Ordinary Least Squares Approach Research Articles

Financial development-income inequality nexus in South Eastern European countries: does the relationship vary with the level of inflation?

The study investigated two aspects using panel data analysis methods: 1) the impact of financial development on income inequality; 2) the role of inflation in the financial development-income inequality nexus in the case of South Eastern European countries (Bulgaria, Greece, Croatia, Montenegro, Romania, Serbia, Slovenia). Without interaction term, fixed effects approach shows that financial development increased income inequality whereas pooled ordinary least squares (OLS) indicates that income inequality was narrowed down by financial development. Using fixed effects, the interaction term between inflation and financial development reduced income inequality. Employing pooled OLS approach, the interaction term between inflation and financial development increased income inequality. The study therefore urges South Eastern European countries to implement policies targeted at reducing inflation in order to enhance financial development's ability to reduce income inequality. South Eastern European countries should also implement policies aimed at deepening their financial markets in order to reduce income inequality.

Signal detection algorithms for interferometric sensors with harmonic phase modulation: miscalibration of modulation parameters.

In the current paper, we have developed an analytical apparatus that allows us to calculate the phase error produced by miscalibration of modulation parameters. The case of harmonic modulation is considered, and the analysis is performed for cases of miscalibration for two parameters: amplitude and start phase. Two demodulation algorithms are considered: a conventional 4-point algorithm, based on an ordinary least-squares approach, and a previously developed 4+1 algorithm with high immunity to phase error, induced by change of target phase on the demodulation interval. Predictions, given by developed analytical equations, are verified by means of numeric modeling.

Spatial non-stationarity analysis to estimate dwelling units in Riyadh, Saudi Arabia

ABSTRACTDwelling unit (population) data at finer zones are important for different applications. The census data are not available every year and published at coarse zones. While the remotely sensed data have addressed this limitation, analysis of spatial non-stationarity in the relationship between dwelling and detailed urban remote-sensing covariates for dwelling estimates is almost novel. Riyadh, Saudi Arabia, is chosen as a case study. The remote-sensing variables have been derived from QuickBird data using an object-based image analysis. To analyse the spatial non-stationarity, ordinary least squares (OLS) and geographically weighted regression (GWR) approaches are applied. The OLS models suggest that utilizing three-residential classes provides more accurate results than built area and residential built area. The GWR models are more accurate than the OLS model. This research proves that the GWR approach cannot completely handle the spatial non-stationarity problem without efficient explanatory variables. For example, the GWR model that uses three-residential classes is the best model to estimate dwelling compared with the GWR model that uses residential built area. This article confirms that the application of the OLS approach with efficient explanatory variables can successfully account the spatial non-stationarity and the results are relatively comparable with the GWR model.

An Iterative BRDF/NDVI Inversion Algorithm Based on <italic>A Posteriori</italic> Variance Estimation of Observation Errors

Current bidirectional reflectance distribution function (BRDF) inversions using ordinary least squares (OLS) criterion can be easily contaminated by observations with residual cloud and undetected high aerosols, which leads to abrupt fluctuations in the normalized difference vegetation index (NDVI) time series. The OLS criterion assumes the noise has Gaussian distribution, which is often violated due to positive noise biases caused by clouds and high aerosols. A changing-weight iterative BRDF/NDVI inversion algorithm (CWI) based on a posteriori variance estimation of observation errors is presented to explicitly consider the asymmetrically distributed noise and observations with unequal accuracy in the BRDF retrieval. CWI employs a posteriori variance estimation and an NDVI-based indicator to iteratively adjust the weight of each observation according to its noise level. The validation results suggest CWI performs better than the Li–Gao and OLS approaches. The rmse was reduced from 0.074 to 0.028, and the relative error decreased from 13.4% to 3.8% at the U.S. Department of Agriculture Beltsville Agricultural Research Center site. Similarly, at the Harvard Forest site, the rmse was reduced from 0.086 to 0.031, and the relative error decreased from 9.5% to 2.7%. The average noise and relative noise of the CWI NDVI time series over ten EOS Land Validation Core Sites from 2003–2009 was smaller (0.028, 3.7%) than those of MOD13A2 (0.041, 5.2%), MYD13A2 (0.039, 4.9%) and MCD43B4 (0.030, 4.4%). The results demonstrate the robustness of the CWI approach in suppressing the influence of contaminated observations in BRDF retrievals by producing results that are less affected by undetected clouds and high aerosols.

Scale Effects of the Relationships between Urban Heat Islands and Impact Factors Based on a Geographically-Weighted Regression Model

Urban heat island (UHI) effect, the side effect of rapid urbanization, has become an obstacle to the further healthy development of the city. Understanding its relationships with impact factors is important to provide useful information for climate adaptation urban planning strategies. For this purpose, the geographically-weighted regression (GWR) approach is used to explore the scale effects in a mountainous city, namely the change laws and characteristics of the relationships between land surface temperature and impact factors at different spatial resolutions (30–960 m). The impact factors include the Soil-adjusted Vegetation Index (SAVI), the Index-based Built-up Index (IBI), and the Soil Brightness Index (NDSI), which indicate the coverage of the vegetation, built-up, and bare land, respectively. For reference, the ordinary least squares (OLS) model, a global regression technique, is also employed by using the same dependent variable and explanatory variables as in the GWR model. Results from the experiment exemplified by Chongqing showed that the GWR approach had a better prediction accuracy and a better ability to describe spatial non-stationarity than the OLS approach judged by the analysis of the local coefficient of determination (R2), Corrected Akaike Information Criterion (AICc), and F-test at small spatial resolution (< 240 m); however, when the spatial scale was increased to 480 m, this advantage has become relatively weak. This indicates that the GWR model becomes increasingly global, revealing the relationships with more generalized geographical patterns, and then spatial non-stationarity in the relationship will tend to be neglected with the increase of spatial resolution.

Estimation of stature in archaeological human skeletal remains from Britain.

For archaeological populations of northwest European origin, the Trotter and Gleser () "White" equations are generally used to estimate stature from long-bone length. The aim of this research is to investigate the reliability of these formulae for this purpose. Stature estimated using the Trotter and Gleser formulae was evaluated by comparing estimates with anatomically reconstructed stature in adult skeletons (N = 40) from Mediaeval England. Performance of the Trotter and Gleser equations based on femur length was compared (using standard error of the estimate (SEE) and mean percentage error (%error)) with others that have been derived from archaeological and recent European ancestry populations. Performance of ordinary least squares (OLS) and reduced major axis (RMA) versions of some of the equations was also evaluated. 14 male and 11 female femoral equations were investigated. For females, the original (OLS) Trotter and Gleser "White" equations produced the lowest SEE and %error. For the males, the most reliable was the RMA version of the Trotter and Gleser "White" WWII equation; the Trotter and Gleser equations based on the Korean War dead performed poorly. In an archaeological target population, stature estimation equations devised using archaeological reference populations from a similar ecogeographic zone did not perform better than those based on recent populations. There was no indication that either the RMA or OLS approach produced consistently lower SEE and %error, but the former more faithfully represented the variation in anatomically reconstructed stature present in the study group.

Energy Consumption and GDP: The Strong Relationship in OECD Countries

The aim of this article is to reexamine the relationship between energy consumption and economic growth for 22 Orginisation for Economic Co-operation and Development countries over the period 1960–2005 by taking strong relation into account. According to the results of fully modified ordinary least squares (OLS) and dynamic OLS approaches, while there exists the strong relation running from economic growth to energy consumption for most cases, the strongest relation running from energy consumption to economic growth is shown only for Iceland and Portugal.

Quantile Regression Analysis of Corporate Liquidity: Evidence from the U.S. Property–Liability Insurance Industry

This study analyses the determinants of corporate liquidity for the U.S. property–liability insurance industry from 2006 to 2010. Unlike previous studies using the ordinary least squares (OLS) approach, this study applies the quantile regression (QR) method. The QR method provides further insights on how insurers’ liquidity level is determined, especially for the firms at the lower and the higher quantiles. We found that leverage and organisational structure have opposite effects on insurers’ liquidity in the lower and the higher quantile groups. The empirical results also show that most firm-specific characteristics and macroeconomic conditions influence the insurers’ liquidity, which are consistent with the findings of the OLS approach in previous studies.

Do Typical RCTs of Education Interventions Have Sufficient Statistical Power for Linking Impacts on Teacher Practice and Student Achievement Outcomes?

For RCTs of education interventions, it is often of interest to estimate associations between student and mediating teacher practice outcomes, to examine the extent to which the study’s conceptual model is supported by the data, and to identify specific mediators that are most associated with student learning. This article develops statistical power formulas for such exploratory analyses under clustered school-based RCTs using ordinary least squares (OLS) and instrumental variable (IV) estimators and uses these formulas to conduct a simulated power analysis. The power analysis finds that for currently available mediators, the OLS approach will yield precise estimates of associations between teacher practice measures and student test score gains only if the sample contains about 150 to 200 study schools. The IV approach, which can adjust for potential omitted variable and simultaneity biases, has very little statistical power for mediator analyses. For typical RCT evaluations, these results may have design implications for the scope of the data collection effort for obtaining costly teacher practice mediators.

A spatial regression analysis of the influence of topography on monthly rainfall in East Africa

AbstractPrecipitation in Kenya is highly variable and dominated by a variety of physical processes. Statistical studies of climate patterns have historically focused on application of ordinary least squares (OLS) regression to test hypotheses related to multiple predictive variables, perhaps in an attempt to better understand the physical mechanisms that drive precipitation, or on use of spatially explicit models, typically kriging‐ or spline‐based analyses, for the purpose of improving predictions. Each of these approaches may be individually useful; however, they all possess limitations. OLS approaches have yielded biased results in the presence of spatially autocorrelated data. Kriging‐ and spline‐based studies often focus on providing improved predictions rather than understanding. Here we use spatial regression, a method not commonly used in analysis of climate data, to assess the role of predictive variables while explicitly incorporating spatial autocorrelation in parameter estimation and hypothesis testing. This approach can yield a better understanding of relationships between precipitation and multiple predictive variables with improved statistical rigour. Using spatial regression, we show that topographic variables such as elevation and slope strongly influence rainfall during the ‘long rains’ and ‘short rains’, which are vital for Kenyan agriculture. Outside these seasons, we find that smaller (mesoscale) variations in elevation are statistically significant. Further, we demonstrate the shortcomings of automated selection procedures such as stepwise regression through the identification of spurious results due to confounding. Copyright © 2010 Royal Meteorological Society

European Regional Convergence Revisited: A Weighted Least Squares Approach

ABSTRACTA plethora of past studies have concluded that unconditional β‐convergence is present in a broad sample of regions, implying that poor regions grow faster than rich ones. All these econometric studies tend to overlook the relative importance or size of each region in the national setting, treating all regional observations as equal. However, this assumption might lead to unrealistic or misleading results. Convergence analysis could be more meaningful if it included a weighting mechanism taking into account the size of regions. The aim of this paper is to investigate whether the inclusion of a weighting mechanism in β‐convergence analysis, giving more weight to larger regions and less to smaller ones, can result in sharply different implications for the regional convergence‐divergence process. For this reason, both unweighted ordinary least squares (OLS) and weighted least squares estimators are used in the analysis of regional (intra‐national) convergence within 10 European Union (EU) countries over the period 1990–2000. The comparison between the two methods reveals that when regions are appropriately weighted for their size, intra‐national divergence, rather than convergence found with the OLS approach, seems to be the dominant experience in the EU.

On the Identification of Fiscal Policy Behavior

In the current literature, fiscal policy is usually characterized by a single-equation rule, in which primary surplus is generally defined as a function of lagged government debt and other controlled variables. To apply Ordinary Least Squares (OLS) method on the single-equation rule has been one of the common approaches to identify fiscal policy behavior. From the rational expectations general equilibrium perspective, this paper illustrates that lagged government debt is generally endogenous and the OLS approach suffers from simultaneity bias. Consequently, the OLS-based identification of fiscal policy behavior is unreliable. As a solution, we apply the Generalized Method of Moments (GMM) for estimation and inference. Monte Carlo experiments demonstrate that GMM provides more reliable results than OLS in terms of accuracy of the estimator, size and power. In short, people should be cautious of the existing OLS-based identification results of fiscal policy behavior and the empirical researchers should not consider OLS regression as a reliable tool when trying to identify fiscal policy behavior in the future.

Week-to-Week Leisure Trip Frequency and Its Variability

Using a 6-week travel diary survey from Germany, this study examined the effect of the frequency of leisure trips per week on the variability in the number of such trips over weeks. The frequency of trips and the variability were measured for six activity types: social contact, sports, recreation, culture and learning, nature, and shopping. A two-stage model, consisting of tobit and ordinary least-squares approaches, was used with dependent variables of trip frequency per week and variability of trips over weeks, respectively. The results showed that the frequency of leisure trips influenced their variability in certain activity types. The effects vary substantially across activity types.

Predicting soil organic carbon percentage from loss-on-ignition using Bayesian Model Averaging

A shortage of data for percentage of organic carbon (C%) makes calculation of soil profile carbon storage difficult. Loss on ignition (LOI) data, which are cheap to obtain and often readily available, can be used to estimate organic C%. This paper simultaneously considers several predictors of organic C%: LOI, parent material, drainage status, type of soil horizon, clay content, and pH. In order to model appropriately the existence of multiple hypotheses and the consequent model uncertainty, a Bayesian Model Averaging (BMA) approach was used. BMA considers all models that result from all possible combinations of explanatory variables. Based on a BMA approach and Scottish Soil Survey data, it was found that the most important factors to predict organic C% were LOI, clay content, a dummy for Countesswells Association (till derived from granite), and a dummy for B horizon soils. The validation analysis showed that prediction accuracy for organic C% was better with the BMA approach than with an ordinary least-squares approach that includes no other predictors apart from LOI (i.e. 22% reduction in horizons A, Ap, and C).

Calibration in a closed system: the case of X-ray diffraction analysis

Knudsen [X-ray Spectrom.(1981),10, 54–561] proposed and demonstrated a least-squares approach to estimating the unknown parameters of a system of equations required for calibration in X-ray diffraction analysis. The approach is an ordinary least-squares approach which does not incorporate information on the errors of the measured intensities for a set of samples used as standards. The purpose of the present paper is to show that a functional relationship model can be applied to the problem to account for all the variation due to sampling and measurement error in the peak intensities. It is also shown that Knudsen's calibration estimator can be regarded as an approximation to a more general and potentially more efficient weighted least-squares estimator derived from the functional relationship model. The closeness of the approximation depends on the nature of the covariance structure of the intensity measurements.

Log transformation benefits parameter estimation in microwave tomographic imaging

Microwave tomographic imaging falls under a broad category of nonlinear parameter estimation methods when a Gauss-Newton iterative reconstruction technique is used. A fundamental requirement in using these approaches is evaluating the appropriateness of the regression model. While there have been numerous investigations of regularization techniques to improve overall image quality, few, if any, studies have explored the underlying statistical properties of the model itself. The ordinary least squares (OLS) approach is used most often, but there are other options such as the weighted least squares (WLS), maximum likelihood (ML), and maximum a posteriori (MAP) that may be more appropriate. In addition, a number of variance stabilizing transformations can be applied to make the inversion intrinsically more linear. In this paper, a statistical analysis is performed of the properties of the residual errors from the reconstructed images utilizing actual measured data and it is demonstrated that the OLS algorithm with a log transformation (OLSlog) is clearly advantageous relative to the more commonly used OLS approach by itself. In addition, several high contrast imaging experiments are performed, which demonstrate that different subsets of data are emphasized in each method and may contribute to the overall image quality differences.

Balancing productivity and consumer satisfaction for profitability: Statistical and fuzzy regression analysis

This paper examines the relationships among productivity, consumer satisfaction and profitability using the conventional statistical regression and the new fuzzy regression approaches. For service firms in the context of Hong Kong, we verify the profit hypothesis that individually both productivity and consumer satisfaction are positively linked to profitability as well as the tradeoff hypothesis that aggregately there are negative interactions between productivity and consumer satisfaction for enhancing profitability. Hence service firms should balance their efforts in productivity and consumer satisfaction, possibly by employing appropriate information technologies to improve productivity while without hurting consumer satisfaction, to optimize their profitability. The study takes advantage of the Hong Kong Consumer Satisfaction Index and deliberately focuses on total rather than partial productivity. Several models are first estimated using the ordinary least squares (OLS) method and the results generally support the two hypotheses, but the OLS approach also leaves two puzzles that estimates of the regression coefficients are: (1) not significant before considering the interactions between consumer satisfaction and productivity but significant after introducing the interaction term, and (2) significant although sample data for productivity and the interaction term are highly correlated. These puzzles, together with the observed imprecision in productivity and profitability measurements and especially the subjectivity in measuring consumer satisfaction, lead us to adopt the fuzzy linear regression (FLR) techniques to further examine the two hypotheses. The popular FLR model continues to favor our research hypotheses but fail to offer any additional insights into the examined relationships over the OLS models. We then propose a revised FLR model which, in addition to reconfirming the hypotheses, does help to explain the encountered puzzles and fuzziness, and hence suggests an encouraging methodology for marketing.

Ecological inference and spatial heterogeneity: an entropy‐based distributionally weighted regression approach

Abstract. In this article we compare two competing approaches to ecological modelling using test data. The first approach is based on the “traditional” method of Ordinary Least Squares (OLS), assuming constancy of parameters across disaggregated spatial units (spatial homogeneity). The second (new) approach is based on the method of Generalised Cross‐Entropy (GCE), assuming varying parameters (spatial heterogeneity). The latter approach is designated as entropy‐based “distributionally weighted regression” (DWR). The two approaches are tested in a real‐world application, using data on per‐capita GDP for the 17 regions and some covariates for the 50 provinces of Spain. Specifically, the performances of the two approaches are assessed by examining their capability in tracking the actual per‐capita GDP data for the provinces (while treating them as if they were not observed by the econometrician), and in showing evidence of spatial heterogeneity. Our findings indicate that the GCE varying‐parameter approach outperforms the OLS approach in terms of predictive power. Specifically, we find that the GCE predictions make efficient use of the lower‐level information that is available. In addition, it is shown that entropy‐based DWR has some potential as a useful technique for investigating spatially heterogeneous relationships at the lower level of analysis that might otherwise be overlooked.

Estimating the Association between SF-12 Responses and EQ-5D Utility Values by Response Mapping

Reliably mapping from generic or disease-specific health status measures into health state utilities would assist health economists. Existing studies mainly use ordinary least squares (OLS) regression equations to predict utility values for particular health states. The authors examine an alternative approach to map between 2 generic health status instruments, the SF-12 and the EQ-5D. Multinomial logit regression is used to estimate the probability that a respondent will select a particular level of response to questions in the EQ-5D, using individual question responses and summary scores from the SF-12 as predictors. Monte Carlo simulation methods are used to generate predicted EQ-5D responses, and utility scores (tariffs) are then attached. Results are compared with an alternative approach based on direct mapping to utility scores using OLS. The authors estimate equations using 12,967 adult survey responses-from the 2000 US Medical Expenditure Panel Survey. They report mean squared error (MSE) and mean absolute error (MAE) of their predicted utilities within this sample, and out-of-sample using 13,304 adults from the 1996 Health Survey for England. The authors obtain an in-sample and out-of-sample MSE of 0.03, compared with 0.02 for the OLS approach. Their MAE of 0.11 is similar to OLS results. The authors' method predicts group mean utility scores and differentiates between groups with or without known existing illness. The authors' approach has higher MSE than the direct OLS approach but gives more descriptive data on domains of health effects. Further out of sample prediction work will help test the validity of these methods.

Application of a geographically‐weighted regression analysis to estimate net primary production of Chinese forest ecosystems

ABSTRACTAim The objective of this paper is to obtain a net primary production (NPP) regression model based on the geographically weighted regression (GWR) method, which includes spatial non‐stationarity in the parameters estimated for forest ecosystems in China.Location We used data across China.Methods We examine the relationships between NPP of Chinese forest ecosystems and environmental variables, specifically altitude, temperature, precipitation and time‐integrated normalized difference vegetation index (TINDVI) based on the ordinary least squares (OLS) regression, the spatial lag model and GWR methods.Results The GWR method made significantly better predictions of NPP in simulations than did OLS, as indicated both by corrected Akaike Information Criterion (AICc) and R2. GWR provided a value of 4891 for AICc and 0.66 for R2, compared with 5036 and 0.58, respectively, by OLS. GWR has the potential to reveal local patterns in the spatial distribution of a parameter, which would be ignored by the OLS approach. Furthermore, OLS may provide a false general relationship between spatially non‐stationary variables. Spatial autocorrelation violates a basic assumption of the OLS method. The spatial lag model with the consideration of spatial autocorrelation had improved performance in the NPP simulation as compared with OLS (5001 for AICc and 0.60 for R2), but it was still not as good as that via the GWR method. Moreover, statistically significant positive spatial autocorrelation remained in the NPP residuals with the spatial lag model at small spatial scales, while no positive spatial autocorrelation across spatial scales can be found in the GWR residuals.Conclusions We conclude that the regression analysis for Chinese forest NPP with respect to environmental factors and based alternatively on OLS, the spatial lag model, and GWR methods indicated that there was a significant improvement in model performance of GWR over OLS and the spatial lag model.