan. The study was based on counts of thermotolerant coliforms in water samples from 129 sources, collected by the humanitarian aid organisation Médecins Sans Frontières in 2010. The factors included hydrogeological settings, land use and socio-economic characteristics. The results showed that the residuals of a conventional probit regression model had a significant positive spatial autocorrelation (Moran's I = 3.05, I-stat = 9.28); therefore, a spatial model was developed that had better goodness-of-fit to the observations. The most significant factor in this model (p-value 0.005) was the distance from a water source to the nearest Tukul area, an area with informal settlements that lack sanitation services. It is thus recommended that future remediation and monitoring efforts in the city be concentrated in such low-income regions. The spatial model differed from the conventional approach: in contrast with the latter case, lowland topography was not significant at the 5% level, as the p-value was 0.074 in the spatial model and 0.040 in the traditional model. This study showed that statistical risk-factor assessments of groundwater contamination need to consider spatial interactions when the water sources are located close to each other. Future studies might further investigate the cut-off distance that reflects spatial autocorrelation. Particularly, these results advise research on urban groundwater quality.

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“…Beron et al (2003) and Beron and Vijverberg (2004) A problem with the approaches just discussed is that they are not feasible for moderate-tolarge samples since they require the inversion and determinant computation of a square matrix of the order of the number of observational units (for McMillen's EM method, LeSage's MCMC method, and Pinkse and Slade's heteroscedastic approach), or treat spatial dependence as a nuisance with no provision of an estimate of the standard error of the spatial error parameter (for the GMM method described in Fleming, 2004), or require the simulation of a multidimensional integral of the order of the number of observational units (for the RIS-based method). 2 Another possible approach is to maintain a relatively restrictive spatial correlation structure that allows a constant correlation within observational units in pre-specified spatial regions, but no correlation in observational units in different spatial regions.…”

Section: Discrete Choice Models With Spatial Error Autocorrelationmentioning

confidence: 99%

A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units

Bhat

Sener

2009

J Geogr Syst

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This study focuses on accommodating spatial dependency in data indexed by geographic location. In particular, the emphasis is on accommodating spatial error correlation across observational units in binary discrete choice models. We propose a copula-based approach to spatial dependence modeling based on a spatial logit structure rather than a spatial probit structure. In this approach, the dependence between the logistic error terms of different observational units is directly accommodated using a multivariate logistic distribution based on the Farlie-Gumbel-Morgenstein (FGM) copula. The approach represents a simple and powerful technique that results in a closedform analytic expression for the joint probability of choice across observational units, and is straightforward to apply using a standard and direct maximum likelihood inference procedure. There is no simulation machinery involved, leading to substantial computation gains relative to current methods to address spatial correlation. The approach is applied to teenagers' physical activity participation levels, a subject of considerable interest in the public health, transportation, sociology, and adolescence development fields. The results indicate that failing to accommodate heteroscedasticity and spatial correlation can lead to inconsistent and inefficient parameter estimates, as well as incorrect conclusions regarding the elasticity effects of exogenous variables.

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Probit in a Spatial Context: A Monte Carlo Analysis

Cited by 107 publications

References 0 publications

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

Applying spatial regression to evaluate risk factors for microbiological contamination of urban groundwater sources in Juba, South Sudan

A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units

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