Classical Regression Estimation Versus Bayesian Regression Estimation: A Simulation-based Analysis of Predictive Performance

In this study,  comparison between the classical ordinary least square (OLS) regression technique and the Bayesian conjugate normal linear regression method when the data satisfy all the necessary assumptions of OLS technique is presented. The Bayesian normal linear regression model was fitted using Normal-Gamma conjugate prior. Results from Monte Carlo study showed that the OLS estimator is as good as the Bayesian estimator in terms of the closeness of their estimated parameters to the true values. However, using the criteria of the mean square errors of parameters’ estimates and other performance indices, the results showed that Bayesian estimator is more efficient,  more consistent and relatively more stable than the classical least squares method even when the sample data satisfy all the necessary assumptions of the OLS method. The apparent better performance of Bayesian estimator over the OLS is justified by the prior information about the data that Bayesian technique employed in its estimation. Therefore, it could be concluded that if reliable information about the data under investigation is available, Bayesian regression technique(s) that would make use of such information should be preferred for efficient model’s estimation and better inference. The R statistical package (www.cran.org) was employed for all the analysis in this study.

Financial inclusion involves decreasing the number of unbanked population through series of activities that will enhance the participation in the financial system. The objective of this study is examining financial inclusion and its implications on growth of small and medium sized enterprises (SMEs) in Nigeria from 1992 to 2020 using data obtained from the Central Bank of Nigeria (CBN) Statistical Bulletin. The study used the classical linear regression model using Ordinary least square (OLS) and Dynamic Ordinary Least Square (DOLS) to analyse the data. The outcome of the analysis revealed that the growth of small and medium sized enterprises (SMEs) in Nigeria is positively and significantly influenced by financial inclusion. The findings further revealed that government needs to steer up efforts in ensuring the dissemination of all banking services to reach everyone at affordability fees regardless of income group and location.

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.

Background: More and more disabled elderly need long-term care as China becomes an aging society. In 2016, there were 220 million people over the age of 60, and nearly 10 million completely disabled elderly people who cannot complete Activities of Daily Living (ADLs). Therefore, the topic of influencing factors for disability among the elderly in China has attracted close attention from researchers, most of which use the traditional empirical methods, such as Ordinary Least Squares (OLS) and logistic.Objective: The purpose of this paper was to introduce the Bayesian Quantile Regression (BQR) method to the topic of the disabled elderly, which was achieved by using BQR to study the influencing factors of disability among the elderly in China during 2003–2016.Methods: This paper was the first attempt to use the BQR for the influencing factors of disability among the elderly in China. Furthermore, a comparison was made between the regression results of BQR, OLS, Quantile Regression (QR), and Bayesian Linear Regression (BLR).Results: It was found that there was a relatively stable relationship between chronic diseases and disability, although there was a little difference in different quantiles. In addition, the BQR can obtain results similar to the traditional method. For instance, the coefficient of chronic diseases (to total disability) obtained by OLS, QR, and BLR were basically consistent (around 0.778), which was similar to BQR. The BQR not only provided estimates for all the quantiles, but also provided upper and lower values of a certain confidence interval.Conclusions: By applying the BQR to the influencing factors of disability among the elderly in China, we reached the conclusion that BQR methods are adaptable for this research topic because of their characteristics and advantages over the traditional methods, such as less strict constraints, the estimates for all quantiles, and the combination of historical information with prior information. Moreover, the BQR method appropriately obtained the lower and upper values in a confidence interval, which can provide prediction space for the future.

Bayesian regression has emerged as a viable alternative for the estimation of curriculum-based measurement (CBM) growth slopes. Preliminary findings suggest such methods may yield improved efficiency relative to other linear estimators and can be embedded into data management programs for high-frequency use. However, additional research is needed, as Bayesian estimators require multiple specifications of the prior distributions. The current study evaluates the accuracy of several combinations of prior values, including three distributions of the residuals, two values of the expected growth rate, and three possible values for the precision of slope when using Bayesian simple linear regression to estimate fluency growth slopes for reading CBM. We also included traditional ordinary least squares (OLS) as a baseline contrast. Findings suggest that the prior specification for the residual distribution had, on average, a trivial effect on the accuracy of the slope. However, specifications for growth rate and precision of slope were influential, and virtually all variants of Bayesian regression evaluated were superior to OLS. Converging evidence from both simulated and observed data now suggests Bayesian methods outperform OLS for estimating CBM growth slopes and should be strongly considered in research and practice.

Multicollinearity poses a significant challenge in econometric modelling, particularly when analysing economic indicators that are inherently interrelated. This study investigated the efficacy of Ridge Regression (RR) and Bayesian Regression (BR) as alternatives to Ordinary Least Squares (OLS) in the presence of multicollinearity. Using both simulated datasets and Nigerian economic data spanning 1995 to 2016, including GDP, oil revenue, education, agriculture, manufacturing, trade, and construction, we compared the predictive and inferential performance of the three methods. Model performance was evaluated using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Squared Prediction Error (MSPE). The findings revealed that while OLS exhibited superior model fit under AIC and BIC, BR outperformed both OLS and RR in predictive accuracy, as indicated by the lowest MSPE. These results underscore the importance of prior distribution assumptions in Bayesian estimation and highlight the need for careful model selection when handling multicollinearity in economic data.

Regional flood frequency analysis (RFFA) techniques are commonly used to estimate design floods for ungauged catchments. In Australian Rainfall and Runoff (ARR), the probabilistic rational method (PRM) was recommended for eastern New South Wales (NSW). Recent studies in Australia have shown that regression-based RFFA methods can provide more accurate design flood estimates than the PRM. This paper compares ordinary least squares (OLS) and generalised least squares (GLS) based quantile regression techniques using data from 96 small-to medium-sized catchments across NSW for average recurrence intervals of 2 to 100 years. The advantages of the GLS regression are that this accounts for the inter-station correlation and varying record lengths from site to site. An independent test based on both the split-sample and one-at-a-time validation approaches employing a wide range of statistical diagnostics indicates that the GLS regression provides more accurate flood quantile estimates than the OLS one. The developed regression equations are relatively easy to apply, which require data for only two to three predictors, catchment area, design rainfall intensity and stream density. The findings from this study together with those from other RFFA studies being examined as a part of ARR upgrade projects will inform the development of RFFA techniques for inclusion in the revised edition of ARR.

Background Neisseria gonorrhea is the second most prevalent sexually transmitted infection (STI) in the US with increasing incidence. Untreated, it leads to devastating sequelae for nonpregnant women, pregnant women, and their neonates. Geographic clustering of gonorrhea coincides with clustering of other risk factors and may help guide interventions. We utilize Geographic Information Systems (GIS) software to map gonorrhea incidence among women in Chicago, and examine factors associated with the spatial distribution of infection. Methods Chicago Department of Public Health data sets and shape files were available through the Chicago Data Portal. ArcGIS was utilized for map illustrating and data analysis. Ordinary Least Squares (OLS) Regression was utilized using the dependent variable of Gonorrhea incidence in women per Chicago Community Area (CCA), with various explanatory variables. Within the OLS, the Koenker Statistic (KS) was reported and from this a Geographically Weighted Regression (GWR) tool was run for combinations with statistically significant KS. Results The highest incidence is shown in the southern and western CCA’s, with hospitals clustered in the northern and southeastern CCA’s & clinics with gaps primarily noted in the southern and northwestern CCA’s. (Figure 1.) Teen pregnancy incidence (TP), infant mortality (IM), and first trimester prenatal care, had statistical significance of the robust probability for all of their explanatory variables, and VIF’s less than 2 for all explanatory variables, JBS were not statistically significant, and AICc were approximately 1170 demonstrating stable OLS. (Figure 2&3) TP & IM did have a statistically significant KS and GWR was run demonstrating random spatial pattern. This confirms TP & IM as predictors for gonorrheal incidence had variable predictability throughout the CCA’s and GWR improves the model outcome. Both combinations spatially explain gonorrhea incidence. Map of Gonorrhea Incidence among Females in 2006-2010 Figure 1:The data of the incidence of gonorrhea in females was mapped with 5 separate classifications created and displayed in the form of a map. Also included on the map were hospitals in the city, and Chicago Department of Public Health clinic locations where free STI management could take place. illustrates gonorrhea incidence rates (per 100,000) within the 77 Chicago Community Areas (CCA) of the city. The darker shades of green correspond with higher incidence. The highest incidence is shown to be greatest in the southern and western CCA’s. Also illustrated are the locations of the hospitals within the city in addition to CDPH clinics that are Federally Qualified Health Clinics (FQHC) that offer services for treatment at a reduced or free cost depending on health insurance status. The majority of the hospitals are shown to clustered in the northern and southeastern CCA’s. The clinics are more evenly spaced out with gaps primarily noted in the southern and northwestern CCA’s. The Ordinary Least Squares (OLS) regression results are illustrated in Table 1 above. The results are shown for six separate regressions: chlamydia incidence, Natality (teen pregnancy incidence [TP], percent of live births that were preterm [Preterm], fetal low birth percentage [LBW], prenatal care in the 1st trimester rate [PNC 1T], infant mortality rate [IM]), poverty (total # below poverty line per 100,000), poverty & chlamydia, TP & IM, TP & IM & PNC 1T, and all coefficients (natality incidence, poverty incidence, chlamydia incidence, fertility rate). Utilizing ArcGIS software, OLS Regression was mapped with the 77 Chicago Community Areas (CCA) with Gonorrhea Infection Incidence per CCA as the dependent variable and Teen Pregnancy (TP), Infant Mortality (IM) and 1st trimester prenatal care (1TM) incidence per CCA as the explanatory variables. Regression reported with standard deviation (SD) and color coded based off quantity of SD. Map shapefile is of the 77 CCA’s. Overlying are Hospitals and Chicago Department of Public Health (CDPH) clinic locations as made available through CDPH public domain website. Conclusion Teen pregnancy rates, infant mortality rates, and prenatal care in the first trimester explain some of the spatial patterns of gonorrhea incidence of females in Chicago. Identification of these factors identified should prompt providers to ensure enhanced testing of gonorrhea and other STI’s to reduce burden in areas of high incidence. Disclosures All Authors: No reported disclosures.

Although ordinary least squares (OLS) is generally regarded as the foundation of econometrics, the vital concept of the empirically determined statistical variance in an OLS prediction is misunderstood and missing. The fundamental deficiency is the failure to appropriately model the deterministic OLS processing of statistical errors. The variance in the OLS prediction is typically described in terms of standard properties of variance. However, those properties fail to correctly model the statistical OLS output. This paper fills that gap. Based on experience with well proven and long established engineering and math modeling techniques, OLS is modeled with methods of estimation theory analogous to the modeling of a signal processor or target tracker. In other words, OLS is a treated as a "black box" with "gosintas" and "gosoutas". A novel derivation of the OLS based on the orthogonality principle establishes the empirically determined statistical OLS output in the form of the prediction, variance, and expected value. Also included is the empirically determined statistical variance of future observations, which are independent of the statistical prediction. Thus, the statistical OLS prediction variance and the statistical variance of any new sample would both contribute to the uncertainty of any future observation. Both statistical variances are empirically estimated by OLS processing in advance.

Matching methods are assumed to reduce the likelihood of a biased inference compared with ordinary least squares (OLS) regression. Using simulations, we compared inferences from propensity score matching, coarsened exact matching, and unmatched covariate-adjusted OLS regression to identify which methods, in which scenarios, produced unbiased inferences at the expected type I error rate of 5%. We simulated multiple data sets and systematically varied common support, discontinuities in the exposure and/or outcome, exposure prevalence, and analytical model misspecification. Matching inferences were often biased in comparison with OLS, particularly when common support was poor; when analysis models were correctly specified and common support was poor, the type I error rate was 1.6% for propensity score matching (statistically inefficient), 18.2% for coarsened exact matching (high), and 4.8% for OLS (expected). Our results suggest that when estimates from matching and OLS are similar (i.e., confidence intervals overlap), OLS inferences are unbiased more often than matching inferences; however, when estimates from matching and OLS are dissimilar (i.e., confidence intervals do not overlap), matching inferences are unbiased more often than OLS inferences. This empirical "rule of thumb" may help applied researchers identify situations in which OLS inferences may be unbiased as compared with matching inferences.

Survey measurements have become the traditional means of obtaining point positions by most surveyors over the centuries. The assertion that a post processed DGPS field data is precise, accurate and can be used to execute any engineering works due to its minimum human errors need to be reviewed; this is because the post processed field data still contains errors and needs to be adjust. Adjustments and computations is one of the main research field in mathematical and satellite geodesy to assess the magnitude of errors and to study their distributions whether they are within or not within the acceptable tolerance. In order to achieve the objective of this study, a DGPS field data was adjusted using the Ordinary Least Square (OLS) and Total Least Square (TLS) techniques. The OLS considers errors only in the observation matrix, and adjusts observations in order to make the sum of its residuals minimum. The TLS considers errors in both the observation matrix and the data matrix, thereby minimizing the errors in both matrices. The limited availability of information on OLS and TLS in adjusting DGPS field data and the uncertainty of which method is optimal, whether the OLS and TLS is the most appropriate technique has called for the need to undertake this study. This study aimed at comparing the working efficiency of the OLS and TLS, assessing their individual accuracy and selecting the most effective method in adjusting DGPS field data. Each model was assessed based on statistical indicators of mean horizontal error (MHE), mean bias error (MBE), mean absolute error (MAE), root mean square error (RMSE), and standard deviation (SD). After applying the OLS and TLS methods independently for the same datasets, it was ascertained that, the OLS method was better in adjusting DGPS field data than the TLS with a MHE and SD of +1.203079 m and +1.663134 m as compared to TLS with MHE and SD of +7.0985507 m and +2.594045 m respectively. This study will therefore create opportunity for geospatial professionals to know the efficiency of OLS and TLS in solving some of the problems in mathematical and satellite geodesy.Keywords: Differential Global Positioning, System, Total Least Square, Ordinary Least Square, Survey Adjustments, Horizontal Position Displacement

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 paper investigates the increased role of extractive industry, particularly oil and gas, within the Dutch disease model between 2000-2018 in the Azerbaijan economy. Dutch disease phenomenon befalls when the national economy produces and exports a single commodity or a particular sector becomes the booming sector. Increased exports of particular goods and spendings of the accumulated mineral revenue appreciate the national currency, decreasing the competitiveness and thus the production or export volume of the non-booming sectors. Azerbaijan is an oil and gas-rich country which naturally actualizes the existence of Dutch disease syndrome . Therefore, the purpose of this research is to separately reveal the Dutch disease effects of resource movement and spending effects based on the theoretical frame­ work constructed from the core theory. The paper contains a comprehensive literature review and overall macroeconomic screening of the Azerbaijan economy to describe the preconditions of Dutch disease. Then, the study employs 42 multivariate linear ordinary least squares (OLS) estimations. The estimated models illustrate the presence of indirect de-industrialization (one form of resource movement effect) and the spending effect of the Dutch disease hypothesis. However, the paper does not find a direct negative influence of booming sectors on aggregated lagging (i.e., manufacturing and agriculture) and non-tradable sectors (services). Moreover, va­riables such as oil price growth rates, real effective exchange rate (REER), nominal effective exchange rate (NEER), and economic crisis periods failed to significantly explain the employment and real wages dynamics. However, these variables described certain influence channels in output and returns on capital growth rates. This paper sheds light on the interconnections between the Azerbaijan economy’s labor resources, government spending, and monetary channels. These interconnections indicate that the Dutch disease hypothesis holds true for Azerbaijan. Of the estimated OLS coefficients, 90.5% were highly stable, which suggests that the results are reliable. This study mainly tests the general theoretical expectations of the original Dutch disease model and presents a common ground to conceptualize the possible harmful effects of the booming oil and gas sectors in Azerbaijan. Any causal derivations should be handled carefully.

Earlier researchers have been working to relate globalisation, trade or free trade as an instrument for bringing peace and reducing conflict in the world. But this study attempts to open up a new debate that how social unrest in terms of lack of pace in nations leads to failure of economic policing and outcomes. In past, few researchers have tried to show peaceful environment as a generator for economic progress by building theoretical models, but limited empirical analysis has been conducted so far. This brings a novelty in the present study that for the first time a large set of data covering 155 nations has been used to explore the relationship between these two desired variables i.e. trade related variables and peace, in new direction and employing new indicators defining extent of peace in nations. Panel co-integration technique has been applied along with Fully Modified Ordinary Least Squares (FMOLS) and Dynamic Ordinary Least Squares (DOLS) models to know the parametric and non-parametric point estimates of variables. Data has been extracted from Economic Institute of Peace and World Bank for the time period 2008-2014. Results showed that lesser number of attacks are associated with more volume of trade among nations and better relations with neighbouring countries are linked positively with trade performance of nations. Nations involved more into hostility acts like conflicts are unable to maximise the benefits from bilateral trade. JEL Classification: F10, D74, L33, C23. Keywords: Globalisation, Trade, Conflict, Terrorism, Panel Model

This study aims to analyze the reduction in energy subsidies and poverty in Indonesia. The method used in this study is the Ordinary Least Square (OLS) model. The data used are annual data the period of 1998-2018. The variables used are government spending, energy subsidies, inflation, and the amount of poverty that comes from the Central Statistics Agency (BPS). The results indicated that there was a positive effect between energy subsidies and poverty but was not significant. The reduction in energy subsidies does not directly affect poverty, due to low use of energy within the poor. The research implies that policy decision makers to reduce energy subsidies do not make a difference between the period before and after, this indicates that all estimation periods did not change significantly. Keywords : Government spending, energy subsidies, inflation, poverty, OLS