A flexible spatial autoregressive modelling framework for mixed covariates of multiple data types

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.

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.

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。

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.

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.

A new class of [formula omitted]-transformations for the spatial analysis of Compositional Data

Spatial autoregressive (SAR) models are frequently applied in geographic research to account for spatial dependence. Although robust estimation methods (e.g. M-estimation) within SAR models have been investigated recently, key challenges remain: (1) How should the loss function be rationally designed in M-estimation for SAR models? (2) How can the scale parameter in M-estimation be evaluated? (3) How can the robust optimization problem be solved efficiently? In this research, we derived a closed-form bias-corrected least-squares estimator that outperforms the popular maximum likelihood estimator both numerically and statistically. We replaced the squared Euclidean norm with rational loss functions and then proposed an iteratively re-weighted least-squares scheme to attain a robust solution numerically. Simulation results demonstrate that our robust M-estimators, particularly redescending types, significantly improve estimation accuracy (reducing bias and root-mean-square error) and computational efficiency. In a real-world application with the Boston housing data, our method correctly identifies the underlying 22 outliers and increases the coefficient of determination from 0.78 to 0.90. Our future work will focus on enhancing computational performance through advanced optimization techniques.

One of the most robust empirical findings in political science is that in multiparty democracies cabinet ministries are distributed in rough proportion to parties’ legislative seat shares, a pattern known as Gamson’s Law. Yet existing research often overlooks the fact that portfolio and seat shares are compositional—mutually dependent parts of a whole. Standard methods treat them as unconstrained, risking bias, misleading uncertainty estimates, and flawed inference. Unfortunately, the most common strategy for handling compositions—the additive log-ratio (ALR) transformation combined with seemingly unrelated regression (SUR)—fails when the number and identity of compositional elements (like parties) vary across cases. We propose the isometric log-ratio (ILR) transformation—new to political science—as an alternative that both respects compositional geometry and adapts to differing compositional structures. Monte Carlo simulations show that ILR sharply outperforms standard approaches, reducing bias, improving coverage probability, and increasing statistical power. While we apply it to portfolio allocation, ILR provides a general solution for modeling compositional outcomes with other potential uses, including in electoral competition, where ALR+SUR has required strong assumptions or ad hoc adjustments. Using this improved methodology, we find that seat–portfolio proportionality is weaker overall than conventionally reported and varies substantially across governments.

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.

Research and analysis that are not only based on time (temporal) but also on space (spatial) require tools in the form of software to ensure that the data analysis and processing yield good, fast, and accurate results. One of the software tools that can be used for this purpose is RStudio software. The advantages of RStudio include being open-source software (OSS), which can be used freely without cost, and it has many packages and functions that can facilitate data processing. One of the spatial-based analyses is spatial data analysis. The structure within RStudio allows users to call functions related to spatial data analysis, perform computations with sparse matrices (matrices with many zero values), such as spatial weight matrices, estimation of spatial model parameters, and so on. This research examines the application of RStudio software in estimating the parameters of a first-order Spatial Autoregressive (SAR) model using the Maximum Likelihood Estimation (MLE) method on the data of the designation of Intangible Cultural Heritage (ICH) in Indonesia. Based on the results of applying RStudio software, a first-order SAR model with a Queen contiguity weight matrix for the categories of Traditional Customs, Rituals, and Celebrations (TCRC) and Performing Arts (PA) with the minimum Akaike Information Criterion (AIC) value and maximum pseudo- value was obtained for predicting the designation data of ICH in Indonesia. The application of RStudio software to the first-order SAR model for the designation data of ICH in Indonesia speeds up and simplifies calculations, making it suitable as a recommendation for relevant agencies such as the Department of Culture, Tourism, Youth, and Sports (Disbudparpora).

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.

Aggregating multiple types of complex data in stock market prediction: A model-independent framework

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.

Loadings and scores of principal component analysis are popularly displayed together in a planar graph, called biplot, with an intuitive interpretation. In case of compositional data, multivariate observations that carry only relative information (represented usually in proportions or percentages), principal component analysis cannot be used for the original compositions. They first need to be transformed using the centered logratio (clr) transformation. If outlying observations occur in compositional data, even the clr (compositional) biplot can lead to useless conclusions. A robust alternative biplot can be computed by using the isometric logratio (ilr) transformation, and by robustly estimating location and covariance. The robust compositional biplot has a big potential in many applications, like in geology, analytical chemistry, or social sciences.