A robust M-estimation framework for spatial autoregressive models: loss function design and optimization strategies

Spatial autoregressive (SAR) models with varying coefficients are useful for capturing heterogeneous effects of the impacts of covariates as well as spatial interaction in empirical studies, and a wide range of popular models can be seen as its special cases, such as linear SAR models. In this study, we will propose a unified model selection method for the SAR model with varying coefficients to achieve two targets simultaneously: (1) variable selection (eliminate irrelevant covariates), and (2) identification of the covariates with constant effect among the relevant covariates. To do so, we follow the idea of group LASSO to incorporate two penalty functions to simultaneously do model selection and estimation. Monte Carlo experiments show that the proposed method performs well in finite samples. Finally, we illustrate the method with an application to the housing data of Chinese cities.

The Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces with the highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatial dependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regression minimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normally distributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR) is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in West Java in 2020 from the Central Bureau of Statistics. This study develops to modeling the Open Unemployment Level in all province in Indonesia using modified spatial autoregressive model with the quantile regression approach. This study compares the estimation results based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model is better than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by the presence of outlier data.

This paper studies the spatial autoregressive (SAR) model for cross-sectional data when the coefficient of the spatial lag of the dependent variable is near unity. We decompose the data generating process into an unstable component and a stable one, and establish asymptotic properties of QMLE, 2SLSE and linearized QMLE of the parameters. The estimator for the spatial effect has a higher rate of convergence, and the estimators for other parameters have the regular rate. The higher rate of convergence reflects how fast the spatial root converges to unity. In contrast to near unit root in time series, the estimators are all asymptotically normal. Similarly to the regular SAR model, QMLE and linearized QMLE are more efficient than 2SLSE. RÉCAPITULATIF la présente communication examine le modèle autorégressif spatial (SAR) pour données transversales lorsque le coefficient de décalage spatial de la variable dépendante est proche de l'unité. Nous décomposons le processus de production de données dans un composant instable et un composant stable, et nous établissons les propriétés asymptotiques de QMLE, 2SLSE et QMLE linéaire des paramètres. L'estimateur pour l'effet spatial présente un taux de convergence supérieur, et les estimateurs pour les autres paramètres présentent le taux normal. Le taux de convergence supérieur reflète la rapidité avec laquelle la racine spatiale converge vers l'unité. Par contraste à la racine proche de l'unité en série temporelle, les estimateurs sont asymptotiquement normaux. De faon similaire au modèle SAR normal, QMLE et QMLE linéaire sont plus efficaces que 2SLSE. EXTRACTO Este trabajo estudia el modelo autorregresivo espacial (SAR) para datos sesgados cuando el coeficiente del vector espacial de la variable dependiente es de casi unidad. Descomponemos el proceso de generación de datos en un componente inestable y uno estable, y establecemos propiedades asimptóticas del QMLE, 2SLSE y QMLE linealizado de los parámetros. El estimador del efecto espacial tiene un índice más alto de convergencia, y los estimadores de otros parámetros tienen el índice regular. El alto índice de convergencia refleja la rapidez con que la raíz espacial converge a unidad. En contraste con la raíz de casi unidad en series de tiempo, los estimadores son todos asimptóticamente normales. 摘要: 本文研究当因变量的空间滞后系数接近一时, 横截面数据的空间滞后 (SAR)模型。我们将数据生成过程分解为非稳定环节和稳定环节, 并确定了参数的 QMLE 2SLSE 和线性化 QMLE 的渐近特性。空间效应的估计量具有较高的收敛速率, 而其他参数的估计量具有正常的 速率。收敛速率越高, 表明空间根收敛成一的速度更快。与时间序列中的近似单位根相反, 估计量都具有渐近正态性。与常规SAR模型类似, QMLE 和线性化 QMLE 比 2SLSE 更有效率。

SummaryThis paper analyzes the endogeneity bias problem caused by associations of members within a network when the spatial autoregressive (SAR) model is used to study social interactions. When there are unobserved factors that affect both friendship decisions and economic outcomes, the spatial weight matrix (sociomatrix; adjacency matrix) in the SAR model, which represents the structure of a friendship network, might correlate with the disturbance term of the model, and consequently result in an endogenous selection problem in the outcomes. We consider this problem of selection bias with a modeling approach. In this approach, a statistical network model is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR model, we capture the correlation between the processes of network and outcome formation, and propose a proper estimation procedure for the system. We demonstrate that the estimation of this system can be effectively done by using the Bayesian method. We provide a Monte Carlo experiment and an empirical application of this modeling approach on the friendship networks of high school students and their interactions on academic performance in the Add Health data. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

Spatial auto-regressive (SAR) models are widely used in geosciences for spatial analyses; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of parameter and forecast estimates strongly depend on the structure of such matrices. The least squares (LS) method is the most flexible and can estimate systems of large dimensions; however, it is not consistent in the presence of multilateral (sparse) matrices. Instead, the unilateral specification of SAR models provides triangular weight matrices which allow good statistical properties to LS and enable the implementation of sequential prediction functions. In this paper we show the better performance in out-of-sample forecasting of unilateral SAR and LS with respect to multilateral and maximum likelihood (ML) methods. This conclusion is supported by extensive numerical simulations and applications to real geological data, both on regular lattice and irregular polygonal form.

This paper studies the fact that 37 percent of the internal migrants in China do not sign a labor contract with their employers, as revealed in a nationwide survey. These contract-free jobs pay lower hourly wages, require longer weekly work hours, and provide less insurance or on-the-job training than regular jobs with contracts. We find that the co-villager networks play an important role in a migrant's decision on whether to accept such insecure and irregular jobs. By employing a comprehensive nationwide survey in 2011 in the spatial autoregressive logit model, we show that the common behavior of not signing contracts in the co-villager network increases the probability that a migrant accepts a contract-free job. We provide three possible explanations on how networks influence migrants' contract decisions: job referral mechanism, limited information on contract benefits, and the mini labor union formed among co-villagers, which substitutes for a formal contract. In the sub-sample analysis, we also find that the effects are larger for migrants whose jobs were introduced by their co-villagers, male migrants, migrants with rural Hukou, short-term migrants, and less educated migrants. The heterogeneous effects for migrants of different employer types, industries, and home provinces provide policy implications.

Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to economics, medicine and meteorology, it becomes necessary to develop flexible SAR models with multiple data types. In this article, we integrate three types of covariates, functional, compositional and numerical, in an SAR model. The new model has the merits of classical functional linear models and compositional linear models with scalar responses. Moreover, we develop an estimation method for the proposed model, which is based on functional principal component analysis (FPCA), the isometric logratio (ilr) transformation and the maximum likelihood estimation (MLE) method. Monte Carlo experiments demonstrate the effectiveness of the estimators. A real dataset is also used to illustrate the utility of the proposed model.

표본조사에서는 일반적으로 지형학적 범위가 넓거나 흔히 우리가 알고 있는 지형적 범위 즉시 또는 도 단위로 표본설계가 이루어진다. 그러므로 지형학적 범위가 작은 소지역은 충분한 표본의 확보가 불가능하며 따라서 정확한 소지역 통계를 얻는 것은 매우 어렵다. 이러한 문제로 정확한 소지역 통계를 얻기 위한 연구가 활발히 진행되고 있다. 최근 신기일과 이상은(2003)은 공간통계 모형을 이용한 소지역 추정을 연구하였다. 본 논문은 신기일과 이상은(2003)의 공간자기회귀(Spatial Autoregressive: SAR) 모형을 확장한 모형인 베이지안 자기 포아송 모형 (Bayesian Auto-Poisson Model: BAPM)을 이용한 소지역 추정에 관하여 연구하였다. 분석에 사용된 자료는 호주의 1998년 장애인 통계 (Survey of Disability, Aging and Cares:SDAC)이 며 MSE, MB 그러고 회귀 분석을 이용한 편의 분석기법이 비교에 사용되었다. In sample survey sample designs are performed by geographically-based domain such as countries, states and metropolitan areas. However mostly statistics of interests are smaller domain than sample designed domain. Then sample sizes are typically small or even zero within the domain of interest. Shin and Lee(2003) mentioned Spatial Autoregressive(SAR) model in small area estimation model-based method and show the effectiveness by MSE. In this study, Bayesian Auto-Poisson Model is applied in model-based small area estimation method and compare the results with SAR model using MSE ME and bias check diagnosis using regression line. In this paper Survey of Disability, Aging and Cares(SDAC) data are used for simulation studies.

Planning a novel regional methane network: Demand forecasting and economic evaluation

Capturing household-level spatial influence in agricultural management using random effects regression

Testing for random effects and serial correlation in spatial autoregressive models

This paper analyzes the current situation of university English teaching and constructs a trinity of EGP+ESP+EIC multiple teaching innovation systems for university English based on the principles of English teaching innovation. In order to analyze this innovative teaching system of English, a stratified statistical model and a spatial autoregressive model are combined, and four ordinal stratified spatial autoregressive Probit models are innovatively constructed to model data where the dependent variable is ordinal, and there is a spatial dependency situation with a stratified structure. The analysis shows that in the process of continuous innovation of English teaching mode, the number of people who are dissatisfied with English teaching decreases by 30%, the number of people who are very satisfied increases by 35%, and the number of people who are very satisfied accounts for 42.5% of the total number of people and 90% of the total number of people who are satisfied in the final stage of innovation of English teaching in university. The English teaching innovation strategy for university students based on this study is feasible.

To reduce the operation and maintenance cost for wind farms, turbine operators are actively developing strategies to, among others, reduce service cost, maximise power production, and prolong lifetime of components and super-structure. All of these tasks require a wind farm model that can accurately predict turbine behaviours in response to the changing environment. Recent studies focus on developing data-based methods for predictive maintenance purposes. This paper proposes a data-based model that aims to capture the spatial and temporal wind variations across a wind farm, as a means to predict the interactions between operating turbines and the environment, which can be useful for wind farm performance monitoring. The proposed method is a Gaussian process-based spatial autoregressive model, which reflects our physical understanding of the wake effect while taking the advantage of a stochastic data-driven learner. In the case study of a simulated wind farm, the proposed model (named here a GP-SPARX model) provides the best predictive accuracy in comparison to two other spatial autoregressive regression models, showing its capability of capturing nonlinear correlations and its potential as a low-cost wake field predictor given inputs from weather station measurements.KeywordsSpatial autoregressive modelGP-SPARXWind turbine wake field modelling

Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models