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ProbitSpatial: Probit with Spatial Dependence, SAR and SEM Models

Abstract : SpatialProbit package allows to fit spatial autoregressive (SAR) and spatial error (SEM) pro- bit models. It also provides functions to simulated spatial binary data, an empirical data set and different methods for the diagnostic of the estimated model. Details : The main function of this package is SpatialProbitFit. It allows to fit both SAR and SEM models for big datasets in a reasonable time. The function is based on the maximisation of the approximate likelihood function. The approximation is inspired by the Mendell and Elston algorithm for com- puting multivariate normal probabilities and take advantage of the sparsity of the spatial weight matrix. Two methods are available for the estimation of the model parameter: the first one is known as conditional method (see Case (1992)) and performs relatively well in terms of accuracy of the estimated parameters and is very rapid. The second method, that minimises the full-log-likelihood, is slower but it should be more accurate. Monte Carlo experiments on simulated data reported in Martinetti and Geniaux (2015) showed that the full-log-likelihood approach is not always overper- forming the conditional method in terms of accuracy. At the present stage, our suggestion is to use the conditional method for a first estimation and only attempt the full-likelihood approach in a second moment, when the dataset size is not bigger than a few thousands. Another feature of the SpatialProbitFit function is the possibility to fit the model using the precision matrix instead of the variance-covariance matrix, since it is usually sparser and hence allows faster computations (see LeSage and Pace (2009)). The output of SpatialProbitFit function is an object of class SpatialProbit, for which the methods residuals, fitted, effects, predict and coef are available. The package also contains the function sim_binomial_probit that allows to simulate data samples of both SAR and SEM models. It can be used to replicate the Monte Carlo experiments reported in Martinetti and Geniaux (2015) as well as the experiment of Calabrese and Elkink (2014). An empirical data set Katrina on the reopening decisions of firms in the aftermath of the Katrina Hurricane in New Orleans is also available (LeSage et al.(2011)). Other packages in CRAN repository on the same subject are McSpatial (McMillen (2013)) and spatialprobit (Wilhelm and Godinho de Matos (2013)). The core functions of the present package have been coded using the Rcpp and RcppEigen libraries (Bates and Eddelbuettel (2013)), that allow direct interchange of rich R objects between R and C++.
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Submitted on : Friday, June 5, 2020 - 7:25:12 PM
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Davide Martinetti, Ghislain Geniaux. ProbitSpatial: Probit with Spatial Dependence, SAR and SEM Models. 2016. ⟨hal-02800483⟩



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