Transfer learning for spatial autoregressive models with missing responses

Is It a Curse or a Blessing to Live Near Rich Neighbors? Spatial Analysis and Spillover Effects of House Prices in Beijing

Previous studies neglected the implicit information in the spatial pattern of the aerosol optical depth (AOD), such as spatial configuration characteristics, spatial heterogeneity and spatial dependence. The understanding of AOD is helpful in accurately estimating the environmental and climatic effects from aerosols. In this study, a method of spatial autocorrelation statistics from geostatistics was applied to investigate the spatial pattern of AOD in Hubei province in central China during the period 2003–2008. Spatial autoregressive models were used to quantize the correlations between AOD and affecting factors, such as elevation, forest coverage and population density. In addition, the difference between the standard linear regression model and the spatial models was discussed. The results were as follows: the spatial pattern of AOD in Hubei province shows significant spatial autocorrelation, indicating that AODs are clustered such that higher AODs tend to be surrounded by higher AOD neighbors, while lower AODs are surrounded by lower AOD neighbors, and the spatial autocorrelation scale of the AOD over Hubei is approximately 400 km. The high–high zone is mainly distributed in the Wuhan city circle and the Jianghan plain areas, while the low–low zones are mainly located in the middle and high mountain areas of northwest Hubei province. The overall degree and pattern of spatial autocorrelation do not change largely from 2003 to 2008, which indicates a stable spatial configuration of AOD. A significant negative spatial autocorrelation exists between AOD and elevation, which may suggest that AOD and elevation have an inverse spatial distribution, and the same applies for forest coverage. Population density and the AOD show a significant positive spatial autocorrelation, which may imply that they have similar spatial distribution, while industrial production and AOD do not show an obvious positive spatial autocorrelation. Spatial autoregressive models show better predictive ability and stability than the standard linear regression model because the spatial autocorrelation of the AOD is taken into consideration.

When employing the spatial diagnostics examined in Chapter 4, social scientists will often find evidence of spatial autocorrelation (see, e.g., Eff 2004). As discussed in Chapter 1, this predisposition of social science data toward spatial autocorrelation often results from interdependence between the units studied by social scientists. In other cases, social science data exhibit spatial dependence not as a result of behavioral interdependence but as a consequence of spatial clustering in the sources of behaviors of interest to social scientists. The spatial dependence, in short, may be consistent with either a spatial lag model or a spatial error model. Substantive theory will often lead scholars to believe that a spatial lag specification or a spatial error specification is more appropriate for their particular substantive application. Scholars may, for example, expect that a spatial diffusion process is at work and thus believe that a spatial lag model is warranted. Although such a specification may seem appropriate, such a theoretical expectation should not go untested. It would be inappropriate to estimate a diffusion model with a spatially lagged dependent variable if the spatial dependence diagnosed via, for example, the univariate Moran's I , is instead produced by spatial clustering in the sources of otherwise independent behaviors. This model misspecification will lead the researcher to inappropriate substantive inferences about the nature of the spatial dependence in her data. Inappropriate spatial model specification is all the more problematic because of the close mathematical relationship between a spatial lag model and a spatial error model with spatial autoregressive error dependence. As this chapter will discuss, a spatial autoregressive error model can be rewritten as a spatial Durbin model with both spatially lagged dependent and independent variables if a set of nonlinear common factor constraints are valid. Because of this close relationship between spatial autoregressive dependence in a spatial lag model and spatial autoregressive dependence in a spatial error model, a significant spatial parameter in a spatial lag model may reflect spatial clustering in omitted sources of the behavior of interest rather than true spatial lag dependence consistent with a diffusion process.

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

Testing for random effects and serial correlation in spatial autoregressive models

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 paper analyzes the determinants of apartments’ prices in Belo Horizonte, MG, Brazil, with the use of hierarchical models, spatial models and a hierarchical-spatial approach. Besides the apartments’ characteristics, such as area, age and building standard, prices were determined by local urban amenities. The hierarchical models indicated that local variables, such as urban violence, infrastructure and services, explained over 75% of prices’ remaining variability. The spatial models analyzed if, after controlling for price variability with the explanatory variables in the second level of the hierarchical models, spatial correlations still existed in price determination. The positive and significant spatial coefficient in spatial autoregressive models (SAR) indicated spatial dependency. The hierarchical-spatial approach showed that over 70% of apartment prices’ remaining variability could be explained by local variables and that the lagged urban services variable explained another 12% of this variability.

Introduction: Infant mortality rate (IMR) is one of the indicator of the success for maternal and child health programs. Infant mortality rates affected by biological, environmental, socioeconomic factors and quality of healthcare services. This study aimed to analyze the factors affecting infant mortality rates in the East Java Province using a spatial regression model.Methods: The research units were all 38 districts and cities in East Java Province. Secondary data from the 2023’ Health Profile of East Java Province was used in this study, which included the number of infant deaths and the biological, environmental, socioeconomic factors, the availability and quality of health services. In this study, spatial modelling was conducted using an area approach and spatial influence using the Spatial Autoregressive Moving Average (SARMA) method with Queen Contiguity spatial weights.Results: Based on R2 and AIC values, the Spatial Autoregressive model was preferable to Ordinary Least Squares. The obtained model showed that low birth weight and the percentage of the population that can access good sanitation were the significant factors influencing infant mortality in this study. The other factors: percentage of deliveries by health workers, obstetric complications handled, percentage of poor people, infants receiving vitamin A, and infants receiving exclusive breastfeeding had no significant effect on Infant Mortality Rates.Conclusion: Factors that had significant effect on infant mortality rates in this study were low birth weight and percentage of residents who had access to proper sanitation.

Stunting in children under 5 years of age is a condition where they have a length or height that is less than -2 standard deviations of the growth standard of Indonesian children. Stunting is caused by chronic malnutrition in the first 1000 days of life. The spatial panel data method was developed to solve problems related to spatial objects that are measured periodically by involving elements of area and time. The purpose of this study was to determine the best model and factors that influence stunting in children under 5 years of age in Indonesia using spatial panel data. The data used were from the website of the Central Statistics Agency and the publications of the Ministry of Health of the Republic of Indonesia in 2015-2019. Determination of the selected model is done by comparing the random effect spatial autoregressive model and spatial error model (SEM) random effect based on the value and Akaike information criterion (AIC). SEM random effect produces the largest value and the smallest AIC. The selected spatial panel data model in determining the factors that influence stunting in children under 5 years of age in Indonesia is the SEM random effect based on the largest and AIC compared to other models. Based on the selected model, children under five with malnutrition and poor nutrition, receiving Vitamin A, and the average monthly per capita expenditure on food have a significant effect on the percentage of stunting in children under five in Indonesia.

The spatial J ‐test ( SJ ‐test) and the spatial JA ‐test ( SJA ‐test) are outlined to determine the appropriate spatial weight structure for the spatial autoregressive model against a single, or a set of, non‐nested alternatives. These two non‐nested tests are based on the maximum likelihood framework and can be applied to both the simple spatial autoregressive model and the general spatial autoregressive model. The M onte C arlo simulation results showed that the SJ ‐test and the SJA ‐test had clearly distinct performance in determining the appropriate spatial weight structure for a spatial autoregressive model against a single alternative and against two alternatives. The SJ ‐test performed better than the SJA ‐test in failing to reject a true null hypothesis when compared against a single alternative, whereas the SJA ‐test performed better than the SJ ‐test in failing to reject a true hypothesis when compared against two alternatives. Therefore, the SJ ‐test should be applied to determine the spatial weight structure against a single alternative, and the SJA ‐test should be applied to determine the spatial weight structure against a set of alternatives. Performance improved with a larger sample size and with a larger magnitude of spatial autocorrelation. The power of the tests depended on the degree of similarity between the alternatives and the underling true structure. The power of the tests was likely to be lower with two alternatives rather than a single alternative. This is due to the introduction of a false spatial weight matrix into the alternative with the true spatial weight matrix. El artículo describe la prueba J espacial ( J‐test o SJ‐test ) y la prueba JA espacial prueba espacial ( SJA‐test ), las cuales son utilizadas para determinar la estructura de ponderación espacial apropiada para el modelo autorregresivo espacial frente a una alternativa nonestad única o frente a un conjunto de alternativas nonnested . Estas dos pruebas nonnested se basan en el marco de máxima verosimilitud ( máximum likelihood‐ ML) y se pueden aplicar tanto al modelo autorregresivo espacial simple como al modelo autorregresivo espacial general. Los resultados de la simulación Monte Carlo presentados aquí muestran que SJ‐test y SJA‐test tienen una performance claramente distintiva en cuanto a la determinación de la estructura espacial de ponderación apropiada para un modelo autorregresivo espacial versus una alternativa única y versus dos alternativas. El SJ‐test funcionó mejor que el SJA‐test al no rechazar una hipótesis nula verdadera cuando se compara con una alternativa única, mientras que el SJA‐test funcionó mejor que el SJ‐test al no rechazar una hipótesis verdadera cuando se le compara con dos alternativas. Por lo tanto, los autores concluyen que el SJ‐test se debe aplicar para determinar la estructura espacial de peso versus una alternativa única, mientras que la SJA‐test se debe aplicar para determinar la estructura espacial de ponderación versus un conjunto de alternativas. Los resultados de performance mejoraron con un tamaño de muestra más grande y con una magnitud mayor de autocorrelación espacial. El poder estadístico de las pruebas depende del grado de similitud entre las alternativas y la estructura espacial verdadera subyacente (la matriz). El poder estadístico de las pruebas analizadas tiende a ser inferior cuando las dos alternativas nonestad son utilizadas en lugar de la alternativa única. Esto se debe a la introducción de una matriz falsa de ponderación espacial en la alternativa que contiene la matriz verdadera de ponderación espacial. 本文阐述了空间J检验(SJ‐test)和JA检验(SJA‐test)，以确定在单个或者一系列非嵌套备择空间自回归模型中恰当的空间权重结构。两种非嵌套检验方法均基于最大似然框架，并可用于简单的和广义的空间自回归模型。蒙特卡洛模拟结果显示，在单个和两种备择方案下，SJ检验和SJA检验对空间自回归模型的空间权重结构的确定效果明显不同。与在单个备择方案比较时，SJ在未能拒绝真实零假设方面检验效果优于SJA检验；反之，在与两个备择方案比较时，SJA检验在未能拒绝真假设方面的效果则优于SJ检验。因此，SJ检验应该应用于单备择的空间权重结构确定，而SJA检验则应用于多备择的空间权重结构确定。当进行更大样本量和更大量级的空间自相关分析时，模型的性能和效果会得到提升。检验方法的能力取决于备择方案与下属真实结构的相似度，在具有两种（或多种）备择方案情况下，模型的检验能力会降低，并可能导致将错误的空间权重矩阵引入真实的空间权重结构矩阵构建中。

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies conservation planning.

If the ordinary least squares (OLS) diagnostics discussed in the previous chapter indicate the existence of spatial lag or spatial error dependence, the researcher will wish to model the type of dependence indicated by these diagnostics. If the OLS diagnostics indicate the presence of a diffusion process, the researcher will wish to estimate a spatial lag model via maximum likelihood (ML) estimation or an instrumental variables specification incorporating instruments for the spatially lagged dependent variable. Alternatively, if the OLS diagnostics indicate the existence of spatial error dependence, the researcher may choose to estimate a more fully specified OLS model to model the spatial dependence or may choose to employ a ML or generalized method of moments (GMM) approach incorporating the spatial dependence in the errors. The spatial dependence diagnosed via the diagnostics discussed in Chapter 5 may alternatively be produced by spatial heterogeneity in the effects of covariates. If this is the only source of spatial dependence, modeling this heterogeneity will be sufficient to capture the spatial dependence. As a consequence, any specification search should also consider the possibility of spatial heterogeneity, which is the focus of Chapter 7. This chapter will first, however, examine alternative approaches for modeling spatial dependence if spatial heterogeneity is not present. This chapter begins by examining ML estimation of spatial lag models that derives from Ord (1975). Next, I explore alternative instrumental variables and GMM estimators for spatial lag dependence. Next, I turn to approaches for estimating spatial error models. I conclude by considering areas of concern in the estimation of spatial models. These include estimators for large sample sizes and diagnostics for continued spatial dependence. MAXIMUM LIKELIHOOD SPATIAL LAG ESTIMATION The mixed regressive, spatial autoregressive model, or spatial lag model, extends the pure spatial autoregressive model considered in Section 3.2 to include also the set of covariates and associated parameters: y = ρ W y +Xβ+e where X is again an N by K matrix of observations on the covariates, β is a K by 1 vector of parameters, and the remaining notation is as discussed in Section 3.2.

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 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.

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.