Quantile Regression Analysis and Other Alternatives to Ordinary Least Squares Regression

Data analyses by classical ordinary least squares (OLS) regression techniques often employ unrealistic assumptions, fail to recognize the source and nature of heterogeneity, and are vulnerable to extreme observations. Therefore, this article compares robust and non-robust M-estimator regressions in a statistical demonstration study. Data from the Erlangen-Nuremberg Development and Prevention Project are used to model risk factors for physical punishment by fathers of 485 elementary school children. The Corporal Punishment Scale of the Alabama Parenting Questionnaire was the dependent variable. Fathers’ aggressiveness, dysfunctional parent-child relations, various other parenting characteristics, and socio-demographic variables served as predictors. Robustness diagnostics suggested the use of trimming procedures and outlier diagnostics suggested the use of robust estimators as an alternative to OLS. However, a quantile regression analysis provided more detailed insights beyond the measures of central tendency and detected sources of considerable heterogeneity in the risk structure of father’s corporal punishment. Advantages of this method are discussed with regard to methodological and content issues.

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Using Quantile Regression to Estimate Intervention Effects Beyond the Mean

Educational and Psychological Measurement ◽

10.1177/0013164419837321 ◽

2019 ◽

Vol 79 (5) ◽

pp. 883-910 ◽

Cited By ~ 1

Author(s):

Spyros Konstantopoulos ◽

Wei Li ◽

Shazia Miller ◽

Arie van der Ploeg

Keyword(s):

Quantile Regression ◽

Least Squares ◽

Large Scale ◽

Social Science Research ◽

Empirical Work ◽

Science Research ◽

Ordinary Least Squares ◽

Least Squares Regression ◽

Intervention Effects ◽

Education Data

This study discusses quantile regression methodology and its usefulness in education and social science research. First, quantile regression is defined and its advantages vis-à-vis vis ordinary least squares regression are illustrated. Second, specific comparisons are made between ordinary least squares and quantile regression methods. Third, the applicability of quantile regression to empirical work to estimate intervention effects is demonstrated using education data from a large-scale experiment. The estimation of quantile treatment effects at various quantiles in the presence of dropouts is also discussed. Quantile regression is especially suitable in examining predictor effects at various locations of the outcome distribution (e.g., lower and upper tails).

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Performance of Deming regression analysis in case of misspecified analytical error ratio in method comparison studies

Clinical Chemistry ◽

10.1093/clinchem/44.5.1024 ◽

1998 ◽

Vol 44 (5) ◽

pp. 1024-1031 ◽

Cited By ~ 83

Author(s):

Kristian Linnet

Keyword(s):

Regression Analysis ◽

Least Squares ◽

Measurement Errors ◽

Method Comparison ◽

Ordinary Least Squares ◽

Least Squares Regression ◽

Analytical Error ◽

First Case ◽

Error Ratio ◽

Deming Regression

Abstract Application of Deming regression analysis to interpret method comparison data presupposes specification of the squared analytical error ratio (λ), but in cases involving only single measurements by each method, this ratio may be unknown and is often assigned a default value of one. On the basis of simulations, this practice was evaluated in situations with real error ratios deviating from one. Comparisons of two electrolyte methods and two glucose methods were simulated. In the first case, misspecification of λ produced a bias that amounted to two-thirds of the maximum bias of the ordinary least-squares regression method. Standard errors and the results of hypothesis-testing also became misleading. In the second situation, a misspecified error ratio resulted only in a negligible bias. Thus, given a short range of values in relation to the measurement errors, it is important that λ is correctly estimated either from duplicate sets of measurements or, in the case of single measurement sets, specified from quality-control data. However, even with a misspecified error ratio, Deming regression analysis is likely to perform better than least-squares regression analysis.

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A Note on Close Elections and Regression Analysis of the Party Incumbency Advantage

Statistics Politics and Policy ◽

10.1515/spp-2014-0003 ◽

2014 ◽

Vol 5 (1-2) ◽

pp. 1-11

Author(s):

Peter M. Aronow ◽

David R. Mayhew ◽

Winston Lin

Keyword(s):

Regression Analysis ◽

Least Squares ◽

Control Strategy ◽

House Of Representatives ◽

Regression Discontinuity ◽

Ordinary Least Squares ◽

Regression Discontinuity Design ◽

Least Squares Regression ◽

Incumbency Advantage ◽

The Us

AbstractMuch research has recently been devoted to understanding the effects of party incumbency following close elections, typically using a regression discontinuity design. Researchers have demonstrated that close elections in the US House of Representatives may systematically favor certain types of candidates, and that a research design that focuses on close elections may therefore be inappropriate for estimation of the incumbency advantage. We demonstrate that any issues raised with the study of close elections may be equally applicable to the ordinary least squares analysis of electoral data, even when the sample contains all elections. When vote share is included as part of a covariate control strategy, the estimate produced by an ordinary least squares regression that includes all elections either exactly reproduces or approximates the regression discontinuity estimate.

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Predictors of Body Mass Index among Pregnant Women in Nigeria: A Comparison of Ordinary Least Squares Regression and Quantile Regression Models Using Machine Learning Approach

Journal of Biometrics & Biostatistics ◽

10.4172/2155-6180.1000402 ◽

2018 ◽

Vol 09 (03) ◽

Author(s):

David Taiwo Ajayi ◽

Segun Bello

Keyword(s):

Machine Learning ◽

Body Mass Index ◽

Quantile Regression ◽

Pregnant Women ◽

Least Squares ◽

Regression Models ◽

Ordinary Least Squares ◽

Learning Approach ◽

Least Squares Regression ◽

Machine Learning Approach

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Insights from analysing tourist expenditure using quantile regression

Tourism Economics ◽

10.1177/1354816616668108 ◽

2016 ◽

Vol 23 (5) ◽

pp. 1138-1145 ◽

Cited By ~ 5

Author(s):

António Almeida ◽

Brian Garrod

Keyword(s):

Quantile Regression ◽

Least Squares ◽

Empirical Studies ◽

Ordinary Least Squares ◽

Estimation Technique ◽

Least Squares Regression ◽

Data Set ◽

Detailed Understanding ◽

Tourism Destinations ◽

Single Data

Mature tourism destinations are increasingly needing to diversify their products and markets. To be successful, such strategies require a very detailed understanding of potential tourists’ levels and patterns of spending. Empirical studies of tourist expenditure have tended to employ ordinary least squares regression for this purpose. There are, however, a number of important limitations to this technique, chief among which is its inability to distinguish between tourists who have higher- and lower-than-average levels of spending. As such, some researchers recommend the use of an alternative estimation technique, known as quantile regression, which does allow such distinctions to be made. This study uses a single data set, collected among rural tourists in Madeira, to analyse the determinants of tourist expenditure using both techniques. This enables direct comparison to be made and illustrates the additional insights to be gained using quantile regression.

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QUANTILE REGRESSION AS A TOOL FOR PORTFOLIO INVESTMENT DECISIONS DURING TIMES OF FINANCIAL DISTRESS

Annals of Financial Economics ◽

10.1142/s2010495211500035 ◽

2011 ◽

Vol 06 (01) ◽

pp. 1150003 ◽

Cited By ~ 3

Author(s):

D. E. ALLEN ◽

R. J. POWELL ◽

A. K. SINGH

Keyword(s):

Quantile Regression ◽

Least Squares ◽

Financial Distress ◽

Global Financial Crisis ◽

Factor Model ◽

Ordinary Least Squares ◽

Least Squares Regression ◽

Financial Return ◽

Investment Tool ◽

The Global Financial Crisis

The worldwide impact of the Global Financial Crisis (GFC) on stock markets, investors and fund managers has lead to a renewed interest in appropriate tools for robust risk management. Quantile regression is a powerful technique and deserves the interest of financial decision makers given its remarkable capabilities for capturing and explaining the behavior of financial return series across a distribution more effectively than ordinary least squares regression methods which are the standard tool. In this paper, we present quantile regression estimation as an attractive additional investment tool, which is more effective than Ordinary Least Squares (OLS) in analyzing information across the quantiles of a distribution. This translates into the more accurate calibration of asset pricing models and subsequent informational gains in portfolio formation. We present empirical evidence of the superior capabilities of quantile regression based techniques as applied across the quantiles of return distributions to derive information for portfolio formation. We show, via stocks in Dow Jones Industrial Index, that at times of financial shocks, such as the GFC, a portfolio of stocks formed using quantile regression in the context of the Fama–French three-factor model, performs better than the one formed using traditional OLS.

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