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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Quality of a quantile regression learner

Given a learning algorithm that selects and trains quantile models, how do we evaluate it? One idea is to - use the algorithm to train a model on a synthetic dataset with labels drawn from an ...
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Quantile regression, minimizer [duplicate]

Let's consider values $z_1, \dots, z_m$ and the minimizer of the function: $$ \min_q (1-\tau) \sum_{z_i<q} (q-z_i) + \tau \sum_{z_i \geq q}(z_i -q)$$ Why does minimizing this function gives the $\...
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Dependent variables, regression

I am trying do make some descriptive statistic. In my dataset I have ID, Age, time from start of being registered, sex, birth-place. The time from start of being registered minus date 15 June 2019 ...
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Nonlinear quantile regression SSReg analogue

I have recently remembered that $SSTot = SSRes + SSReg$ fails to hold in the case of nonlinear regression. $$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \hat{y_i}) + (\hat{y_i} - ...
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Is quantile regression a special case of OLS?

Quantile regression is often advertised as a way of "predicting change in the dependent variable that is not the mean." It seems like one can do this with linear regression, however. Am I correct? ...
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In quantile regression how do you use the equivariance property with many variables $Q_{h(x,\epsilon)|x}(u|x)$?

I have seen in a text book that if we assume monotonicity and independence then if $Q_{y|x}(u|x)$ is the conditional quantile function. and $Y=h(x,\epsilon)$ then $Q_{y|x}(u|x)= h(x,Q_{\epsilon|...
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What is the median of $y_{i}$ given $x_{i}$ for the function $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$

$y_{i}$ is a kx1 matrix, $x_{i}$ is a kxk matrix, $\beta$ is a 1xk matrix of coefficients and $u_{i}$ is a kx1 matrix of error terms. $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$ and $med(u_{i}|x_{i}...
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Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...
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Quantile Regression loss function/ check function proof

Can anyone help me to show that this statement is true. I have looked in Koenker's Quantile Regression (2000) and a load of other sources but I cannot find a solution. There seems to be a trick ...
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How do I formulate logistic quantile regression models?

Which of these models is most appropriate given the data (prediction is my goal), and why? I haven't had much experience with quantile regression, and I have so far assumed (probably niavely) that ...
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How does quantile regression compare to logistic regression with the variable split at the quantile?

I googled a bit but didn't find anything on this. Suppose you do a quantile regression on the qth quantile of the dependent variable. Then you split the DV at the qth quantile and label the result ...
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Method to combine quantile regression forecasts

I am predicting electricity usage for customers which is highly skewed. Regular regression models did not fit well due to skewed distribution, hence I tried quantile regression. I'm obtaining the ...
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The use of the quantile regression

I would like your help regarding the quantile regression. I was wondering if it makes sense to use the quantile regression when the relation of the number of data between variable x and y is 1 to 1, ...
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76 views

Making a model to predict the error of another model

So basically I have a machine learning model where I want to have a prediction interval, the model is XGBoost so it is tricky to do Quantile Regression and I was looking for an alternative method to ...
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Interpret Intercept Plot from Series of Quantile Regressions in R

Essentially, I am looking at a set of housing data from 2000-2017 and I am examining 'affordability' by year through quantile regression. The Y variable (affordability) is a ratio of what an ...
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What are the advantages of linear regression over quantile regression?

The linear regression model makes a bunch of assumptions that quantile regression does not and, if the assumptions of linear regression are met, then my intuition (and some very limited experience) is ...
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25 views

Interaction term and sample selection

I have a dependent variable Y which is continuous. I want to study the impact of X on Y using OLS in a linear model, but I suspect the impact of X is more important for observations with a high value ...
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Should log-log relationship of relative std.err. vs. sample size always be linear?

I am seeing a strong linear relationship between log-log plot of number of samples vs std.error of the mean estimate. As far as I can tell, this is expected (e.g. link). Since std. error is calculated ...
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76 views

Evaluation metric for prediction interval?

In quantile regression (https://en.wikipedia.org/wiki/Quantile_regression), what are some suitable evaluation metrics? Intuitively, I think a good model should have: good accuracy, i.e. the ...
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determine quantile for prediction with quantile regression (forests)

Having a fitted quantile regression (forest) model is great. However, how does one choose the best quantile to perform the actual prediction? One idea would be to use bootstrapping. In other words, ...
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Fastest algorithm to solve quantile regression with single predictor and no intercept

I was wondering what would be the most efficient algorithm to solve quantile regression with a single predictor and no intercept? I tried a Brent line search, but unfortunately that's no faster than ...
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2-Stage Least Absolute Deviations (2SLAD) Estimator with Quantile Regression in R

I was reading a paper, in which they introduce the following analysis, but without much further explanation as to what is being done: Since our key variables of interest are endogenous, we follow ...
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Quantile regression line formulation

I want to apply a quantile regression model to my data, and of course would like to understand at least in principle what quantile regression does to my data. Now I understand the basic concept and I ...
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Confidence Bands for Quantile Regression

Can anyone suggest a way to construct confidence bands on a particular quantile regression line? I am working with the quantreg package in R.
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Formulating quantile regression as Linear Programming problem?

How do I formulate quantile regression as a Linear Programming problem? When looking at the median quantile problem I know it is \begin{align} \text{minimize } & \sum_{i=1}^n |\beta_0 + X_i \...
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heteroskedasticity and quantile regression

I am working on a quantile regression. I saw that there are tests for heteroskedasticity like a test by machado and silva (MSS) and a KB test. However, i have also read that having errors with ...
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Derivatives of quantile loss function [duplicate]

I'm reading a text - Roger Koenker (2005) Quantile Regression [page 8] - that goes like this: Consider the function $$R(\xi) = \sum_{i=1}^n \rho_\tau(y_i-\xi)$$ where $$\rho_\tau(y_i-\xi) =(y_i-\xi)(\...
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partial dependence plot for quantile regression forest

I am using this code: ...
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Quantile-Regression and Grid-Search

i am currently experimenting with quantile-regression in h2o. I am building prediction intervals. For the individual regression models i am looking after R^2, RMSE and also quantile-loss. I performed ...
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SGD and quantile regression

It is my understanding that the quantile loss is not differentiable (at 0) so base gradient descent cannot be used. However, Vowpal Wabbit which is an SGD-based learner very much includes quantile ...
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using rstanarm for quantile regression

I understand that rstanarm can be used for GLMs, GAMs and hierarchical models. Does anyone know, if I can use it to estimate quantile regression models? If not, are there other Baysian R package, ...
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quantile regression and high cost of under-predicting

I have a regression problem where it is better to over-predict than under-predict (i.e. the cost of under-predicting is higher). I think the use of quantile regression with a tau above the median - e....
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How to you measure the accuracy of a model that gives quantile forecasts or distributions of forecasts?

I've come across some recent demand forecasting approaches that present methods where instead of generating just a point forecast, the model outputs a set of forecast quantiles, or a distribution of ...
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145 views

Similarity LAD and quantile regression

With Least Absolute Deviations (LAD) regression coefficients are estimated through minimization of the sum of the absolute values of the residuals. Quantile regression aims at estimating either the ...
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In multivariable quantile regression, how can we determine which observation corresponds with a particular quantile?

I'm trying to use quantile regression to solve an areal interpolation problem as described in this paper: https://www.tandfonline.com/doi/abs/10.1080/00045608.2011.627054 Basically I have a set of ...
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Quantile Regression - What is the “bandwith”?

I am trying to perform a Quantile Regression on hundreds of series. From time to time, I have very small series that issue a warning. Here's a sample code to reproduce : ...
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How does quantile regression behave when having more variables than observations?

When having a dataset with a larger number of variables than observations, it is not possible to build a linear regression model, because such a model would have an infinite number of possible ...
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difference-in-difference regression run as quantile regression

The usual regression equation used to estimate difference-in-difference is the following: y i t = β 0 + β 1 Treat + ...
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How to visualize the relation between the variance of y and the interaction of x and z

I want to show that the variance of a dependent variable y is a function of the interaction of two independent variables x and <...
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Understanding Quantile Regression with Scikit-Learn

I have a case where I want to predict a time value in minutes. This is the problem of regression. I also want to predict the upper bound and lower bound. I can do it two ways: Train 3 models: one ...
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Regression model with some regressors depending on other regressors

We want to investigate which variables determine the final grade in a University exam (say Y_2), which can assume integer values between 18 and 32. We think that Y_2 depends on: 1) Personal variables ...
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Optimal subset from training data used in Random Forest

I have a set of say 10,000 spatial locations with associated values of a soil property (e.g. soil clay). In addition, I have 100 spatial covariates (e.g. elevation) which cover entirely my study area. ...
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Is it possible to fit a quantile regression fixed effects model on a repeated measures, panel data, with a nested structure?

In the rqpd package manual it is demonstrated how to fit a fixed effects model on a repeated measures data structure. I am looking for ways to extend this to a repeated measures nested structure, i.e. ...
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Geometrical interpretation of L1 regression

I have found the following image (or a similar version) in a lot of books related to penalized linear models. I get the insight of this image. The ellipsoids are the solution of the linear regression ...
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Quantile Regression and False Discovery

Context: quantile regression with a binary predictor, but this question can be generalized to other quantile regression model structures and possibly splines/adaptive models. In quantile regression ...
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Interpreting quantile regression estimates

I am reading the paper of Roger Koenker about Quantile Regression. Specifically in Figure 4, I can see that at the lower quantiles, the effect of Mother's Age is strongest than at other higher ...
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249 views

Quantile regression for count data & the extended log-F family

I'm working on a project where we want to estimate how many of a particular bird species there potentially could be in every 10-km square in England. For this I want to use quantile regression to get ...
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what's the difference between unconditional quantile and generalized quantile regression? [duplicate]

what's the difference between unconditional quantile and generalized quantile regression(Powell,2016)?
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Can you recover regression coefficients from quantile regression coefficients on censored data?

Suppose you have data that you know to be well-fit by a GLM with a specified link and variance function. You would like to estimate that model. However, you do not have access to the data; instead, ...
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294 views

Difference between confidence or prediction interval vs. quantile regression

I have a data set (x1,y1),(x2,y2),...,(xn,yn) and will do a simple linear regression with unequal variance assumption. (If you see the scatterplot of x-y, then the range of y increases as x increases) ...