Page 447 - Special Topic Session (STS) - Volume 3

STS555 Mohamed Salem Ahmed et al.

Generalized partially linear spatial probit models
and applications
1
2,3
1
Mohamed Salem Ahmed , Sophie Dabo-Niang , Michael Genin
1 University of Lille, laboratory CERIM, EA 2694, France
2 Laboratory LEM-CNRS 9221, University of Lille, Villeneuve d’Ascq, France
3 INRIA Lille Nord-Europe, MODAL-Team

Abstract
Generalized partially linear probit regression model for spatially dependent
data is considered. Conditional heteroscedasticity and non-identically
distributed observations and a linear process for disturbances are assumed
allowing various spatial dependencies. The estimation procedure proposed
combines a weighted likelihood and a generalized method of moments.
Consistency of the parametric and non-parametric components estimators
and asymptotic normality results are established under sufficient conditions.
Numerical experiments including real economic and environmental data
applications to investigate the finite sample performance of the estimators are
given.

Keywords
spatial data; probit models; generalized partially linear models; non-
parametric

1. Introduction
Agriculture, economics, environmental sciences, urban systems,
epidemiology activities are of-ten located in space. Therefore, modeling such
activities requires to find a kind of correlation between some random variables
in one location with others at neighboring locations, see for instance Pinkse
and Slade (1998). This is a significant feature of spatial data analysis. Spatial
econometrics/statistics provides tools to solve such modeling. A lot of studies
on spatial effects in statistics and econometrics in many divers models have
been published; see Anselin (1988), Cressie (1993) and Arbia (2006) for a
review.
Two main ways of incorporating the spatial dependence structure can be
distinguished basically for geostatistics and lattice data. In the domain of
geostatistics, the spatial location is valued in a continuous set of R , N ≥ 2.
N
However, for many activities, the spatial index or location does not vary
continuously and may be of the lattice type, the baseline of this current work.
This is, for instance, the case in a number of problems. In images analysis,
remote sensing form satellites, agriculture and so one, data are often received
as regular lattice and identified as the centroids of square pixels, whereas a

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