Quantile Regression Estimation Research Articles

Willingness to pay for sheep traits and their heterogeneous effects on prices: Evidence from primary livestock markets in Ethiopia

We test the hypothesis whether levels of key traits of sheep heterogeneously affect market prices of sheep in a rural setting. Feasible generalized least squares and (un)conditional quantile regression estimations were made on a dataset of 1153 sheep transactions in two primary small ruminant markets in the Amhara region of Ethiopia. The empirical results show that animal traits affect the observed prices of sheep differently, but only partly explain the sheep price differences. Our results also reveal that in addition to animal traits, the type of buyers and seasonality of sheep marketing cause heterogeneity in the observed prices. These findings imply that targeting the animal traits demanded by the market and access to price information that enables farmers to respond to the seasonal changes in livestock markets are essential to increase the income of sheep keepers.

Investigating Asymmetric Relationship between Financial Development and Global Competitiveness in Developed and Developing Countries

Globalization led to economic integration, which increased the competitiveness of economies through interconnection and interdependence. Financial Development (FD) is considered as an engine of Economic Growth (EG) that significantly contributes in economic productivity and raising prosperity in an economy. This study aims to analyze the relationship between FD and global competitiveness from a global perspective. For this purpose, panel data of 87 developed and 60 developing countries have been used for the period 2000- 2020. The Panel Quantile Regression (PQR) estimation technique has been used for the analysis. The results demonstrate that sustainable FD significantly increases the competitiveness of all countries. However, this impact is non-linear across different quantile groups which suggests evidence of an inverted U-shaped relationship. The linearized marginal effect indicates that all developed economies lie before the maturity of the inverted U-shaped curve. In contrast, except Bolivia, Cabo Verde, Egypt, India, Indonesia, Korea Rep of, Lebanon, Mongolia, Morocco, Nigeria, Pakistan, Philippines, Siri Lanka, Tunisia, and Vietnam, all remaining developing nations also lie before the maturity of an inverted U-shaped curve. This indicates that FD accelerates global competitiveness up to a certain optimal point, and excessive financialization may lead to the misallocation of resources and raising financial risk. The study suggests that developing countries need to implement policies to attain optimal level of sustainable FD, which boosts their competitiveness. The major contribution of the present study is to help the policy makers to formulate proper policies to increase global competitiveness.

Between Exchange Rate Returns and Crude Oil Returns in Oil-Importing Countries

Fluctuations in the financial markets stem from the reactions of investors to both market activities and more wide-ranging macroeconomic indices. This research examines the interconnectivity between returns on exchange rates and crude oil prices for ten oil-importing countries. Quarterly data spanning the period from 2000Q1 to 2022Q4 was used in the estimation. Returns had to be calculated from raw data, which were exchange rates and crude oil prices. The research methodologies include quantile regression and VAR-GARCH estimations. The study revealed a long-term association between crude oil market returns and foreign exchange markets, with currency fluctuations negatively impacting crude oil returns. The spill-over effect from the currency market to the oil market is weaker than the transmission effect from the oil market to the currency market of oil-importing countries. In particular, it was empirically established that shocks from past volatility in the currency markets of countries that import oil had commensurately lower volatility in the oil market by 6 percent. Whereas, the spillover from the crude oil market to the currency market depicts that increased turbulence on the crude oil market in the current period stimulated 55.66 percent amplified volatility in the currency market for oil-importing nations. Oil returns had a volatility persistence value of 0.1255, ratifying the weak volatility persistence of oil returns. The size of the volatility persistence of exchange rate returns is 0.997, an indication of high volatility persistence for currency returns. The study found the absence of leverage effects for currency values given a positive coefficient with a magnitude of 0.8529. In other words, bad news does not cause higher turbulence in exchange rate returns than good news will. For crude oil returns, the size of the leverage effects term is -0.0529, which is negative and significant (p<.05), implying that bad news in oil-importing economies has asymmetric impacts on the volatility of returns on crude oil prices. In effect, the oil price returns react more strongly to bad news than these returns react to good news. The findings of the study underscore the intricate relationships between local currencies and energy prices within the context of a global financial market, highlighting the significance of understanding these dynamics for effective decision-making and risk management in an increasingly interconnected world. It was recommended, among others, that international collaboration amongst countries is crucial given the global nature of energy markets.

Synergy for climate actions in G7 countries: Unraveling the role of environmental policy stringency between technological innovation and CO2 emission interplay with DOLS, FMOLS and MMQR approaches

The significant and indestructible repercussions of global warming have an enormous effect on economies worldwide. Inevitably the preservation of the environment remains a crucial element in the pursuit of sustainable development goals. The primary aim of this study is to assess the moderating effect of environmental policy stringency (EPS) between technological innovation (INV) and CO2 emission and direct association between financial development (FD), and financial globalization (FG) and environmental quality among the G7 countries. This analysis is conducted using a dataset covering the time period from 1990 to 2020, employing the Dynamic Ordinary least Square (DOLS), Fully Modified Ordinary Least Square (FMOLS), Canonical Cointegration Regression (CCR), and Method of Moment Quantile Regression (MMQR) estimation approaches. The results of DOLS, FMOLS, & CCR indicates that INV*EPS increase environmental quality by −0.21168, −0.21257 and −0.21255, respectively. Further, the outcomes of MMQR demonstrate that combine effect of INV & EPS contributes −0.2003 to −0.2264 across all quantiles from 20th to 80th. This indicates that technological innovation leads to enhanced environmental quality by mitigating CO2 emissions and implementation of more stringent environmental rules enhance the positive effects of green technologies by employing eco-friendly technologies to achieve carbon neutrality target. In order to effectively attain sustainable development goals, the study suggests that in economies that exhibit a higher degree of innovation, strong financial system, the adoption and implementation of environmentally sustainable technologies have a significant influence on the mitigation of CO2 emissions and the enhancement of environmental conditions. The study findings suggest few polices to policymakers: enhancing the green finance structure and strengthening the design of environmental regulations to promote green innovation. Research and development (R&D) activities have the potential to significantly contribute to the reduction of CO2 emissions through the effective application of scale effects and the implementation of efficient marketing tactics.

Self-employment, financial access and economic welfare: empirical evidence from Africa

Purpose This study aims to investigate the empirical linkages between self-employment, financial access and economic welfare in Africa. It particularly examines the moderating role of financial access in the self-employment-economic welfare nexus and determines relevant thresholds. Design/methodology/approach The paper samples 52 African economies from 2000 to 2018 and deploys the fixed effects and bootstrap quantile regression estimators. Findings The results show that self-employment has a negative and significant relationship with economic welfare, while access to finance has a positive and significant relationship with welfare. More notably, the conditional effect of self-employment and finance is significant and positive, confirming a synergetic effect. The result suggests that pushing more people into self-employment does not necessarily enhance economic welfare, other than the avoidance of unemployment, due to the large number of replicative and necessity entrepreneurs. However, granting the self-employed more access to affordable finance that boosts entrepreneurial activities enhances economic welfare. Practical implications African governments and relevant policymakers must recognize that deepening the financial sector is crucial in creating sustainable opportunity entrepreneurs and boosting general economic welfare. Originality/value The uniqueness of this paper centers on the exposé of the relevance of financial access/development in promoting the economic welfare of self-employed persons and entrepreneurs. It also determines relevant thresholds at which finance is most significant in procuring positive impacts on economic welfare. In addition, the simultaneous quantile regression is used to show snapshots of human development index at which this impact is paramount.

Exploring the nexus of geopolitical risk, green financing, and natural resource rents: A study of Russia's economic growth

Geopolitical risk encompasses various uncertainties arising from political, social, and economic factors, which can significantly influence a country's economic performance. Therefore in this study we analyzed the impact of geopolitical risk (GPR), green financing, and natural resource rents (NRR) on Russia's economic growth during 2000–2022 is examined in this study. The collected data is analyzed using simple quantile regression, the ADF unit root test, Johansen Co-integration, and other time series methods. A unit root test shows that level (1) data is stable and that variables are co-integrated. Quantile regression research shows that GPR positively impacts economic growth at the median and higher quantiles. In addition, green finance and commerce boost economic growth across all quantiles. The results support the resource curse hypothesis, which claims that NRR negatively affects economic growth. The Granger causality test shows that GDP and its explanatory components are causally related. These findings were compatible with quantile regression estimates after a parametric examination. The policy implications for researchers and politicians concerned with green finance, natural resource sustainability, and geopolitical dangers to economic growth are significant.

Discovering the determinants of energy intensity of Indian manufacturing firms: a panel data approach

Our study pores on evaluating the impact of firm specific and macro level determinants of energy intensity of Indian firms belonging to manufacturing and power sector. We collect a panel dataset of 3316 firms for 10 years ranging from 2010 to 2020. We employ the advanced biased corrected method of moments estimator and the quantile regression estimator for panel data models for our empirical analysis. We find that poor labor efficiency is largely responsible for increasing energy intensity of the sample firms. Energy intensity can be optimized by investing in better plant and machinery. Moreover, machineries that require frequent repairs and maintenance need to be replaced with latest tools. While larger firms are found to be energy intensive, profitable firms are found to be in a better position to enhance their energy efficiency. Under macroeconomic scenario, GDP growth and trade openness lead to boosting up the energy consumption at the firm level whereas, the global energy prices act as a constraint and necessitate careful use of energy. Based on our findings we provide certain policy recommendations and suggestions in order to limit energy intensity and enhance energy efficiency of the Indian manufacturing firms.

Concave and convex effects of ESG performance on corporate sustainable development: Evidence from China

Research background: Corporate sustainable development (CSD) is essential to a company's success and survival. Environmental, social, and governance (ESG) are regarded as major factors in measuring the impact of CSD. Companies that perform well in terms of ESG can maintain a competitive advantage and achieve sustainable development. Poor management of ESG performance and involvement in controversial activity can harm a company's credibility and reputation in the market, as well as negatively impact sustainable development. Purpose of the article: Drawing on the stakeholder and signaling theories, this paper investigates the curvilinear nexus between ESG performance and CSD. Methods: Empirical studies were conducted on a sample of 697 Chinese listed manufacturing firms that disclosed ESG information from 2010 to 2020, with a total of 5699 firm-year observations. Quantile regression analysis and the U-test were used to examine the curvilinear ESG-CSD relationship. This technique was supplemented by conducting instrumental variables tests and propensity score matching to address concerns relating to the potential existence of endogeneity problems. Findings & value added: The results of the quantile regression estimation confirm the concave-convex (inverted U-shaped and U-shaped) ESG-CSD relationship via the U-test. The relationships between the environmental and social components and CSD follow an inverted U-shaped or half-inverted U-shaped pattern, while the relationship between the governance component and CSD exhibits a concave-convex pattern. A concave ESG-CSD nexus is evident in environmentally sensitive industries, whereas a half concave-convex ESG-CSD nexus is confirmed in non-environmentally sensitive industries. This study improves scholars’ understanding of ESG performance and provides a comprehensive perspective on the double-edged effects (positive and negative consequences) of ESG practices. The instrumentalization of ESG practices for management to seek personal gain has a negative impact on CSD, while ESG practices that add value for stakeholders have a positive impact. These findings provide empirical evidence for Chinese publicly listed manufacturing firms to effectively conduct ESG practices.

The Effect of Interest and Inflation Rates on Stock Returns: Quantile Regression Analysis for Türkiye

According to financial theory, there is an inverse relationship between interest rate and stock returns and prices. In the framework of the Liquidity Preference Theory, the rise in interest rates causes the money to move towards higher interest rates, so demand for stock market decreases and returns fall. The behaviour of stock prices on interest rates and inflation has been investigated by various time series analysis methods. However, in this study, the subject is handled in a different approach by using the Quantile Regression (QR) method. In the study, nominal interest rate is decomposed into real interest rate and inflation components and effects on stock prices are examined for the period January 2013 - July 2023 separately for services, financial, industrial and technology sector indices. When it comes to the impact of nominal and real interest rates on returns in QR estimates, it is seen that the service and industrial sectors differ in terms of both tail and sign. The similarities between Least Squares estimates and QR estimates are striking. However, the effect of volatility in variables on the differentiation in relationships is also an issue that should be emphasized.

Uncertainty impacts on China’s agricultural commodity futures: a quantile perspective

ABSTRACT This study employs rolling quantile regression and non-parametric estimation methods, specifically Quantile-on-Quantile (QQ) and Causality-in-Quantiles (QC), to investigate the impact of uncertainty indices (Geopolitical Uncertainty (GPR), Climate Policy Uncertainty (CPU), and Economic Policy Uncertainty (EPU)) on China’s agricultural commodity futures. The rolling window quantile regression coefficients vary over time, with CPU having the most significant impact on agricultural commodity futures. The empirical results from the non-parametric estimation QQ method reveal when agricultural commodities are in a prosperous market, CPU and EPU exhibit relatively strong correlation, while GPR shows weaker or insignificant correlation. According to the non-parametric estimation QC method, the evidence suggests that the second-order (variance) causality relationship is relatively stronger than the first-order (mean) causality relationship, and the first-order mean causal relationship between CPU and corn and between EPU and wheat is not significant across the entire range of quantiles. The results on Hedging Effectiveness reveal that the efficiency of uncertainty hedging is substantiated. The hedging effectiveness of EPU exhibits improvement post-COVID-19, whereas the effectiveness of GPR and CPU is more pronounced in the pre-COVID-19 period.

The effect of public funding and government effectiveness on CO2 emissions in developing countries: Evidence from panel quantile analysis

AbstractEnvironmental concerns emphasize the need for sustainable finance now more than ever. The study aims to provide a comprehensive analysis of whether public funding for renewable energy impacts environmental degradation in developing countries over time. It emphasizes the relationship between green finance, renewable energy adoption, and government effectiveness in driving sustainable development. This study examines the relationship between CO2 emissions, gross domestic product, renewable energy consumption, investments in renewable and government effectiveness. The study sample includes 34 developing countries for the period between 2000 and 2020. The analysis specifically employs public flows as a measure to gauge a country's commitment to green finance. It also employs a simultaneous panel quantile regression estimator. The results reveal a cointegrating relationship among variables, with notable findings: GDP increase correlates with CO2 emissions rise, while higher renewable energy consumption correlates with CO2 emissions decrease. Interestingly, increased public funding correlates with reduced CO2 emissions for the upper quantile. Furthermore, the analysis uncovers that government policies have yet to fully align with the sustainable development goals. These findings hold critical implications for informed policymaking. Developing countries should opt for sustainable financing and create a favorable environment for investment. Moreover, funders should ensure equitable distribution of public flows within developing countries and fund less mature technologies.

How does green investment respond to ICT and financial development?

Green investment has become the most effective option to support the efforts to mitigate worldwide climate change. Due to the efficacy of green investment in tackling climate change and global warming, researchers are searching for the factors that can boost green investment. Therefore, this analysis aims to investigate the efficacy of information and communications technology (ICT) and financial development in promoting green investment in the most polluted economies. The study analyzes aggregate data from the most polluted economies using the 2SLS, GMM, and instrumental variables quantile regression estimators. In addition, we also perform regional analysis by disaggregating the data into four regions: Asia, America, Africa, and Europe. The results reveal that ICT, financial development, financial institutions, and financial markets boost green investment in the most polluted economies. However, the regional analysis confirms the favorable influence of ICT on green investment in all the regions, while financial development boosts green investment in all the regions except Africa; financial institutions and financial market development promote green investment in America and Europe. Therefore, we suggest that policymakers must increase their reliance on ICT and the financial sector while designing a policy to promote green investment.

Urbanization and economic growth in China: empirical evidence based on a SIVQR approach

PurposeWe seek to quantify the relationship between urbanization and economic growth in China using recent advances in econometric techniques.Design/methodology/approachThis study adopts a smoothed instrumental variables quantile regression (SIVQR) estimator to obtain consistent estimates of the effects of urbanization on economic growth in China. Our approach accounts for the differential impacts of urbanization across the conditional distribution of economic growth while allowing for an identification strategy that addresses the endogeneity of urbanization. Our main findings reveal that ignoring urbanization endogeneity leads to inconsistent estimates of urbanization effects. Further, we find a positive relationship between urbanization and growth resembling an inverted U-shape. This supports the hypothesis that the beneficial effects of urbanization intensify at initial stages while diminishing beyond a certain threshold, due perhaps to weakening scale economies.FindingsOur main results indicate that the individual productivity gains brought by urbanization outweigh the negative effects thereof that impede productivity, thus contributing to the economic growth in China. Further, we find that ignoring differential impacts of urbanization underestimates the beneficial effects of urbanization for provinces whose quality of governance is in the vicinity of the center of quality distribution. Ignoring the endogeneity of urbanization generates inconsistent estimates of the elasticity of economic growth with respect to urbanization. Finally, we estimate an inverted U-shape resembling relationship between urbanization and growth.Research limitations/implicationsFirst, future studies would benefit from incorporating more data as provinces further east on the mainland become more urbanized and urbanization runs its course. Second, controlling the barriers to rural-urban mobility would contribute to the robustness of the estimated relationship between urbanization and growth once such data became available. Unveiling the impact of government-imposed barriers is key to designing optimal policies that help fuel economic growth in the country. Finally, future research could benefit from information on urbanization sources not considered here such as inter-provincial migration, as such data become publicly available.Practical implicationsQuantifying the beneficial effects of urbanization on economic growth can help guide the government in China to further fuel the growth through a set of relevant policy tools that promote urbanization.Social implicationsRural-urban migration in China lays the groundwork for economic advancement in recipient cities and economies, as it may induce scale economies. This can benefit both the economy at large and the migrants.Originality/valueThe SIVQR estimator accounts for potential heterogeneous effects of urbanization across the entire conditional distribution of growth while allowing for an identification strategy that addresses the endogeneity of urbanization. An additional distinguishing feature of the current study is our use of the most recent novel, provincial-level data obtained from the National Bureau of Statistics of China. Our focus on a single country allows sidestepping issues arising from the inconsistency of the definition of urban across different countries while accounting for intra-country urbanization drivers intrinsic to China, such as natural features and geographic characteristics. Therefore, our approach has the potential to sidestep the bias resulting from the differences in mechanisms behind urbanization-growth relationships across different countries.

Quantifying Environmental Degradation through Renewable Energy, Financial Development and Economic Sustainability: Insights from Panel Quantile Regression Analysis

The degradation of the environment is a global concern that needs serious attention, including the environmental Kuznets curve (EKC) hypothesis. This article examines the effects of renewable energy, financial development and economic sustainability on the environmental quality of newly industrialized countries (NICs) from 1998 to 2021 in light of the increasing severity of environmental problems associated with industrialization. This study utilized different panel cointegration estimation techniques and panel quantile regression (PQR) estimates to obtain robust findings by examining the variance of each quantile. The results of the cointegration tests confirm the long-run relationship among the variables. Nevertheless, the outcomes from the PQR unveiled that renewable energy negatively and significantly influences CO2 emissions in NICs, namely in the lower and middle quantiles (20th–50th). Financial development showed heterogeneity in the results of all the quantiles. It results in an increase in CO2 emissions from the 70th to 90th quantiles in NICs. The EKC hypothesis is relevant to these findings as this study presents the economic sustainability index, which postulates that when NICs achieve sustainability, they give greater importance to environmental preservation and sustainability. This shift is characterized by reduced emissions throughout all quantiles, ranging from the 10th to the 90th. Economic sustainability corresponds to the falling part of the U-shaped curve of the EKC, wherein sustainability gets priority, resulting in reduced CO2 emissions. Analogous results have been confirmed by comparing heterogeneous panel estimators; nonetheless, there was a significant variation in the intensity of their parameters. Moreover, the robustness analysis through quantile slope equality and symmetric quantiles tests proved legitimate results. The study’s findings offer policymakers with valuable policy recommendations. JEL Codes: C1, F36, F43, O44, Q56

Averaging Estimation for Instrumental Variables Quantile Regression

AbstractThis paper proposes two averaging estimation methods to improve the finite‐sample efficiency of the instrumental variables quantile regression (IVQR) estimator. I propose using the usual quantile regression for averaging to take advantage of cases when endogeneity is not too strong. I also propose using two‐stage least squares to take advantage of cases when heterogeneity is not too strong. The first averaging method is to apply a recent proposal for GMM averaging to the IVQR model based on this proposed intuition. My implementation involves many computational considerations and builds on recent developments in the quantile literature. The second averaging method is a new bootstrap model averaging method that directly averages among IVQR, quantile regression, and two‐stage least squares estimators. More specifically, I find the optimal weights from bootstrapped samples and then apply the bootstrap‐optimal weights to the original sample. The bootstrap method is simpler to compute and generally performs better in simulations, but uniform dominance results have not been formally proved. Simulation results demonstrate that in the multiple‐regressors/instruments case, both the GMM averaging and bootstrap estimators have uniformly smaller risk than the IVQR estimator across data‐generating processes with a variety of combinations of different endogeneity levels and heterogeneity levels.

Macroeconomic Environment and Stock Price Movement in Nigeria: An Evaluation of Fama’s Model of Efficient Market

The study examined the link between macroeconomic environmental dynamics and stock price movements in Nigeria using Fama’s model of efficient market approach. The macroeconomic climate posed issues for Nigerian stock markets. The buying power of local currency occasionally impacted unfavourable changes in the majority of macroeconomic variables. In this study, an ex post facto research design was used. The study looked at certain macroeconomic variables and the evolution of Nigerian stock prices between 1985 and 2021. To test the hypothesis, quantile regression estimates of the Fama-French three-factor coefficient were derived. The findings showed that the interest rate and stock price movement have a negative and negligible association. Additionally, a strong and positive correlation was observed between the exchange rate and changes in stock prices. It was recommended that in order to promote stock market activity and, by extension, enhance stock prices in Nigeria, a suitable monetary policy and a sufficient amount of money supply must be implemented. Also, well-diversified portfolios that mirror the entire market portfolio should be recommended to investors to protect themselves against stock price volatility. This would serve as a guide to protect them against shocks resulting from the macroeconomic environment.

Taylor Approximation of Inventory Policies for One-Warehouse, Multi-Retailer Systems with Demand Feature Information

We consider a distribution system in which retailers replenish perishable goods from a warehouse, which, in turn, replenishes from an outside source. Demand at each retailer depends on exogenous features and a random shock, and unfulfilled demand is lost. The objective is to obtain a data-driven replenishment and allocation policy that minimizes the average inventory cost per time period. The extant data-driven methods either cannot guarantee a feasible solution for out-of-sample feature observations or generate one with excessive computational time. We propose a policy that resolves these issues in two steps. In the first step, we assume that the distributions of features and random shocks are known. We develop an effective heuristic policy by using Taylor expansion to approximate the retailer’s inventory cost. The resulting solution is closed-form, referred to as Taylor Approximation (TA) policy. We show that the TA policy is asymptotically optimal in the number of retailers. In the second step, we apply the linear quantile regression and kernel density estimation to the TA solution to obtain the data-driven policy called Data-Driven Taylor Approximation (DDTA) policy. We prove that the DDTA policy is consistent with the TA policy. A numerical study shows that the DDTA policy is very effective. Using a real data set provided by Fresh Hema, we show that the DDTA policy reduces the average cost by 11.0% compared with Hema’s policy. Finally, we show that the main results still hold in the cases of correlated demand features, positive lead times, and censored demand. This paper was accepted by J. George Shanthikumar, data science. Funding: Y. Yang acknowledges financial support from the NSFC [Grants 72125004, 71821002]. W. Zhou acknowledges financial support from the NSFC [Grants 72192823, 71821002]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.04241 .

Generative Quantile Regression with Variability Penalty

Quantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this article, we introduce a deep learning generative model for joint quantile estimation called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from many random quantile levels, allowing us to infer the conditional distribution of a response variable given a set of covariates. Our method employs a novel variability penalty to avoid the problem of vanishing variability, or memorization, in deep generative models. Further, we introduce a new family of partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile curves. A major benefit of PGQR is that it can be fit using a single optimization, thus, bypassing the need to repeatedly train the model at multiple quantile levels or use computationally expensive cross-validation to tune the penalty parameter. We illustrate the efficacy of PGQR through extensive simulation studies and analysis of real datasets. Code to implement our method is available at https://github.com/shijiew97/PGQR.

Summarizing quantile estimates of weight at length to compare condition: Geographic and temporal variation in Arctic Grayling

AbstractObjectiveWe developed a novel, simple approach to summarize variation in quantile regression estimates of weight at length across multiple levels of grouping factors (locations or years) and demonstrate its utility for comparing fish condition using Arctic Grayling Thymallus arcticus data. We compared condition among 28 geographic locations of Arctic Grayling populations and among 12 and 25 years for two populations.MethodsWe summarized variation among locations and among years within locations using percentiles (maximum, 75th, 50th, 25th, and minimum) of predicted quantiles of weight at length, allowing us to simplify the distributions of predicted quantiles of weight into highest to lowest fourths (quartiles) across locations or years. One part of this summary information, 75th percentiles of median (0.50 quantile) predicted weights at length across populations, is identical to summary statistics used to develop standard weight equations for computing relative weights. However, our approach avoids biases inherent in fitting a single standard weight equation and can accommodate among‐fish variation in weight at length via multiple quantiles when developing reference standards for comparative or diagnostic purposes. A selected new weight at length can be compared with the distribution of quantile predictions among locations in terms of weights or as proportionate weights similar to relative weight.ResultArctic Grayling in 28 geographic locations, from the southern limit of their distribution in Montana and Wyoming north through Canada and Alaska to the Arctic coast, had considerable variation in allometric exponents in weight–length relationships and in predicted weights at length. Predicted weights of Arctic Grayling for heavier fish (0.90 quantiles) in populations with less (lower quartiles) to greater (upper quartiles) weights were 127–194 g and 336–510 g at total lengths = 250 and 350 mm, respectively. Lighter fish (0.10 quantiles) in populations with less to greater weights were 100–133 g and 259–364 g, at the same total lengths, respectively. We provide statistical code and tabled values that can be used as reference standards as a replacement for standard weight equations for comparing new samples of fishes. We also quantified annual variation in condition within two intensively sampled populations, the Kuparuk River in Alaska (25 years, 1985–2012) and Red Rock Creek, Montana (12 years, 1994–2016). Annual distributions of weights at length were greater for Arctic Grayling in Red Rock Creek than those in the Kuparuk River. Variation in predicted distributions of weights at length among years was also greater for Red Rock Creek, although fish from both locations exhibited substantial among‐year variation that exceeded half the variation estimated among geographic locations.ConclusionOur estimates indicated that there was substantial spatial and temporal variation in condition of Arctic Grayling that might be investigated further to help understand constraints on populations to aid conservation and management of the species. Our summary approach can be easily extended to other investigations of fish weight at length relationships where multiple quantile estimates are made across many levels of grouping factors.

Bayesian Quantile Regression Models for Complex Survey Data Under Informative Sampling

Abstract The interest in considering the relation among random variables in quantiles instead of the mean has emerged in various fields, and data collected from complex survey designs are of fundamental importance to different areas. Despite the extensive literature on survey data analysis and quantile regression models, research papers exploring quantile regression estimation accounting for an informative design have primarily been restricted to a frequentist framework. In this paper, we introduce different Bayesian methods relying on the survey-weighted estimator and the estimating equations. A model-based simulation study evaluates the proposed methods compared to alternative approaches and a naïve model fitting ignoring the informative sampling design under different scenarios. In addition, we illustrate and conduct a prior sensitivity analysis in a design-based simulation study that uses data from Prova Brasil 2011.