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Addressing the Utilization of Popular Regression Models in Business Applications
Published in K. Hemachandran, Sayantan Khanra, Raul V. Rodriguez, Juan R. Jaramillo, Machine Learning for Business Analytics, 2023
Meganathan Kumar Satheesh, Korupalli V. Rajesh Kumar
Quantile regression, which is an extension of quantile function (conditional), is used for the estimation of a conditional-based model (Koenker & Hallock, 2001). The word quantile means a sample is divided into equal sized and sub groups, which means 25%, 50%, and 75% are the sample quantiles (Yu, Lu, & Stander, 2003) that can be used to observe extreme values of the samples (Jareño, Ferrer, & Miroslavova, 2016). Linear regression will use only the average relationship between dependent and independent variables, whereas the quantile regression will give a clear picture of the relationship between both variables by plotting quantile regression curves (Yu et al., 2003). The coefficients obtained by quantile regression will be distributed by the outliers (Jareño et al., 2016) due to the usage of a weighted sum of absolute deviation, and the estimators of quantile regression will deliver an effective performance than ordinary least square due to error terms that are not in the normal distribution (Hung, Shang, & Wang, 2010).
The hitchhiker's GUIDE to modern decision trees
Published in Brandon M. Greenwell, Tree-Based Methods for Statistical Learning in R, 2022
GUIDE is not just for simple classification and regression problems, and can be used in all sorts practical situations, including: quantile regression;Poisson regression (i.e., for modeling count data and rates);multivariate outcomes;censored outcomes;longitudinal data [Loh and Zheng, 2013] (e.g., when multiple subjects are continually measured over time);propensity score grouping;variable reduction;subgroup identification [Loh et al., 2015];and more.
Regional Observational Studies: Deriving Evidence
Published in Susan B. Norton, Susan M. Cormier, Glenn W. Suter, Ecological Causal Assessment, 2014
Jeroen Gerritsen, Lester L. Yuan, Patricia Shaw-Allen, Susan M. Cormier
Biological responses to candidate stressors frequently show a wedgeshaped plot, as in Figure 12.6. The stressors in Figure 12.6, percentage of sand and fines, and total nitrogen, co-occur with many other stressors in the stream. If the only stressor in the data set were sandy sediment, then other stressors (e.g., total N, organic enrichment) would not affect the mayfly richness, and it would be expected that a relationship would look more linear, similar to Figures 12.3 or 12.4. Quantile regression models such a relationship, typically near the top of a wedge, to represent the “best” biological condition in the assumed absence of other stressors. More precisely, quantile regression uses a specified conditional quantile of a dependent (response) variable and one or more independent (explanatory) variables (Cade and Noon, 2003). Modeling the 50th quantile of a response variable produces the median line under which 50% of the observed responses are located, and modeling the 90th quantile produces a line under which 90% of the observed responses are located (see Figure 12.6). Quantile regressions can have more than one explanatory variable, but we limit the following discussion to the univariate case. As with mean regression, the relationship is often assumed to be a straight line.
Who benefits more? The heterogeneous impact of highways on employment growth
Published in Transportation Planning and Technology, 2021
Ryan Terry, Mahmut Yasar, Jianling Li
We also examine the growth impact of interstate highway kilometers at various quantiles of the conditional distribution of county growth rates while simultaneously controlling for endogeneity. Using IVQR, the standard quantile regression can be illustrated as follows (Koenker and Bassett 1978; Buchinsky 1998; Yasar, Nelson, and Rejesus 2006):8where m denotes the independent variables in (1) and β denotes of corresponding parameters to be estimated. Qθ signifies the θth conditional quantile of ΔlnEMPit given mit. The quantile regression estimator for quantile θ (0 < θ < 1) minimizes the following function: where ρθ (.) is the ‘check function’ expressed as follows: By changing θ continuously from zero to one and using linear programming methods to minimize the sum of weighted absolute deviations (Koenker and Bassett 1978; Buchinsky 1998; Yasar, Nelson, and Rejesus 2006), we estimate the employment growth impact of covariates at various points of the conditional employment growth distribution.9 In contrast to standard regression methods, which estimate the effect of covariates at the conditional average of the outcome variable, quantile regression allows for slope heterogeneity as the parameter estimates differ by quantile, providing richer information.
Comparative Assessment of Regression Techniques for Wind Power Forecasting
Published in IETE Journal of Research, 2023
Rachna Pathak, Arnav Wadhwa, Poras Khetarpal, Neeraj Kumar
An advantage of quantile regression over the least squares regression is that its estimates are more robust against outliers in the response measurements. Here, “quantiles” of the dependent variable as modeled as functions of the independent variables; instead of the mean of the dependent variable. It was experimentally observed that quantile regression loss function based gradient boosting regressor does not generalize well over large number of samples having a near zero output. The model performed 500 boosting stages, depth of individual regression estimators was 4 and learning rate was 0.1.
Sectoral electricity consumption modeling with D-vine quantile regression: The US electricity market case
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2023
Ozan Evkaya, Bilgi Yilmaz, Ebru Yüksel Haliloğlu
The most widely used framework for the linear quantile regression is given by Koenker and Bassett (1978). It extends the ordinary least squares estimation but differs in terms of how the response variable is treated. The classical approach using least-squares is to predict the conditional mean, but instead the quantile regression allows us to investigate the impact of predictors on response variables at different quantile levels. Further explorations are practiced to improve the method (Bouye and Salmon 2009; Fenske, Kneib, and Hothorn 2011; Li, Lin, and Racine 2013; Noh, Ghouch, and Van Keilegom 2015; Spokoiny, Wang, and Hardle 2013). However, the assumptions on quantile regression are too restrictive, questioning the robustness of the method (Bernard and Czado 2015). For example, normal distribution assumption is a fragile requirement when the relationship between the response and covariates deviates from normality (Kraus and Czado 2017). Additionally, the classical quantile regression has various drawbacks concerning covariates selection, consideration of interactions, and multicollinearity. To overcome some of these issues, copulas might be incorporated in the quantile regression setting. Copulas are powerful probabilistic tools that allow for deriving the dependence among the variables flexibly. For higher dimensions, the multivariate densities can be explored using vine copulas and built-in pair copula functions. Recently, with pair copula construction, the shape of conditional quantiles gained more freedom to overcome the aforementioned restrictions. As a particular case, D-vine copula is adapted for relaxing imposed assumptions on the classical quantile regression with further flexibility on the underlying dependence between the response variable and covariates (Kraus and Czado 2017).