Adaptive Handling of Dependence in High-Dimensional Regression Modeling

ABSTRACTThis article considers both Partial Least Squares (PLS) and Ridge Regression (RR) methods to combat multicollinearity problem. A simulation study has been conducted to compare their performances with respect to Ordinary Least Squares (OLS). With varying degrees of multicollinearity, it is found that both, PLS and RR, estimators produce significant reductions in the Mean Square Error (MSE) and Prediction Mean Square Error (PMSE) over OLS. However, from the simulation study it is evident that the RR performs better when the error variance is large and the PLS estimator achieves its best results when the model includes more variables. However, the advantage of the ridge regression method over PLS is that it can provide the 95% confidence interval for the regression coefficients while PLS cannot.

Purpose This study aims to contribute to the ongoing assessment of executive compensation by investigating the nexus between managerial entrenchment factors, adopting a multifaceted perspective encompassing both economic and non-economic dimensions. Design/methodology/approach This research employs pooled cross-sectional Ordinary Least Squares (OLS) regression and Least Squares with Dummy Variables (LSDV) models with fixed effects to examine the determinants of Chief Executive Officer (CEO) compensation. Findings This research identifies firm size, performance (via ROA and Tobin’s Q), and CEO characteristics (age, tenure, stock ownership, MBA degree) as significant determinants of executive compensation at the 0.05 level. In contrast, the prestige of educational institutions, doctoral degrees, and the MBA’s relevance to short-term performance, along with CEO tenure, do not significantly affect pay. Additionally, the study highlights the significance of industry type (manufacturing vs technology) in shaping compensation, emphasizing the role of firm metrics and CEO credentials in designing executive pay packages. Originality/value This research introduces an innovative approach to controlling unobserved heterogeneity and adjusting for the dynamic nature of CEO compensation attributes across diverse CEO characteristics. By integrating both pooled Ordinary Least Squares (OLS) and Least Squares Dummy Variable (LSDV) models, the study addresses the challenges posed by time-invariant variables and unobservable heterogeneity. Such issues have historically skewed the accuracy of traditional OLS models in identifying the comprehensive array of factors—both economic and non-economic—that influence CEO compensation. This novel methodological framework significantly advances the examination of unobservable variables that may vary not only across the firms selected for analysis but also over time periods, thereby offering a more detailed understanding of the determinants of CEO pay.

The objective of this study was to compare the predictions of the protein contents and hardness values by partial least squares regression (PLSR) and principal components regression (PCR) models for bulk samples of Canadian wheat, which were obtained from different locations and crop years. Wheat samples of Canada Western Red Spring (CWRS), Canada Western Hard White Spring (CWHWS), Canada Western Soft White Spring (CWSWS), and Canada Prairie Spring Red (CPSR) classes were obtained from nearby agricultural farms in the main wheat growing locations in the Provinces of Alberta, Saskatchewan, and Manitoba from 2007, 2008, and 2009 crop years. Wheat samples were conditioned to moisture levels of 13, 16, and 19 % (wet basis) and pooled together for developing the regression models. A database of the near-infrared (NIR) hyperspectral image cubes of bulk samples of wheat classes was created in the wavelength region of 960–1,700 nm with 10 nm intervals. Reference protein contents and hardness values were determined using the Dumatherm method and single kernel characterization system (SKCS), respectively. A tenfold cross-validation was used for the ten-factor partial least squares regression (PLSR) and principal components regression (PCR) models for prediction purposes. Prediction performances of regression models were assessed by calculating the estimated mean square errors of prediction (MSEP), standard error of cross-validation (SECV), and correlation coefficient (r). Using the full data set in the protein prediction study, the ten-component PLSR model gave 1.76, 1.33, and 0.68 for the estimated MSEP, SECV, and r, respectively, which were better than the results for the ten-component PCR model (2.02, 1.42, and 0.62, respectively). For the hardness prediction, the estimated MSEP, SECV, and r values were 147.7, 12.15, and 0.82, respectively, for the ten-component PLSR model using the full data set. The PLSR models prediction performances outperformed the PCR models for predicting protein contents and hardness of wheat.

Background: A review of the health behavior literature on the statistical modeling of days of physical activity (PA) indicates that in many instances linear regression models have been used. It is inappropriate statistically to model a count dependent variable such as days of physical activity with Ordinary Least Squares (OLS). Many count variables have skewed distributions, and, also, have a preponderance of zeroes. Count variables should not be treated as continuous and unbounded. If OLS is used, estimations of the regression will frequently turn out to be inefficient, inconsistent and biased, and such outcomes could well have incorrect impacts on health programs and policies. Methods: We considered three statistical methods for modelling the distribution of days of PA data for respondents in the 2013 Health Information Trends Survey (HINTS). The three regression models analyzed were: Ordinary Least Squares (OLS), Negative Binomial (NBRM), and Zero-inflated Negative Binomial (ZINB). We used the exact same predictor variables in the three models. Our results illustrate the differences in the results. Results: Our analyses of the PA data demonstrated that the ZINB model fits the observed PA data better than either the OLS or the NBRM models. The coefficients and standard errors differed in the zero-inflated count models from the other models. For instance, the ZINB coefficient for the association between income and PA behavior was not statistically significant (p>0.05), whereas in the NBRM and in the OLS models, it was statistically significant (p<0.05). Conclusions: The inappropriate use of regression models could well lead to wrong statistical inferences. Our analyses of the number of days of moderate PA demonstrated that the ZINB count model fits the observed PA data much better than the OLS model and the NBRM.

This study investigates the interconnections among sustainability reporting, social performance, and firm value across the BRICS nations (Brazil, Russia, India, China, and South Africa). Employing a quantitative research design, the study utilizes firm-level data from the Refinitiv database, covering 862 firms operating in the BRICS countries from 2017 to 2022. The analysis begins with Ordinary Least Squares (OLS) regression and extends to models incorporating year-fixed effects and firm-fixed effects to account for heterogeneity and omitted variable bias. Robustness checks are conducted using OLS regression with robust standard errors, fixed effects regression with Driscoll–Kraay standard errors, and an instrumental variable approach to address potential endogeneity concerns. To examine the moderating role of sustainability reporting, interaction terms are incorporated into the regression models and margin plots are used for visualization. The findings reveal that social performance positively impacts firm value, underscoring the role of social responsibility in driving financial performance. Furthermore, sustainability reporting strengthens this relationship, indicating that firms with well-established reporting frameworks can effectively leverage social initiatives to enhance market valuation. Therefore, this study contributes to the literature by providing empirical evidence on the moderating effect of sustainability reporting in emerging markets. The findings offer valuable implications for policymakers, investors, and corporate leaders seeking to optimize CSR strategies and enhance firm value in dynamic economic environments.

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.

Partial Least Squares - Diffusion Tensor Imaging (PLS-DTI): A novel approach for biomarker imaging in breast cancer

The relationship between stock trading volume and stock price has been widely debated, with prior research reporting both positive and negative correlations. Understanding this relationship is essential for identifying potential arbitrage opportunities and anticipating market movements. This study examines the correlation between trading volume and price by applying an Ordinary Least Squares (OLS) regression model specifically to index fund data. The analysis reveals a modest correlation of 3.25%, with an adjusted value of 3.22%, suggesting that while the relationship is weak, the variables are not statistically independent. Additionally, the results indicate that, for the given dataset, the Laplacian error metric offers a better fit than the Gaussian metric. These findings provide a nuanced perspective on volume–price dynamics and highlight the potential benefits of alternative error modeling approaches in financial time series analysis.

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.

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.

Though agriculture continues to dominate the national economy of Ethiopia, both in terms of overall agricultural production and productivity, the sector suffers from major structural problems. The majority of farmers in Ethiopia are smallholders, producing mostly for own consumption and generating only a small marketed surplus. This study tries to assess the major determinants of marketed surplus particularly Niger seed. To conduct the study, both primary and secondary data sources were used. A multi stage sampling technique were applied to collect primary data from 120 small farm households. The study employed both descriptive statistics and econometrics model in the analysis of the data. Ordinary Least Squares(OLS) method were applied to assess the determinants of Niger seed marketed surplus in the study area. Prior to OLS estimation, the explanatory variables were tested for Multicollinearity and Heteroscedasticity. The result of the regression analysis shows that age of the households, Tropical livestock holdings, and farm size of the households significantly affects Niger seed marketed surplus in the study area. Keywords: Niger Seed, Marketed Surplus, Households, Wollega, Ethiopia DOI: 10.7176/JESD/11-9-02 Publication date: May 31 st 2020

Spatial autoregression modeling of site-specific wheat yield

This study explores the interplay between intellectual capital (IC), digital transformation (DT), and innovation in Chinese manufacturing firms, emphasizing the moderating role of DT. Utilizing data from Shenzhen Stock Exchange-listed firms from 2013 to 2023, the research employs Ordinary Least Squares (OLS) and Partial Least Squares (PLS) regression models to test the hypotheses. The findings reveal that DT significantly enhances the positive effect of IC on innovation. The study underscores the importance of fostering IC through human, structural, and relational capital and leveraging DT to maximize innovative outcomes. These insights are particularly relevant for policymakers and business leaders aiming to boost innovation in the knowledge economy. The results advocate for regulatory frameworks and incentives that support innovation driven by IC and DT, highlighting the substantial economic benefits these elements can bring. This research contributes to a deeper understanding of how IC and DT interact to drive innovation, offering valuable implications for technology management, entrepreneurship, and economic policy.

With the fast urbanization process, how does the vegetation environment change in one of the most economically developed metropolis, Shanghai in East China? To answer this question, there is a pressing demand to explore the non-stationary relationship between socio-economic conditions and vegetation across Shanghai. In this study, environmental data on vegetation cover, the Normalized Difference Vegetation Index (NDVI) derived from MODIS imagery in 2003 were integrated with socio-economic data to reflect the city’s vegetative conditions at the census block group level. To explore regional variations in the relationship of vegetation and socio-economic conditions, Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models were applied to characterize mean NDVI against three independent socio-economic variables, an urban land use ratio, Gross Domestic Product (GDP) and population density. The study results show that a considerable distinctive spatial variation exists in the relationship for each model. The GWR model has superior effects and higher precision than the OLS model at the census block group scale. So, it is more suitable to account for local effects and geographical variations. This study also indicates that unreasonable excessive urbanization, together with non-sustainable economic development, has a negative influence of vegetation vigor for some neighborhoods in Shanghai.

Purpose- The study investigates the effect of financial deepening on stock market performance in selected Sub-Saharan African countries by determining the relationship that exist between financial deepening and stock market performance. Expansion in the financial services to reach out to the underbanked or unbanked in our society enables these individuals to assess banking services, thereby boosting economic activities. Methodology- The study considers four selected countries in Sub-Saharan African over the period 2001 to 2019. Multiple regression analysis techniques were used with Seemingly Unrelated Regression (SUR) to analyse the data. SUR used in this analysis provides the lowest standard errors of the estimated parameters. Findings- Ordinary Least Square (OLS) gives consistent results. However, it is not as efficient as the SUR method, which amounts to feasible generalised least squares with a specific form of the variance matrix. It solves the problem of endogeneity. The study conducted Augmented Dicky Fuller (ADF) test, Hausman test, and Bruce Pagan test to avoid any challenges associated with data normality. Conclusion- The research finds out that broad money supply, a proxy for financial deepening, positively and statistically significantly impacted stock market performance in each of the four countries. It was recommended that all countries involved in this study and others implement policies that seek to enhance financial deepening in increasing broad money supply as a percentage of GDP. The increase in overall money supply allows for investment in productive sectors of the economy. Keywords: Sub-Saharan Africa, seemingly unrelated regression, Augmented Dicky Fuller, investigates, ordinary least squares. JEL Codes: E51, F21