Questions tagged [quantile-regression]

Quantile regression allows us to estimate the effect of a set of predictor variables over the entire distribution of the outcome variable or any particular quantile.

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Control Variate Estimator for Quantile Regression

I want to understand how a control variate estimator for quantile regression is computed. Therefore I read Ma and Koenker (2006). I'am unsure if I understood every step to achieve the CV (control ...
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Compute the inverse of a conditional quantile regression output

Brunello et al (2009) show that extended compulsory schooling leads to increased wages respectivly to the individual gender. Their empirical model first uses quantile regression to show the impact of ...
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Coefficient of the Intercept of quantile regression is surprisingly high [closed]

I'am worried about my quantile regression fit results which has the following formula ...
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rq() delivers the same coefficient results for all tau

I created a large module (52 covariates mostly factors), to estimate the effect of compulsory schooling on log_earnings. I used the quantile regresion technique. Since I do my study in R I go with a ...
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How to construct cognitive ability as in Brunello et al (2009)?

I try to replicate the study of Brunello et al (2009) but I do not understand how I construct or generate the ability variable of an individual. Can someone explain how $$ a \sim G_a(0,\sigma^2_a)$$ ...
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Some questions regarding the conditional quantile regressions of Brunello et al (2009)

I want to replicate the study of Brunello et al (2009) using only the data of SHARE. The main idea of the paper, as I understood, is to show wheter aditional years of compulsory schooling have an ...
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Quantile regression vs probability density estimation

If you want to predict a range for a regression problem using a deep network, you can do quantile regression and go with (for example) 5% and 95% quantiles. The other option is predicting a ...
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redundant level dummy variable [closed]

In classical statistical regression analysis (e.g. linear regression) one level of the categorical variable is usually not used to create a dummy variable to create a reference (e.g. there is only one ...
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monotonicity constraint question

I used this model: quantile regression neural network successfully in a couple of project. I am now faced with requiring monotonic decreasing rather than monotonic non-decreasing behaviour. Could I ...
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quantile regression (cross validation in R) [closed]

How can I do a cross validation for quantile regression in R or any other methods to compare between multiple regression and quantile regression?
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Is there a joint test of model coefficients, effectively testing for main and interaction effects in quantile linear mixed model?

I am just reading this paper: Linear Quantile Mixed Models: The lqmm Packagefor Laplace Quantile Regression. Let us assume I have a repeated observation experiment, where I want to assess the effect ...
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How Do I Build a Quantile Regression Model with GradientBoostingRegressor from sklearn?

I am building a quantile regression model using scikit-learn's GradientBoostingRegressor algorithm. I was going to use GridSearchCV for hyperparameter optimization. Two questions: Does it make sense ...
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Is there a way to analyse main effects on quantile mixed-effect regression in the spirit of the “ANOVA” procedure (now for medians)?

I would like to analyse my data using quantile regression with random effect. The problem is I have also categorical covariates, which will "split" the output into corresponding levels. I ...
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Modeling Expected Value Using Quantile Regression as an Ensemble

I'm trying to find a primer on a topic that I'm sure must have been studied, but I can't find anything on. Suppose we'd like to do regression in a supervised learning setting to learn the expected ...
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Quantile regression for panel data - what is a tolerable zero tolerance in `rqpd`?

I'm using the R package rqpd to perform quantile regression on panel data with penalized fixed effects and running into singularity issues. The issue can be "fixed" by simply decreasing the <...
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What does, actually, the quantile regression asseses, assuming single two-level categorical covariate, difference in medians or median of differenes?

I know that, for a single, two-level categorical covariate, like sex={Male, Female}, the linear regression coefficients are about difference in means. It's like the t test. Does the quantile ...
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Singular Design matrix error for a weighted quantile regression from quantreg R

My question is related to the question from this thread (Cause of singularity in matrix for quantile regression). But I am not able to solve my specific issue. My data-set includes 2000 observations (...
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MAE regression gives biased regression parameters for symmetric error?

Consider a linear model, $$ y_i = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i. $$ From the Gauss-Markov theorem, I know that, under nice conditions, the $\hat{\beta}_{OLS}=(X^TX)^{-1}X^Ty$ ...
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Koenker & Machado (1999) goodness-of-fit criterion (R1)

Has anyone come across a journal paper or a book providing a rule of thumb regarding what R1 is appropriate in research that focuses on the impact of macroeconomic or bank-specific variables on bank ...
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Unconditional Quantile Regressions – interpretation

I'm using the contributions by Firpo et al. (2009) for my research on determinants of inequality and particularly the effects of cash transfers on income inequality. With a continuous covariate the ...
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Global Estimates for Quantile Regression

Quantile regression (QR) provides information at each quantile of interest (e.g., .1, .2 ... .8, .9), but to compare QR results with those from an ordinary least squares regression, you'd need to ...
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Using quantile regression results to select and weight variables for models

Linear regression is commonly used to identify predictor(s) (e.g., scores on cognitive ability or personality assessments) of job performance. Typically, predictors that exhibit a significant ...
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Formal method to predict probability of a continuous variable

I am trying build a regression to model cdf, i.e to predict the probability that a continuous variable exceeds an arbitrary threshold. I explored using quantile regression, but it seems that I have ...
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Power calculation for outcome tested using quantile regression

I am looking to power a study where the primary outcome will be tested using quantile regression (median time). Does anyone have any advice on how to power this & determine the sample size? In ...
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How to compute custom contrasts for linear quantile mixed model from lqmm

I would like to get custom pairwise contrasts and Holm adjustment for a linear quantile mixed model generated using the lqmm and glht functions, but my attempt generates an error. For comparison, I ...
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Can I treat count data as continuous in Quantile regression?

I have data with the response is the number of dengue disease incidence per year from 2013-2019. The number of incidence per year is a big number, many values of 1000, minimum values is 228. I am ...
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Why are the intercept values of my QR non-monotonic?

I was led to believe that when conducting quantile regression you would expect intercept values to increase as you go up quantiles. However, I have run a quantile regression and the intercepts are as ...
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Appropriate Data Analysis when Criterion has Heavy-Tailed Distribution

I have a data set where my independent variables (i.e., personality assessment scores) are continuous and follow a normal distribution. The criterion, sales performance, is heavy-tailed and follows a ...
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How, if ever, is quantile linear mixed model compatible with the signed rank test?

Paired Wilcoxon test evaluates median change rather than difference in medians. Quantile linear mixed model (defined for medians) evaluates change in the medians, rather than median change, as any ...
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Interpretation of the coefficients in quantile regression - a discrepancy between sources

In various sources you can find, that interpretation of the quantile regression is pretty much like in the linear regression, with the difference now it's about the medians, rather than means. Like ...
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Is it possible to have ANOVA-type assesment of main efects in quantile mixed linear regression?

As in the title. I would like to assess the main effects by applying a joint test to the quantile regression. In R it's done by lqmm(), but neither anova, Anova, emmeans, or multcomp support it. I ...
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How to assess a Quantile Regression Model

I am trying to learn more about quantile regressions. In OLS Models, we can use statistics such as R-sqd and RMSE, MAE, MAPE etc to assess the accuracy/predictability of a model. Is there any way to ...
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What is Directional Quantile Regression?

I am coming from a computer science background and I am reading this research paper https://www.sciencedirect.com/science/article/pii/S0047259X10001636 There are so many math equations that I don't ...
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Understanding and interpreting quantile regression

I am trying to better understand what quantile regressions are and how we can interpret them. I know that quantile regressions are used to model a specific conditional quantile $\tau$ of a response ...
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Is performing a quantile regression different than using slope interaction dummies?

Just becoming introduced to the concept of quantile regression. It seems rather useful, but I'm not sure if I completely understand the concept yet. Does a quantreg essentially set slope interaction ...
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imbalanced regression problem + lower bound prediction + custom error weighting

I'm looking for a simple approach (e.g. defining a new target label / sample weights and then using some off-the-shelf regressor with some standard objective) for the following problem: I want to ...
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How to interpret coefficient for rq()

Suppose my prediction equation code is: model = rq(y ~ a+b+c+d+a:b, data=df) I used quantile regression. and I obtain the coefficient: ...
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Estimate distribution from mean and prediction intervals

I'm using an ML-model (gradient boosting) to predict mean, upper and lower quantiles of a target variable which is gamma distributed. I want to construct distributions for the predictions and figured ...
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Model to be used with only median data and weights

I am finding a decent method to demonstrate if there is trend in the median age at diagnosis of multiple cancers. I do not have a breakdown of individual ages though, all I have is only (1) Median age ...
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Quantile loss 50th is MAE, is it? [duplicate]

I'm not sure the above sentence is true, but I read it here, here and here that quantile loss function percentile 0.5 is MAE(mean absolute error), Is it true(Yes or No)? and How?
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For non-parametric regression which one has better interpretation and properties, GAM or quantile regression?

As in the topic. I want to interpret data for which I have no clues about the distribution. It's neither count, percentage, continuous. I don't want any transformations. Instead I would like to ...
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Efficiency of OLS versus Quantile regression estimator

If I have a linear model $ y_i = x_i'\boldsymbol\beta + \epsilon_i $ and I assume that OLS estimator of $\boldsymbol\beta$ is unbiased and consistent and Least absolute deviation (LAD) estimator of $...
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Quantile regression estimator - conditions for consistency and efficiency

What are the conditions for consistency and efficiency of Quantile regression estimator (for example LAD) in a linear regression model?
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Why does quantile regression not work for the newsvendor model?

I want to use quantile regression to solve the newsvendor model for a critical fractile of 2/3. Surprisingly the quantile that minimizes the cost in my study is not the 2/3 quantile but the 80%. ...
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How do I select predictors for my quantile regression model?

I'm using a housing dataset that contains predictors such as # of bedrooms, bathrooms, car spots, distance from city center etc. to predict the price of sold houses. I'll be performing quantile ...
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Quantile regression does not give expected result regarding costs

I want to predict the length of an event. When I underestimate the event length it costs me 2€ (per minute) while an overestimation costs 1€ (per minute). To capture this price inbalance I tried using ...
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1answer
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How to fill the bins?

Consider 1 million people earning money, sorted in increasing order. The kth decile, i.e. the kth 100,000 of them has an income share of $f(k)$ with $f(k)<f(k+1)$ and $\sum_{k=1}^{10} f(k)=1$. Let ...
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Quantile regression and mean log predictive score

During my research, I got stuck with an evaluation of my quantile regression models (qr). I have two QR models that model some economic variable in time. I would like to evaluate which model is better ...
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Assumptions of L1 Regression [duplicate]

I know that the L2 regression (regression-based L2 loss function/least square regression) assumptions are as follows. 1- Little or no Multicollinearity between the features. 2- Homoscedasticity ...
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How could one estimate $Y = X\beta \times \epsilon$ with $\epsilon \sim \text{Beta}(a,b)$?

Suppose the data generating process is $$Y_i=f(X_i)M_i.$$ where $M_i$~$Beta(a,b)$ and $f$ linear, for example,$f(X_i)=\alpha_0+\alpha_1X_i$. This is equivalent to $$M_i=Y_i/f(X_i).$$ I'm trying to ...

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