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

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.

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.

Applying an intertemporal multivariate probit model, we reveal complex complementarity and substitution effects as well as new insights on the drivers of adopting input-intensive and natural resource management (NRM) practices in rural Ethiopia. First, the latent factor that drives each practice is positively and significantly correlated across time, suggesting persistency in adoption decisions. Second, the significant synergies and tradeoffs between the input-intensive and NRM practices underscore that these practices are highly compatible and, hence the importance of promoting technology packages. Third, the covariates that drive adoption significantly differ between practices, reflecting the heterogeneity in farmer behavior. Farm size was associated with the adoption of several input-intensive and NRM practices while off-farm income has the reverse effect. These findings have significant implications for food security policy in sub-Saharan Africa.

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.

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。

Testing for random effects and serial correlation in spatial autoregressive models

Findings in the observational retail food environment and obesity literature are inconsistent, potentially due to a lack of adjustment for residual confounding. Using data from the CARDIA study (n = 12 174 person-observations; 6 examinations; 1985-2011) across four US cities (Birmingham, AL; Chicago, IL; Minneapolis, MN; Oakland, CA), we used instrumental-variables (IV) regression to obtain causal estimates of the longitudinal associations between the percentage of neighbourhood food stores or restaurants (per total food outlets within 1 km network distance of respondent residence) with body mass index (BMI), adjusting for individual-level socio-demographics, health behaviours, city, year, total food outlets and market-level prices. To determine the presence and extent of bias, we compared the magnitude and direction of results with ordinary least squares (OLS) and random effects (RE) regression, which do not control for residual confounding, and with fixed effects (FE) regression, which does not control for time-varying residual confounding. Relative to neighbourhood supermarkets (which tend to be larger and have healthier options than grocery stores), a higher percentage of grocery stores [mean = 53.4%; standard deviation (SD) = 31.8%] was positively associated with BMI [β = 0.05; 95% confidence interval (CI) = 0.01, 0.10] using IV regression. However, associations were negligible or null using OLS (β = -0.001; 95% CI = -0.01, 0.01), RE (β = -0.003; 95% CI = -0.01, 0.0001) and FE (β = -0.003; 95% CI = -0.01, 0.0002) regression. Neighbourhood convenience stores and fast-food restaurants were not associated with BMI in any model. Longitudinal associations between neighbourhood food outlets and BMI were greater in magnitude using a causal model, suggesting that weak findings in the literature may be due to residual confounding.

The linear regression model based on the ordinary least square (OLS) estimation is a commonly used method for crop yield predicting. But it is not adequate in many cases because spatial autocorrelation among variables may violate the underlying assumption that observations are independent. In this study, we compared the OLS regression model and the spatial autoregressive model for predicting corn yield in Iowa. The spatial autoregressive model indicated a significant improvement in model performance over OLS model. The spatial autoregressive model can provide better prediction than OLS model and is capable of adjusting the spatial autocorrelation, which is often ignored by the OLS model. The study demonstrated that NDVI and precipitation are the major predictors for forecasting corn yield in Iowa.

Over the past two decades, regions have been the primary scale for Australian natural resource management (NRM) planning. From the mid-1990s, regional NRM bodies have been established in each Australian state and territory, and charged by governments with responsibility for preparing regional NRM plans and coordinating their implementation in partnership with local groups. The form of this experiment with devolved NRM (Lockwood, Davidson, Curtis, Stratford, & Griffith, 2009: 169) has evolved through a succession of Australian Government policy changes and been the subject of numerous reviews and analyses. Academics, independent reviewers and auditors have analyzed governance quality across this polycentric system of national, state, regional and local institutions, interrogated its effectiveness and recommended remedies for the problems that their investigations have uncovered. However, despite NRM plans being the key instrument for translating both government policy and community aspirations into strategies to guide implementation of NRM action, comparatively few analyses have examined the quality of these plans. In this chapter we develop a framework for undertaking such an analysis, and apply it to a sample of regional NRM plans from different policy regimes and jurisdictions. We identify the strengths and limitations of regional NRM plans and their capacity to fulfill their role as the key instrument for incorporating strategic direction into NRM practice.

Detailed information about spatial distribution of soil properties is important in ecological modelling, environmental prediction, precision agriculture, and natural resources management, as well as land-use planning. In the present study, a recently developed method called geographically weighted regression (GWR) is applied to predict spatial distribution of soil properties (pH, soil organic matter, available nitrogen, available potassium) based on topographical indicators, climate factors, and geological stratum at a regional scale. In total, 1914 soil samples collected from a depth of 0–20 cm were used to calibrate and validate the models. Performances of the GWR models were compared with the traditional, ordinary least-squares (OLS) regression. The results indicated that the GWR models made significant improvements to model performances over OLS regression, based on F-test, coefficient of determination, and corrected Akaike information criterion. GWR models also improved the reliability of the soil–environment relationships by reducing the spatial autocorrelations in model residuals. Meanwhile, the use of GWR models disclosed that the relationships between soil properties and environmental variables were not invariant over space but exhibited significant spatial non-stationarity. Accordingly, the GWR models remarkably improved the prediction accuracies over the corresponding OLS models. The results demonstrated that GWR could serve as a useful tool for digital soil mapping in areas with complex terrain.

Spatial autoregression modeling of site-specific wheat yield

The study analyse sigma and beta convergence of provincial government revenues and expenditures in Indonesia (APBD) by using panel data 30 provinces over the period 2000-2012. The variables used in this study consists of real income per capita and the revenues and expenditures variables in the APBD. The study also included a spatial weights matrix to analyse dependency among provinces. Spatial weights matrix used consists of two types of weights, the real income per capita and the geographical distance. Testing for the presence of spatial dependency performed using Moran’s I. The model used in this study are spatial autoregressive model (SAM) and the spatial error model (SEM). The models are estimated using panel least squares, fixed effects, random effects, as well as both GMM first difference (GMM-DIFF) and system GMM (GMM-SYS). Based on sigma convergence approach, the results of the study showed that during the period of 2000-2012 occurred convergence on total revenue, income, tax, fund balance, total spending, employee spending, and goods spending, but not for the real income per capita. Estimation with beta convergence approach conducted on four variables as each sample (in per capita value), namely: total income, tax, total spending, and goods spending. Estimation with beta convergence is done by using additional explanatory variables which include: economic growth, the degree of openness, as well as economic growth. Based on the beta convergence approach, the study results indicate the occurrence of convergence on total income, tax, total spending, and goods spending. Estimates also lead to the conclusion that there are spatial dependencies between provinces either use distance and income per capita weight. Keywords: Sigma and Beta convergence, spatial weights, panel data, revenue and expenditure, the provincial budget (APBD)JEL Classification: H7,R1

Ordinary least-square (OLS) regression is fundamental to quantitative research in many ecological disciplines. However, spatially explicit methods have recently been proposed that allow the incorporation of spatial autocorrelation into ecological models. We compared the spatial error simultaneous autoregressive model (SARerr) and generalized least squares regression (GLS) with the results of simple and multiple OLS regressions, to analyze the relationship between white-tailed deer ( Odocoileus virginianus) population density and environmental conditions in two regions dominated by tropical dry forests in central Mexico. The spatially explicit methods presented better goodness of fit than the OLS regression; we also observed a miscalculation in the probabilities obtained with the OLS regression, which in this method led to an incorrect interpretation. In general, we suggest the application of spatially explicit methods to analyze species-habitat relationships when SAC is observed in model residuals. We also discuss the management implications of these results.

ABSTRACTThis article addresses the gap between demands for participatory approaches in natural resource management (NRM) policies and lack of such approaches in the work of environmental authorities. The analysis draws on practice theory, using the case of NRM practice created by Swedish County Administrative Board (CAB) officials. The data originate from officials’ reflections during courses designed to strengthen their participatory and collaborative competences. Based on practice theory, officials are seen as participants of a routinised practice in which their interpretations of their work and roles are socially constructed. The analysis shows that the objective of this practice is to protect nature and mitigate resistance from stakeholders through information. These interpretations have acquired a reified nature, making them taken for granted. This stabilises the practice, maintaining the gap between demands in national policies and their implementation. To enable change in the CAB practice, the objective constructed by officials needs to be reinterpreted to produce a rule of law that can be justified and which concurrently permits stakeholder participation. To achieve changes in NRM officials’ practice, these need to be seen in their institutional context and comprise the whole system, from international/EU auditing levels to Swedish CABs and the officials’ everyday activities.

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.