SpatialProbit package allows to fit spatial autoregressive (SAR) and
spatial error (SEM) probit models. It also provides functions to simulated
spatial binary data, an empirical data set and different methods for the
diagnostic of the estimated model.
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 computing 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
overperforming 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
coef are available.
The package also contains the function
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
The core functions of the present package have been coded using the
RcppEigen libraries (Bates and Eddelbuettel (2013)),
that allow direct interchange of rich R objects between R and C++.
D. Bates and D. Eddelbuettel. Fast and elegant numerical linear algebra using the RcppEigen package. Journal of Statistical Software 52, 1–24, 2013.
A. C. Case. Neighborhood Influence and Technological Change. Regional Science and Urban Economics 22, 491–508, 1992.
R. Calabrese and J.A. Elkink. Estimators of binary spatial autoregressive models: a Monte Carlo study. Journal of Regional Science 54, 664–687, 2014.
J. LeSage and R.K. Pace. Introduction to Spatial Econometrics, CRC Press, chapter 10.1.6, 2009.
P. LeSage, R. K. Pace, N. Lam, R. Campanella and X. Liu. New Orleans business recovery in the aftermath of Hurricane Katrina. Journal of the Royal Statistical Society A, 174, 1007–1027, 2011.
D. Martinetti and G. Geniaux. Approximate likelihood estimation of spatial probit models. Regional Science and Urban Economics, submitted, 2015. https://urbansimul.paca.inra.fr/urbansimul/pdf/recherche/
D. McMillen. McSpatial: Nonparametric spatial data analysis. R package version 2.0, http://CRAN.R-project.org/package=McSpatial, 2013.
N. Mendell and R. Elston. Multifactorial qualitative traits: genetic analysis and prediction of recurrence risks. Biometrics 30, 41–57, 1974.
S. Wilhelm and M. Godinho de Matos. Estimating Spatial Probit Models in R. The R Journal 5, 130–143, 2013.
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