Approximate likelihood estimation of spatial probit models

Martinetti, Davide; Géniaux, Ghislain

doi:10.1016/j.regsciurbeco.2017.02.002

Cited by 46 publications

(34 citation statements)

References 47 publications

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“…From the model specification in Equation , at least three nested‐model specifications can be derived. By letting

bold-italicθ = 0

and for notational convenience

{boldW}_{1, n} = {boldW}_{n}

, a spatial (first‐order) autoregressive–regressive probit model with (first‐order) autoregressive disturbances (SARAR(1,1)–probit) can be defined, see, for example, Billé and Leorato () and Martinetti and Geniaux (), in the following way:

\begin{matrix} true \\ right {boldy}_{n}^{*} & = & left ρ W_{n} y_{n}^{*} + X_{n} β + u_{n}, u_{n} = λ M_{n} u_{n} + ε_{n}, ε_{n} \sim N_{n} (() {bold0}_{n}, {normalΣ}_{ε}) \\ right {boldy}_{n} & = & left I_{n} (() {boldy}_{n}^{*} > {bold0}_{n}) . \end{matrix}

Additional conditions are needed for the identification of

(ρ, λ)

in a SARAR(1,1)–probit model. Specifically,

M_{n}

and

W_{n}

are assumed to be different thus allowing for different mechanisms to govern spatial correlation between shocks affecting the latent model and spatial dependence of the latent variables themselves.…”

Section: Sdc Model Specificationsmentioning

confidence: 99%

“…From the model specification in Equation (1), at least three nested-model specifications can be derived. By letting θ = 0 and for notational convenience W 1,n = W n , a spatial (first-order) autoregressiveregressive probit model with (first-order) autoregressive disturbances (SARAR(1,1)-probit) can be defined, see, for example, Billé and Leorato (2017) and Martinetti and Geniaux (2017), in the following way: y * n = ρW n y * n + X n β + u n , u n = λM n u n + ε n , ε n ∼ N n (0 n , ε ) y n = I n y * n > 0 n .…”

Section: Spatial Binary Probit Modelsmentioning

confidence: 99%

“…For this reason, MSL/GMM approaches are still computationally unfeasible. Important contributions are those of Klier and McMillen (2008) in a GMM environment, of Bhat (2011) and Mozharovskyi and Vogler (2016) in the realm of the composite ML estimation, and of Martinetti and Geniaux (2017) for approximate ML estimation. However, the estimator proposed by Klier and McMillen (2008) (a linearization of the GMM proposed by Pinkse and Slade, 1998) has good properties only if the true autocorrelation coefficient is small.…”

Section: Binary Variablesmentioning

confidence: 99%

See 2 more Smart Citations

Spatial Limited Dependent Variable Models: A Review Focused on Specification, Estimation, and Health Economics Applications

Billé

Arbia

2019

Journal of Economic Surveys

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Modeling individual choices is one of the main aim in microeconometrics. Discrete choice models have been widely used to describe economic agents' utility functions and most of them play a paramount role in applied health economics. On the other hand, spatial econometrics collects a series of econometric tools, which are particularly useful when we deal with spatially distributed data sets. Accounting for spatial dependence can avoid inconsistency problems of the commonly used statistical estimators. However, the complex structure of spatial dependence in most of the nonlinear models still precludes a large diffusion of these spatial techniques. The purpose of this paper is then twofold. The former is to review the main methodological problems and their different solutions in spatial nonlinear modeling. The latter is to review their applications to health issues, especially those appeared in the last few years, by highlighting the main reasons why spatial discrete neighboring effects should be considered and suggesting possible future lines of development in this emerging field. Particular attention has been paid to cross‐sectional spatial discrete choice modeling. However, discussions on the main methodological advancements in other spatial limited dependent variable models and spatial panel data models are also included.

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“…From the model specification in Equation , at least three nested‐model specifications can be derived. By letting

bold-italicθ = 0

and for notational convenience

{boldW}_{1, n} = {boldW}_{n}

\begin{matrix} true \\ right {boldy}_{n}^{*} & = & left ρ W_{n} y_{n}^{*} + X_{n} β + u_{n}, u_{n} = λ M_{n} u_{n} + ε_{n}, ε_{n} \sim N_{n} (() {bold0}_{n}, {normalΣ}_{ε}) \\ right {boldy}_{n} & = & left I_{n} (() {boldy}_{n}^{*} > {bold0}_{n}) . \end{matrix}

Additional conditions are needed for the identification of

(ρ, λ)

in a SARAR(1,1)–probit model. Specifically,

M_{n}

and

W_{n}

Section: Sdc Model Specificationsmentioning

confidence: 99%

Section: Spatial Binary Probit Modelsmentioning

confidence: 99%

Section: Binary Variablesmentioning

confidence: 99%

See 1 more Smart Citation

Spatial Limited Dependent Variable Models: A Review Focused on Specification, Estimation, and Health Economics Applications

Billé

Arbia

2019

Journal of Economic Surveys

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show abstract

“…The Generalised Method of Moment (Pinkse and Slade, 1998); maximum Likelihood using the Expectation-Maximization algorithm (McMillen, 1992) or Bayesian Gibbs sample approach proposed by LeSage (2000). In this paper we use the procedure based on conditional maximum Likelihood recently developed by Martinetti and Geniaux (2017) because is very efficient and reliable since conditional estimators outperform the respective full-likelihood estimators.…”

Section: Type II Spatial Probit Modelmentioning

confidence: 99%

The impact of geographical factors on churn prediction: an application to an insurance company in Madrid's urban area

Llave

Hernández

Angulo

2018

Scandinavian Actuarial Journal

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Geography has previously been noted as a decisive factor in business literature. This paper provides evidence of the significant role geography plays in customer lapse behaviour in an urban environment. This novel approach is based on the idea that the customers who cancel all policies and leave the company are not randomly distributed; rather, a mimetic performance of close individuals is noted. The physical proximity of the customer to the geographical focus (strategical centre, as insurance offices) and the interaction with nearby customer are spatial factors that increase (or decrease) the probability of churning. An empirical analysis using more than 7,000 spatially georeferenced offline customers of a Spanish insurance company in the urban area of Madrid (Spain) demonstrated that the customer's proximity to offices of such insurance company under study decreases the probability of churning, whereas high lapse risk was detected in customers in the surroundings of the company's competitor branches. In addition, we identified spatial autocorrelation in churn probability, thus demonstrating that the probability of churn of a customer increases if nearby customers churn.

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“…Despite its power, the MARS algorithm is still seldom used in spatial economics. To the best of our knowledge, there are only two regional economics studies using MARS: Martinetti and Geniaux (2017) and De la Llave et al (2019). However, both cases only apply the MARS algorithm to make an automatic pre-selection of non-spatial variables and not to select spatial term in a model with spatial effects.…”

Section: Introductionmentioning

confidence: 99%

The MARS Algorithm in the Spatial Framework: Non-Linearities and Spatial Effects in Hedonic Models

Hernández

Kholodilin

2020

SSRN Journal

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Multivariate Adaptive Regression Spline (MARS) is a simple and powerful non-parametric technique that automatizes the selection of non-linear terms in regression models. Non-linearities and spatial effects are natural characteristics in numerous spatial hedonic pricing models. In this paper, we propose using the MARS data-driven methodology combined with the Instrumental Variables method in order to account for potential non-linearities and spatial effects in hedonic models. Using a large data set of more than 6,000 dwellings in Hamburg and about 17,000 in St. Petersburg, we confirm the presence of both effects (non-linearities and spatial autocorrelation). The results also show that there is a non-linear effect of the prices of neighboring houses on the price of each house. High prices for neighboring houses have a lower impact on the house price than low prices of neighboring houses. Finally, an extensive Monte Carlo exercise evaluates the ability of MARS to incorporate the correct spatial spillover terms in spatial regression models simultaneously including at same time non-linear effects.

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Approximate likelihood estimation of spatial probit models

Cited by 46 publications

References 47 publications

Spatial Limited Dependent Variable Models: A Review Focused on Specification, Estimation, and Health Economics Applications

Spatial Limited Dependent Variable Models: A Review Focused on Specification, Estimation, and Health Economics Applications

The impact of geographical factors on churn prediction: an application to an insurance company in Madrid's urban area

The MARS Algorithm in the Spatial Framework: Non-Linearities and Spatial Effects in Hedonic Models

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