Page 448 - Special Topic Session (STS) - Volume 3

STS555 Mohamed Salem Ahmed et al.
mapping forms often an irregular lattice. Basically, statistical models for lattice
data are linked to nearest neighbors to express the fact that data are nearby.
Two popular spatial dependence models have received a lot of attention in
lattice data: the spatial autoregressive (SAR) dependent variable model and
the spatial autoregressive error model (SAE, where the model error is a SAR),
which extend regression in time series to spatial data.
In a in theoretical point of view, various linear spatial regression SAR and
SAE models, their identification and estimation methods by the two stage least
squares (2SLS), the three stage least squares (3SLS), the maximum likelihood
(ML) or quasi-maximum likelihood (QML) and the generalized method of
moments (GMM) methods have been developed and summarized by many
authors, such as Anselin (1988), Kelejian and Prucha (1999), Conley (1999), Lee
(2004), Garthoff and Otto (2017). Nonlinearity into the field of spatial linear
lattice models have less attention, see for instance Robinson (2011) who
generalized the kernel regression estimation to spatial lattice data. Su (2012)
proposed a semiparametric GMM estimation for some semiparametric SAR
models. Extending these models and methods to discrete choice spatial
models have less attention, only a few number of papers were concerned in
recent years. This may be, as pointed out by Fleming (2004), due to the "added
complexity that spatial dependence introduces into discrete choice models".
Estimating the model parameters with a full ML approach in spatial discrete
choice models, often requires solving a very computationally demanding
problem of n-dimensional integration, where n is the sample size.
As for linear models many discrete choice models are fully linear and make
use of a continuous latent variable, see for instance Smirnov (2010) and Wang
et al. (2013) that proposed pseudo ML methods and Pinkse and Slade (1998)
who studied a method based on GMM approach.
When the relationship between the discrete choice variable and some
explanatory variables is not linear, then a semiparametric model may be an
alternative to fully parametric models. This kind of models is known in
literature as partially linear choice spatial models and is the baseline of this
current work. When the data are independent, these choice models can be
viewed as particular cases of the famous generalized additive models (Hastie
and Tibshirani, 1990) and have received a lot of attention in the literature,
various methods of estimation have been explored (see for instance Severini
and Staniswalis, 1994; Carroll et al., 1997).
To the best of our knowledge, semiparametric spatial choice models, have
not yet been investigated in a theoretical point of view. To fill in this gap, this
work addresses a SAE spatial probit model when the spatial dependence
structure is integrated in a disturbance term of the studied model. We propose
a semiparametric estimation method combining the GMM approach and the
weighted likelihood method. It consists to first fix the parametric components

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