Quantile Regression Coefficients Research Articles

Understanding the rural and urban household saving rise in China

This paper analyzes the different factors that drive saving rate rises of both rural and urban households in China. Using data from the Chinese Household Income Project 1995 and 2002, I first show that the whole saving rate distribution shifts up for both rural and urban households. The shift, however, differs between rural and urban households and is heterogeneous across the distribution: while rural saving increased the most at lower percentiles, urban saving experienced a larger shift at higher percentiles. Moreover, decomposition in the saving distribution shows that most of the increase in the rural saving rate is due to rising income. In contrast, only a small portion of the increase in the urban saving rate can be explained by changes in household characteristics including income. The rising urban saving rates are instead explained by changes in quantile regression coefficients over time, especially at the top of the saving distribution.

Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors

Censored quantile regression is an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the usual central covariate effects, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treating mismeasured covariates as error-free would result in estimation bias. Under censored quantile regression, we propose smoothed and corrected estimating equations to obtain consistent estimators. We establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients. Compared with the naive estimator, the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions. We conduct simulation studies to examine the finite-sample properties of the new method and apply it to a lung cancer study. Supplementary materials for this article are available online.

Predicting the long-term citation impact of recent publications

A fundamental problem in citation analysis is the prediction of the long-term citation impact of recent publications. We propose a model to predict a probability distribution for the future number of citations of a publication. Two predictors are used: the impact factor of the journal in which a publication has appeared and the number of citations a publication has received one year after its appearance. The proposed model is based on quantile regression. We employ the model to predict the future number of citations of a large set of publications in the field of physics. Our analysis shows that both predictors (i.e., impact factor and early citations) contribute to the accurate prediction of long-term citation impact. We also analytically study the behavior of the quantile regression coefficients for high quantiles of the distribution of citations. This is done by linking the quantile regression approach to a quantile estimation technique from extreme value theory. Our work provides insight into the influence of the impact factor and early citations on the long-term citation impact of a publication, and it takes a step toward a methodology that can be used to assess research institutions based on their most recently published work.

Beyond the Mean: Quantile Regression to Explore the Association of Air Pollution with Gene-Specific Methylation in the Normative Aging Study.

BackgroundAir pollution has been related to mean changes in outcomes, including DNA methylation. However, mean regression analyses may not capture associations that occur primarily in the tails of the outcome distribution.ObjectivesIn this study, we examined whether the association between particulate air pollution and DNA methylation differs across quantiles of the methylation distribution. We focused on methylation of candidate genes related to coagulation and inflammation: coagulation factor III (F3), intercellular adhesion molecule 1 (ICAM-1), interferon gamma (IFN-γ), interleukin-6 (IL-6), and toll-like receptor 2 (TRL-2).MethodsWe measured gene-specific blood DNA methylation repeatedly in 777 elderly men participating in the Normative Aging Study (1999–2010). We fit quantile regressions for longitudinal data to investigate whether the associations of particle number, PM2.5 (diameter ≤ 2.5 μm)black carbon, and PM2.5 mass concentrations (4-week moving average) with DNA methylation [expressed as the percentage of methylated cytosines over the sum of methylated and unmethylated cytosines at position 5 (%5mC)] varied across deciles of the methylation distribution. We reported the quantile regression coefficients that corresponded to absolute differences in DNA methylation (expressed in %5mC) associated with an interquartile range increase in air pollution concentration.ResultsInterquartile range increases in particle number, PM2.5 black carbon, and PM2.5 mass concentrations were associated with significantly lower methylation in the lower tails of the IFN-γ and ICAM-1 methylation distributions. For instance, a 3.4-μg/m3 increase in PM2.5 mass concentration was associated with a 0.18%5mC (95% CI: –0.30, –0.06) decrease on the 20th percentile of ICAM-1 methylation, but was not significantly related to the 80th percentile (estimate: 0.07%5mC, 95% CI: –0.09, 0.24).ConclusionsIn our study population of older men, air pollution exposures were associated with a left shift in the lower tails of the IFN-γ and ICAM-1 methylation distributions.CitationBind MA, Coull BA, Peters A, Baccarelli AA, Tarantini L, Cantone L, Vokonas PS, Koutrakis P, Schwartz JD. 2015. Beyond the mean: quantile regression to explore the association of air pollution with gene-specific methylation in the Normative Aging Study. Environ Health Perspect 123:759–765; http://dx.doi.org/10.1289/ehp.1307824

Associations of blood pressure with common factors among left-behind farmers in rural China: a cross-sectional study using quantile regression analysis.

The whole range of blood pressure (BP) has important implications. Yet, published studies focus primarily on hypertension and hypotension, the two extremes of BP continuum. This study aims at exploring quantile-specific associations of BP with common factors. The study used cross-sectional survey, collected information about gender, age, education, body mass index (BMI), alcohol intake, diet risk behavior, life event index, physical activity, fasting capillary glucose (FCG), and systolic/diastolic blood pressure (SBP/DBP) and pulse pressure (PP) from farmers living in 18 villages from rural Anhui, China, and performed descriptive and multivariate and quantile regression (QR) analysis of associations of SBP, DBP, or PP with the 9 factors surveyed. A total of 4040 (86.3%) eligible farmers completed the survey. Average hypertension prevalence rate and SBP, DBP, and PP values estimated 43.20 ± 0.50% and 141.37 ± 21.98, 87.76 ± 12.23, and 53.63 ± 15.72 mm Hg, respectively. Multivariate regression analysis revealed that all the 9 factors were significantly (P < 0.05) associated with one or more of SBP, DBP, and PP. QR coefficients of SBP, DBP, or PP with different factors demonstrated divergent patterns and age, BMI, FCG, and life event index showed substantial trends along the quantile axis. Hypertension prevalence rate was high among the farmers. QR modeling provided more detailed view on associations of SBP, DBP, or PP with different factors and uncovered apparent quantile-related patterns for part of the factors. Both the population group studied and the trends in QR coefficients identified merit specific attention.

Unconditional and Conditional Standards Using Cognitive Function Curves for the Modified Mini-Mental State Exam: Cross-Sectional and Longitudinal Analyses in Older Chinese Adults in Singapore.

The conventional practice of assessing cognitive status and monitoring change over time in older adults using normative values of the Mini-Mental State Exam (MMSE) based on age bands is imprecise. Moreover, population-based normative data on changes in MMSE score over time are scarce and crude because they do not include age- and education-specific norms. This study aims to develop unconditional standards for assessing current cognitive status and conditional standards that take prior MMSE score into account for assessing longitudinal change, with percentile curves as smooth functions of age. Cross-sectional and longitudinal data of a modified version of the MMSE for 2,026 older Chinese adults from the Singapore Longitudinal Aging Study, aged 55-84, in Singapore were used to estimate quantile regression coefficients and create unconditional standards and conditional standards. We presented MMSE percentile curves as a smooth function of age in education strata, for unconditional and conditional standards, based on quantile regression coefficient estimates. We found the 5th and 10th percentiles were more strongly associated with age and education than were higherpercentiles. Model diagnostics demonstrated the accuracy of the standards. The development and use of unconditional and conditional standards should facilitate cognitive assessment in clinical practice and deserve further studies.

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.

Genome‐wide polygenic scoring for a 14‐year long‐term average depression phenotype

BackgroundDespite moderate heritability estimates for depression-related phenotypes, few robust genetic predictors have been identified. Potential explanations for this discrepancy include the use of phenotypic measures taken from a single time point, rather than integrating information over longer time periods via multiple assessments, and the possibility that genetic risk is shaped by multiple loci with small effects.MethodsWe developed a 14-year long-term average depression measure based on 14 years of follow-up in the Nurses' Health Study (NHS; N = 6989 women). We estimated polygenic scores (PS) with internal whole-genome scoring (NHS-GWAS-PS). We also constructed PS by applying two external PS weighting algorithms from independent samples, one previously shown to predict depression (GAIN-MDD-PS) and another from the largest genome-wide analysis currently available (PGC-MDD-PS). We assessed the association of all three PS with our long-term average depression phenotype using linear, logistic, and quantile regressions.ResultsIn this study, the three PS approaches explained at most 0.2% of variance in the long-term average phenotype. Quantile regressions indicated PS had larger impacts at higher quantiles of depressive symptoms. Quantile regression coefficients at the 75th percentile were at least 40% larger than at the 25th percentile in all three polygenic scoring algorithms. The interquartile range comparison suggested the effects of PS significantly differed at the 25th and 75th percentiles of the long-term depressive phenotype for the PGC-MDD-PS (P = 0.03), and this difference also reached borderline statistical significance for the GAIN-MDD-PS (P = 0.05).ConclusionsIntegrating multiple phenotype assessments spanning 14 years and applying different polygenic scoring approaches did not substantially improve genetic prediction of depression. Quantile regressions suggested the effects of PS may be largest at high quantiles of depressive symptom scores, presumably among people with additional, unobserved sources of vulnerability to depression.

On Testing the Equality of Mean and Quantile Effects

Abstract This paper proposes tests for equality of the mean regression (MR) and quantile regression (QR) coefficients. The tests are based on the asymptotic joint distribution of the ordinary least squares and QR estimators. First, we formally derive the asymptotic joint distribution of these estimators. Second, we propose a Wald test for equality of the MR and QR coefficients considering a single fixed quantile, and also describe a more general test using multiple quantiles simultaneously. A very salient feature of these tests is that they produce asymptotically distribution-free nature of inference. In addition, we suggest a sup-type test for equality of the coefficients uniformly over a range of quantiles. For the estimation of the variance-covariance matrix, the use sample counterparts and bootstrap methods. An important attribute of the proposed tests is that they can be used as a heteroskedasticity test. Monte Carlo studies are conducted to evaluate the finite sample properties of the tests in terms of size and power. Finally, we briefly illustrate the implementation of the tests using Engel data.

Censored quantile regression with recursive partitioning-based weights

Censored quantile regression provides a useful alternative to the Cox proportional hazards model for analyzing survival data. It directly models the conditional quantile of the survival time and hence is easy to interpret. Moreover, it relaxes the proportionality constraint on the hazard function associated with the popular Cox model and is natural for modeling heterogeneity of the data. Recently, Wang and Wang (2009. Locally weighted censored quantile regression. Journal of the American Statistical Association 103, 1117-1128) proposed a locally weighted censored quantile regression approach that allows for covariate-dependent censoring and is less restrictive than other censored quantile regression methods. However, their kernel smoothing-based weighting scheme requires all covariates to be continuous and encounters practical difficulty with even a moderate number of covariates. We propose a new weighting approach that uses recursive partitioning, e.g. survival trees, that offers greater flexibility in handling covariate-dependent censoring in moderately high dimensions and can incorporate both continuous and discrete covariates. We prove that this new weighting scheme leads to consistent estimation of the quantile regression coefficients and demonstrate its effectiveness via Monte Carlo simulations. We also illustrate the new method using a widely recognized data set from a clinical trial on primary biliary cirrhosis.

The effect of fruits and vegetables in the elevated plasma homocysteine: experience of using a quantile regression approach.

The purpose of this issue is to investigate the effect of folate from fruits and vegetables (FV) intake on plasma homocysteine concentration (tHcy), using a quantile regression (QR) approach that allow us to explore whether and how covariates influence various parts of the conditional distribution of tHcy. The study population, selected from the Health Survey in São Paulo‐Brazil, consisted of 574 individuals who completed a 2×24 hr dietary intake protocol and had a blood sample collected. To remove the effects of the within‐person variation and estimate individual intake, we used the Multiple Source Method (MSM). The QR coefficients were estimated for percentiles from 5th to 95th, and compared with results from multiple linear regression using Ordinary Least Squares models. The tHcy was dependent variable and FV intake was the independent variable, adjusted for age, sex, serum B6 and B12, natural folate (other sources than FV), folic acid, betaine, methionine, MTHFR genetic variants, and an interaction between age and FV intake. The association between tHcy with FV intake was inverse and significant. The QR coefficient at 90th percentile was almost twice at 65th (−1.77 and −1.03 respectively). Using the linear regression, the coefficient was −0.97. The association between FV intake and tHcy is not constant through the percentiles of tHcy and tend to be stronger as the tHcy increases. Research support: FAPESP and CNPq.

Reconciling quantile autoregressions of firm size and variance–size scaling

The aim of this paper is to understand what economic mechanisms may cause the Law of Proportionate Effect to break down for fast-growing and shrinking firms. Recent evidence has highlighted that the first-order coefficients of quantile auto-regression of firm size decline across quantiles. Our theoretical results show that negative variance–size scaling is sufficient to yield a decline in quantile auto-regression coefficients if firm log-size is Laplace-distributed, conditional on size one period ahead. However, it is sufficient only for declining auto-regression coefficients for fast-growing firms under Asymmetric Laplace conditional log-size if skewness is decreasing with size. In other words, if the growth of large firms is less dispersed and more left-skewed, size is a disadvantage for the growth of fast-growers, but not necessarily an advantage for fast-decliners. Thus, size-related determinants of negative growth skewness, such as diseconomies of growth, market power, and managerial attention issues, impact on how the LPE is violated. Using data on Dutch manufacturing companies from the Business Register of Enterprises observed between 1994 and 2004, our empirical estimates of quantile regression models confirm the evidence of declining quantile regression coefficients for small–medium firms (20–199 employees) mainly in the right-most quantiles, and for the same subsample, we find that growth rates variance and skewness are decreasing with size. The theoretical propositions of the paper are thus corroborated.

Invariant scaling relationship between functional dissimilarity and co‐occurrence in fish assemblages of the Patos Lagoon estuary (Brazil): environmental filtering consistently overshadows competitive exclusion

Determining how assembly rules (e.g. limiting similarity, environmental filtering and neutrality) shape community structure along environmental gradients and across spatial scales is still controversial. The study of functional relationships between coexisting species may help to disentangle among these assembly rules. Here, we compared pairwise functional dissimilarities between fish species to their corresponding pairwise co‐occurrences. Fish assemblages (n = 835) were sampled monthly in Patos‐Mirim system (Brazil) using both bottom trawling and beach seining. Species occurrences were recorded and functional traits related to locomotion and food acquisition were measured on several individuals from each species. The region studied was divided in two areas corresponding to each side of a floodgate located in São Gonçalo Channel: a freshwater channel up the floodgate and, down the floodgate, the Patos Lagoon estuary. The relationship between functional dissimilarity and co‐occurrence between species pairs was assessed using quantile regressions for each month and at different spatial scales. Overall, quantile regression coefficients between functional dissimilarities (either based on locomotion types or feeding habits) and co‐occurrence values were negative, suggesting that co‐occurrence increases with functional redundancy regardless of spatial scale. Our results support the assumption that environmental filters have more influence than biotic interactions on the structure of fish assemblages even locally.

Average Collapsibility of Distribution Dependence and Quantile Regression Coefficients

Abstract. The Yule–Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth introduced the concept of distribution dependence between two random variables X and Y, and gave two dependence conditions, each of which guarantees that reversal of qualitatively similar conditional dependences cannot occur after marginalizing over the background variable. Ma, Xie and Geng studied the uniform collapsibility of distribution dependence over a background variable W, under stronger homogeneity condition. Collapsibility ensures that associations are the same for conditional and marginal models. In this article, we use the notion of average collapsibility, which requires only the conditional effects average over the background variable to the corresponding marginal effect and investigate its conditions for distribution dependence and for quantile regression coefficients.

Genetic Markers of Obesity Risk: Stronger Associations with Body Composition in Overweight Compared to Normal-Weight Children

BackgroundGenetic factors are important determinants of overweight. We examined whether there are differential effect sizes depending on children's body composition.MethodsWe analysed data of n = 4,837 children recorded in the Avon Longitudinal Study of Parents and Children (ALSPAC), applying quantile regression with sex- and age-specific standard deviation scores (SDS) of body mass index (BMI) or with body fat mass index and fat-free mass index at 9 years as outcome variables and an “obesity-risk-allele score” based on eight genetic variants known to be associated with childhood BMI as the explanatory variable.ResultsThe quantile regression coefficients increased with increasing child's BMI-SDS and fat mass index percentiles, indicating larger effects of the genetic factors at higher percentiles. While the associations with BMI-SDS were of similar size in medium and high BMI quantiles (40th percentile and above), effect sizes with fat mass index increased over the whole fat mass index distribution. For example, the fat mass index of a normal-weight (50th percentile) child was increased by 0.13 kg/m2 (95% confidence interval (CI): 0.09, 0.16) per additional allele, compared to 0.24 kg/m2 per allele (95% CI: 0.15, 0.32) in children at the 90th percentile. The genetic associations with fat-free mass index were weaker and the quantile regression effects less pronounced than those on fat mass index.ConclusionsGenetic risk factors for childhood overweight appear to have greater effects on fatter children. Interaction of known genetic factors with environmental or unknown genetic factors might provide a potential explanation of these findings.

Conditional Quantile Processes Based on Series or Many Regressors

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantile-specific coefficients and estimate the function-valued coefficients from the data. We develop large sample theory for the empirical QR coefficient process, namely we obtain uniform strong approximations to the empirical QR coefficient process by conditionally pivotal and Gaussian processes, as well as by gradient and weighted bootstrap processes.We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence, large sample distributions, and inference methods based on strong pivotal and Gaussian approximations and on gradient and weighted bootstraps. All of the above results are for function-valued parameters, holding uniformly in both the quantile index and in the covariate value, and covering the pointwise case as a by-product. If the function of interest is monotone, we show how to use monotonization procedures to improve estimation and inference. We demonstrate the practical utility of these results with an empirical example, where we estimate the price elasticity function of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption.

Modeling tropical cyclone intensity with quantile regression

AbstractWind speeds from tropical cyclones (TCs) occurring near the USA are modeled with climate variables (covariates) using quantile regression. The influences of Atlantic sea‐surface temperature (SST), the Pacific El Niño, and the North Atlantic oscillation (NAO) on near‐coastal TC intensity are in the direction anticipated from previous studies using Poisson regression on cyclone counts and are, in general, strongest for higher intensity quantiles. The influence of solar activity, a new covariate, peaks near the median intensity level, but the relationship switches sign for the highest quantiles. An advantage of the quantile regression approach over a traditional parametric extreme value model is that it allows easier interpretation of model coefficients (parameters) with respect to changes to the covariates since coefficients vary as a function of quantile. It is proven mathematically that parameters of the Generalized Pareto Distribution (GPD) for extreme events can be used to estimate regression coefficients for the extreme quantiles. The mathematical relationship is demonstrated empirically using the subset of TC intensities exceeding 96 kt (49 m/s). Copyright © 2008 Royal Meteorological Society

Intergenerational Earnings Mobility Among Daughters and Sons: Evidence from Sweden and a Comparison with the United States

AbstractThis article adopts Chadwick and Solon's (2002) model by using family earnings in the study of intergenerational earnings mobility with a highlight on the role of assortative mating. I analyze mean and quantile regression coefficients as well as transition matrices to investigate family earnings mobility between parents and daughters and parents and sons from Swedish register data. My findings indicate that Sweden has a higher degree of mobility compared to the United States, and that assortative mating also plays an important role as a channel through which income status is transmitted across generations in Sweden. However, the difference in intergenerational mobility patterns between the two countries does not, inherently, depend on factors that affect the marriage match. Swedish daughters and sons exhibit a rather similar scheme of intergenerational earnings transmission. Daughters tend to be slightly more mobile than sons, and the difference between their elasticity estimates is small but statistically significant. The quantile regression approach reveals that parents' family earnings are less important as an explanatory variable at the upper end of the children's earnings distribution than they are at the bottom, while transition matrices show substantial earnings persistence in the top earnings class.

Changes in the distribution of house prices over time: Structural characteristics, neighborhood, or coefficients?

Quantile hedonic house price function estimates imply that appreciation rates were higher between 1995 and 2005 for high-priced homes in Chicago. Decompositions of temporal changes in the house price distribution suggest that the types of homes sold and their location do not account for the change in the price distribution. Rather, higher appreciation rates for high-priced homes are explained by differences in the quantile regression coefficients over time.

On a generalization of a result of W. G. Cochran

SUMMARY A relationship due to W.G. Cochran showing the effect on least squares regression coefficients of marginalizing over or conditioning on an explanatory variable is generalized to quantile regression coefficients. The condition under which conditioning does not induce interaction or effect reversal is shown. Examples are given. The discussion is simplest when all variables are continuous; the extension to discrete variables is outlined.