Spatial autoregression modeling of site-specific wheat yield

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.

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

Purpose – The aim of this study is to examine some of the antecedents and consequences of psychological empowerment among Singaporean IT employees.Design/methodology/approach – Ninety‐nine employees from the Singaporean subsidiary of an American multinational organisation participated in this study. An ordinary least square (OLS) regression analysis was used to investigate the role of access to information, employee participation, supervisory social support and job security on predicting psychological empowerment. OLS regression was used also to examine the role of psychological empowerment on organisational commitment and job satisfaction. Moderated multiple regression was used to assess the moderating effect of supervisory social support on the relationship between job satisfaction and psychological empowerment.Findings – The findings of this study have shown that several factors are antecedents of psychological empowerment and that empowerment can increase organisational commitment and job satisfaction...

An assumption of ordinary least squares (OLS) is constant variance across the domain of a regressor. Often, however, the random error term variance is not constant when modeling biological data and therefore weighted least squares (WLS) is commonly used to estimate parameters. Less emphasis is placed on observations of the dependent variable with larger variances when using WLS, which is thought to produce more “efficient” parameter estimates. Statisticians often use WLS instead of OLS when the random error variance is not constant. However, as natural resource managers, we are often most interested in values of the dependent variable where the variance is greatest. What then are the biological, economic, and management implications of using WLS versus OLS in natural resource modeling? In this article, parameters of the combined-variable volume equation were estimated for individual trees in loblolly pine plantations using both OLS and WLS. A growth-and-yield model was used to predict stand development over time of two planting densities (303 and 1,090 seedlings/ac) and individual tree volumes were predicted using OLS and WLS parameter estimates. Economic analyses were then conducted. Our results show that the choice of OLS or WLS can have a substantial impact on predicted economic returns. Thus, when using WLS, landowners may decide to invest in additional management treatments that may, in fact, not be economically feasible. This study provides further evidence that landowners need to be aware of model structures when basing harvest-age decisions on growth and yield projections.

Regional regression models can be employed to estimate hydrologic statistics at ungauged river sites. The increased availability of watershed characteristics and the use of GIS-based methods to process this data have created situations where a large number of highly correlated watershed characteristics are available as potential model explanatory variables. The use of ordinary least squares (OLS) regression procedures with highly correlated variables can produce multicollinearity, creating highly sensitive parameter estimators with inflated variances, and improper model selection. A Monte Carlo simulation is developed to compare four techniques for handling multicollinearity: OLS, OLS with Variance Inflation Factor screening (VIF), principal component regression (PCR), and partial least squares regression (PLS). Results show the impact of multicollinearity is magnified at smaller samples sizes, higher correlations, and larger model error variances. Although PCR and PLS yield parameter estimators with reduced variances, there is no improvement in model prediction compared to OLS and VIF. Using VIF for screening variables produced small improvements in model predictions. The use of OLS appears warranted as the complexity of using biased regression techniques to address multicollinearity does little to improve model predictions.

This research article primarily focuses on the estimation of parameters of a linear regression model by the method of ordinary least squares and depicts Gauss-Mark off theorem for linear estimation which is useful to find the BLUE of a linear parametric function of the classical linear regression model. A proof of generalized Gauss-Mark off theorem for linear estimation has been presented in this memoir. Ordinary Least Squares (OLS) regression is one of the major techniques applied to analyse data and forms the basics of many other techniques, e.g. ANOVA and generalized linear models [1]. The use of this method can be extended with the use of dummy variable coding to include grouped explanatory variables [2] and data transformation models [3]. OLS regression is particularly powerful as it relatively easy to check the model assumption such as linearity, constant, variance and the effect of outliers using simple graphical methods [4]. J.T. Kilmer et.al [5] applied OLS method to evolutionary and studies of algometry.

This research examines the factors that influence health-related stereotypes against immigrants, with a focus on how human capital, conservative ideology, and economic anxiety impact these perceptions across different immigrant groups in the United States. The study uses Ordinary Least Squares (OLS) regression analysis of data from the 2020 Collaborative Multi-racial Post-Election Survey to assess attitudes towards all immigrants, as well as specifically Mexican and Chinese immigrants. Objective: Health stereotypes often depict immigrants as carriers of diseases and burdens on society, which affect public opinion and policy. This study aims to analyze the roles of human capital, political ideology, and economic conditions in shaping these stereotypes. Method: Using OLS regression, the analysis explores the association between stereotyping and various predictors, including conservative ideology (measured objectively and subjectively), human capital, and economic anxiety. Disaggregating the data by immigrant group allows for nuanced insights into the interplay of these factors. Results: The results reveal moderate levels of stereotyping across all groups, with variations by immigrant origin. Objective measures of conservative ideology show a strong correlation with increased stereotyping, particularly against Mexican immigrants. Higher human capital is associated with reduced stereotyping, while economic anxiety consistently exacerbates negative stereotypes across all groups. Furthermore, Republican affiliation and racial identity are correlated with heightened stereotyping, especially against Chinese immigrants. Discussion: The findings highlight the complexity of the factors contributing to health-related stereotypes and emphasize the importance of addressing educational and economic elements to mitigate these biases. Tailored interventions that take into account the distinct dynamics of each immigrant group are crucial for reducing stereotypes and improving integration and health outcomes.

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.

The general purpose of this study was to conduct a spatial analysis of the dynamics of rural land values in Louisiana. Specifically, spatial econometric procedures and hedonic price analysis were used to evaluate the impact of land characteristics on land prices across rural land markets in Louisiana. Initially, hedonic models were estimated by ordinary least squares (OLS) procedures to test for the presence of spatial autocorrelation using Lagrange Multiplier tests. Results suggested that there was spatial autocorrelation in the error terms. Hedonic models were then estimated using maximum likelihood (ML) spatial error techniques. Log likelihood numbers and likelihood ratio tests where used to compare OLS and ML model estimation, and the ML was better for these data. Information for this study includes sales that were collected for the time period January 1, 1993 through June 30, 1998, and data collected as a part of this study for the period July 1, 1998 through June 30, 2002. Data on 3,542 Louisiana rural land sales were collected during the two periods using mail survey techniques. Geo-reference of these sales indicated that sales were evenly dispersed throughout the state. Results from the data indicate that there is a substantial variation in rural real estate prices across the state. Results from hedonic model estimation showed that cropland, pastureland, government program cotton base acreage, month of sale, value of improvements, paved road access, reasons for purchase residential, commercial and investment; residential, commercial, and highway influences; statistical metropolitan areas, and inverse of travel time had statistically significant positive influences on per acre land values. Meanwhile, size of tract, distance to nearest town, travel time to nearest town, flood influence, and reasons for purchase farm expansion and recreational had a statistically significant inverse relationship with per acre rural land values. Marginal implicit prices were estimated using the results from models estimated by OLS and ML spatial procedures. Results indicated that, in several instances, marginal implicit prices were overestimated or underestimated when using results from OLS estimation. In general, spatial econometric techniques can be used to improve the accuracy of rural land value estimates.

Problem statement: In the presence of multicollinearity, the estimation of parameters in multiple linear regression models by means of Ordinary Least Squares (OLS) is known to suffer severe distortion. An alternative approach was to use the modified OLS which was based on the latent roots and latent vectors of the correlation matrix of the independent and dependent variables. This procedure is called the Latent Root Regression (LRR) which serves the purpose to improve the stability of the estimates for data plagued by multicollinearity. However, there was evidence that the LRR estimators were easily affected by a few atypical observations that we call outliers. It is now evident that the robust method alone cannot rectify the combined problems of multicollinearity and outliers. Approach: In this study, we proposed a robust procedure for the estimation of the regression parameters in the presence of multicollinearity and outliers. We called this method Latent Root-M based Regression (LRMB) because here we employed the weight of the M-estimator in the weighted correlation matrix. Numerical examples and some simulation studies were presented to illustrate the performance of the newly proposed method. Results: Results of the study showed that the LRMB method is more efficient than the existing methods. Conclusion/Recommendations: In order to get a reliable estimate, we recommend using the LRMB when both multicollinearity and outliers are present in the data.

Common econometric estimators such as least squares, least absolute deviations (LAD), instrumental variables, maximum likelihood, and semiparametric estimators are non-robust against data contamination. Despite the known superiority of high-breakdown point (HBP) estimators in such situations, the HBP estimators have rarely been used in economics. This article presents some applications of an HBP estimator called the S-estimator (Rousseeuw and Yohai, Robust and Nonlinear Time Series Analysis (Eds) W.H. Franke and R.D. Martin, Springer-Verlag, NY, pp. 256–72, 1984) to the estimation of a linear regression model and compares the results with those obtained by ordinary least squares (OLS) and LAD methods. It is found that significance of variables as well as signs of coefficient estimates can be quite different under HBP estimation than under OLS and LAD estimation.

The urban heat island (UHI) effect is an important topic for many cities across the globe. Previous studies, however, have mostly focused on UHI changes along either the spatial or temporal dimension. A simultaneous evaluation of the spatial and temporal variations is essential for understanding the long-term impacts of land cover on the UHI. This study presents the first evaluation and application of a newly developed spatiotemporal weighted regression framework (STWR), the performance of which was tested against conventional models including the ordinary least squares (OLS) and the geographically weighted regression (GWR) models. We conducted a series of simulation tests followed by an empirical study over central Phoenix, AZ. The results show that the STWR model achieves better parameter estimation and response prediction results with significantly smaller errors than the OLS and GWR models. This finding holds true when the regression coefficients are constant, spatially heterogeneous, and spatiotemporally heterogeneous. The empirical study reveals that the STWR model provides better model fit than the OLS and GWR models. The LST has a negative relationship with GNDVI and LNDVI and a positive relationship with GNDBI for the three years studied. Over the last 20 years, the cooling effect from green vegetation has weakened and the warming effect from built-up features has intensified. We suggest the wide adoption of the STWR model for spatiotemporal studies, as it uses past observations to reduce uncertainty and improve estimation and prediction results.

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.

Ordinary least-squares (OLS) regression is routinely applied by transportation analysts to forecast energy use, trip attractions, trip productions, automobile emissions, VMT growth, pavement condition, and accident occurrence to name a few examples. An important challenge when estimating OLS models is to derive an appropriate specification. Common misspecification errors include omission of important variables, inclusion of irrelevant variables, and inclusion of variables in an incorrect functional form. These errors often produce biased parameter estimates, inefficient parameter estimates, and an inability to conduct accurate hypothesis tests. Analysts typically rely on previous empirical research, a priori knowledge, and underlying theory to identify acceptable model functional forms, to determine important interactions, and to derive defensible models. In exploratory research, however, the analyst rarely knows a priori the correct form of the relationships being modeled, and previous research illuminating the “correct” relationships is scant. This paper presents an iterative modeling method that combines desirable properties of OLS with a heuristic procedure known as hierarchical tree-based regression (HTBR). This combined approach, named iteratively specified tree-based regression (ISTBR), is shown to provide insight into data structure provided by hierarchical tree-based regression, while retaining the desirable parametric properties of OLS. ISTBR equips the modeler with improved tools for exploring and identifying alternative model specifications and affords the analyst insight into systematic patterns or “structure” in data that might otherwise go undetected. An example of the ISTBR approach is provided using trip generation data from Michigan.

Estimating fractional cointegration in the presence of polynomial trends