Semi-functional partial linear spatial autoregressive model

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.

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.

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

Retracted: Evaluation and Numerical Simulation of Music Education Informationization Based on the Local Linear Regression Method

The quality of object proposal plays an important role in boosting the performance of many computer vision tasks, such as, object detection and recognition. Due to the absence of manually annotated bounding-box in practice, the quality metric towards blind assessment of object proposal is highly desirable for singling out the optimal proposals. In this paper, we propose a blind proposal quality assessment algorithm based on the Deep Objectness Representation and Local Linear Regression (DORLLR). Inspired by the hierarchy model of the human vision system, a deep convolutional neural network is developed to extract the objectness-aware image feature. Then, the local linear regression method is utilized to map the image feature to a quality score, which tries to evaluate each individual test window based on its k-nearest-neighbors. Experimental results on a large-scale IoU labeled dataset verify that the proposed method significantly outperforms the state-of-the-art blind proposal evaluation metrics.

Event detection has an important role in detecting the switching of the state of the appliance in the residential environment. This paper proposed a robust smoothing method for cepstrum estimation using double smoothing i.e. the cepstrum smoothing and local linear regression method. The main problem is to reduce the variance of the home appliance peak signal. In the first step, the cepstrum smoothing method removed the unnecessary quefrency by applying a rectangular window to the cepstrum of the current signal. In the next step, the local regression smoothing weighted data points to be smoothed using robust least squares regression. The result of this research shows the variance of the peak signal is decreased and has a good performance with better accuracy. In noise enviromment, performance prediction quite good with values greater than 0.6 and relatively stable at values above 0.9 on SNR> 25 for single appliances. Furthermore, in multiple appliances, performance prediction quite good at SNR> 20 and begins to decrease in SNR <20 and SNR> 25.

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。

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.

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.

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.

Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias

In this paper we study a statistical method of implementing quasi-Bayes estimators for nonlinear and nonseparable GMM models, that is motivated by the ideas proposed in Chernozhukov and Hong (2003) and Creel and Kristensen (2011) and that combines simulation with nonparametric regression in the computation of GMM models. We provide formal conditions under which frequentist inference is asymptotically valid and demonstrate the validity of the use of posterior quantiles. We also show that in this setting, local linear regression methods have theoretical advantages over kernel methods that are also reected in nite sample simulation results. Our results also apply to both exactly and over identied models. These estimators do not need to rely on numerical optimization or Markov Chain Monte Carlo simulations. They provide an eective compliment to the classical M-estimators and to MCMC methods, and can be applied to both likelihood based models and method of moment based models.

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.

Introduction: Research suggests obesity may be transmitted through social networks. A possible pathway is social influence on food choice. We investigated peer influence on the healthfulness of worksite food choices using social network analysis in a large hospital employee population, hypothesizing that socially-connected employees’ food choices would be correlated. Methods: Data on all food purchases in 2016 were obtained from the hospital’s cash register database. The cafeteria system uses traffic light labels to mark foods as healthy (green), less healthy (yellow), or unhealthy (red). Employees’ food purchases were identified through the use of cafeteria debit cards; social ties among employees were inferred based on a validated algorithm using demographics and time/location of purchases. We used spatial autoregression (SAR) and generalized estimating equation (GEE) models to calculate associations between the proportions of employees’ and coworkers’ purchases that were labeled green (or red). SAR models assessed concurrent purchases of an employee and coworker, weighting the association between their purchases by the frequency and inferred strength of the social tie. GEE models assessed longitudinal relationships between purchases coworkers’ made in the presence of an employee in one 8-week period and the employee’s purchases in the next 8-week period. Food and beverages were analyzed separately. Models adjusted for employee and coworker confounders (age, sex, race/ethnicity, job type, education). Results: In all, 5,118 employees used cafeteria debit cards to make purchases. Up to 536,240 employee/coworker interactions were observed, depending on the model (SAR, GEE) and outcomes (green/red, food/beverages). SAR models showed that a 1 percentage point increase in the network-weighted average of coworkers’ green-labeled (healthy) food purchases was associated with a 0.39 percentage point increase in an employee’s concurrent green-labeled food purchases (p<.001). Positive associations were also observed for red foods (0.20), and green (0.14) and red (0.31) beverages (all p<.001). Longitudinal GEE models showed that employees, as a population, increased purchases of green-labeled items by 0.013 percentage points on average when coworkers with whom they visited cafeterias in the prior 8 weeks increased their purchases of green items by 1 percentage point (p<.001). Similar associations were observed for red foods (0.013), and for green (0.006) and red beverages (0.020) (all p<.003). Conclusions: Employees’ healthy and unhealthy food choices are correlated. Although one explanation is that people eat with others who have similar preferences, the longitudinal findings suggest that people create social norms for eating that influence peers. Worksite and other social networks may be novel targets for population-level interventions to promote healthy diet.