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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259 views

Quantile regression - power analysis

I need to put together a (likely simulation-based) power analysis of a quantile regression. The analysis should include changing effect size (increasing slope). In ...
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90 views

Fitting Gaussian distribution with indirect observations

I want to estimate the mean and variance of a gaussian random variable $X$. The realizations of $X$, i.e. $x$, are not observable. Instead, $a$ and $b$ are observed, which are related to $X$ via $...
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183 views

Standard errors from quantile regression in SAS

Why the standard errors obtained from PROC GLM (for analysis of multiple regression) is larger compared to those from PROC QUANTREG (for analysis of quantile regression)?
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2k views

ARIMA quantile regression in R

I would like to perform a quantile regression of a autoregressive integrated moving average (ARIMA) model (p,0,q) of a stock return in R. My question is: how can I include the moving average process ...
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1answer
1k views

How to calculate MSE in a quantile regression simulation study

I am working on a simulation study on quantile regression. So what I did is to simulate data based on a given model, which is different from the true underlying model of the data, in other words, a ...
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2answers
268 views

Quantile Regression with Regression Discontinuity

Sort of a methodological question: If one has an exogenous binary treatment and a continuous outcome variable Y and wants to estimate quantile treatment effects by exploiting a (sharp) discontinuity ...
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1answer
1k views

What is the interpretation of (panel data) Quantile Regression?

I estimated a (panel data) quantile regression model using qregpd in Stata 13. It is not clear what is the interpretation of the estimate. Let's say that I choose the 50th quantile, and I find that ...
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820 views

Addressing singularity in matrix during quantile regression

I am using quantile regressions in R, using quantreg. I want to use locally linear fitting as per the example on page 13 of the vignette. I have a response variable ...
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1answer
861 views

variance-covariance matrix of coefficients in quantile regression

I am using quantile regression to estimate the effect of a categorical variable AG_SEP2 on a response outcome ScoreGSA according to the distribution of this outcome variable, while adjusting on other ...
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1answer
778 views

Choosing the proper quantile for prediction

To give a simple hypothetical example, suppose one was interested in using linear regression to predict how horses would perform in a race. Let's suppose the race includes 10 horses and that I have a ...
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3answers
685 views

Why are the predictions of a quantile regression model changed by an increasing transformation of the DV?

Take a dataset and suppose we fit two quantile regression models to it, one with the raw dependent variable (DV) and one with the logged DV. Then look at each model's predictions for the training data,...
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642 views

quantile regression for unbalanced panel data in R

I am using Canay's R program to explore quantile regression for panel data. In the example given, Grunfeld data is used. Following the Example.R file everything goes smoothly. However, when I delete ...
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1answer
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Heteroskedasticity and Distribution of the Dependent Variable in Linear Models

I am running a multivariate ols model where my dependent variable is Food Consumption Score, an index created by the weighted sum of the consumption occurrences of some given food categories. ...
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1answer
2k views

Getting prediction intervals from GBM models

I am working with GBM regression models(in H2O) and am using Quantile distribution for the distribution parameter. I am looking for a method to provide prediction intervals in addition to point value ...
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2answers
4k views

Rule of Thumb for Accepting the Null Hypothesis

Usually, hypothesis testing is performed with the goal to make a conclusions about the statistical significance of an effect, i.e. $H_0 \ \hat{=} \ \text{No Effect} $ vs. $H_1 \ \hat{=} \ \text{Effect}...
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Is there such a thing as an adjusted $R^2$ for a quantile regression model?

Having included an quantile regression model in a paper, the reviewers want me to include adjusted $R^2$ in the paper. I have calculated the pseudo-$R^2$s (from Koenker and Machado's 1999 JASA paper) ...
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1answer
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How to calculate the power of my quantile regression model?

I have a quantile regression model that I fit with the rq() function in the quantreg package ...
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1answer
466 views

Integral formula using R

I have to implement this formula: $K(x) = \int_{0}^{0.5}q_{\theta}(x)d{\theta}$ where $q_{\theta}(x)$´s are the conditional quantiles in some $\theta$. using a range of $\theta = [0.45; 0.40; 0.35; ...
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1answer
95 views

How should I define qoffset for QuantReg family in mboost?

The QuantReg family of the mboost package has two parameters: tau (the target quantile) and <...
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1answer
128 views

Is quantile regression a better option than total least squares RMA in this case

I have paired cobalt concentrations in bird blood and feathers. Blood levels give me an idea of how recent the cobalt exposure was (<30days), feather give the 6 month accumulated total. Previous ...
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1answer
2k views

Scoring quantile regressor

Let's suppose that there is a real random variable $Y$ that is generated by some random process that depends somehow on vector $\vec x.$ I've built a model that for given $\vec x$ predicts $\tau$-...
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1answer
1k views

Quantile regression with categorical variable

I would like to include the following variables in my quantile regression model: y=real hourly wages x1= sex (male=1, female=2) x2= yeaedu (years of education) x3= race (has many categorie, around 8) ...
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2answers
2k views

Best regression correcting for non-normality, outliers and heteroskedasticity

We are performing a regression on cross-sectional data for $Y$ = subjective well-being (scale 0-10) and $X$ = working hours (divided into 5 dummy categories; less than 27 hours, 27-32 hours etc). ...
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Quantile Regression Expected Value

I know this is probably painfully simple, but can someone help me with the following? $\textbf{Model:}$ $y=x'\beta(u)$ where $u|x\text{~}Uniform\,[0,1]$ and for any $x,\, x'\beta(\tau)$ is a ...
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1answer
947 views

Log transformed outcome in quantile regression

I know in OLS, back transformation is not recommended so smearing estimators are often employed. As I understand it, this is not an issue in quantile regression -- you can simply exponentiate to back-...
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119 views

Derivative of a Riemann-Stieltjes integral (quantile regression)

(Moved from the mathematics site as I didn't receive any response there) In pp. $5−6$ of Roger Koenker's Quantile Regression, the author minimizes the function $(\tau-1)\int_{-\infty}^\hat{x}(x-\hat{...
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When the dependent variable is Median Time of a specific event, have we to use Quantile Regression or OLS Regression works well?

I am asked to make a regression model and the dependent variable is Median Time of a specific event. I think I can consider the Median Time of that event as a random variable and therefore the ...
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988 views

Why use quantile regression instead of splitting the data in quantiles and calculating multiple linear regressions?

Why use quantile regression instead of splitting the data in quantiles and calculating multiple linear regressions? What are the advantages and disadvantages of these methods? As far as I understand ...
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1answer
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Quantile regression versus OLS with dummies

I want to regress a variable Y on another variable X (with appropriate control variables and fixed effects) in a panel data setting. Two approaches come to mind: Use quantile regression; Use OLS ...
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152 views

Quantile instrumental variable models (Chernozhukov and Hansen)

I am trying to implement a quantile IV model, and I must confess that I'm not fully familiar (read: comfortable) with the theory, although I have read the Chernozhukov and Hansen paper. However, the ...
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1answer
1k views

Linear Properties of the Quantile Function

Suppose $X$ is a random variable with continuous distribution function $F(x)$ and quantile function $Q_X(p)$ and let $Y = aX + b$ for some constants $a > 0$ and $b$. How can I prove that $Q_Y(p) = ...
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1answer
2k views

How can I predict a distribution (from a set of predictors) that I can simulate from?

Let's say I have the following regression problem: Given a person's age and height, I want to predict how many years they've spent playing basketball. However, instead of just regressing on these ...
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1answer
518 views

Quantreg : Unbalanced residuals

I'm trying to use the quantreg package to fit an exponential curve. Here is a reproductible example. IRL I have much more complex data with outliers, that's why I ...
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251 views

What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
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2k views

Quantile regression on non linear data

R and statistics beginner here, trying to do a quantile regression on a non-linear dataset. I want to identify datapoints that have a higher y axis value that expected given their value on the x ...
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1answer
990 views

Quantile regression explained to a beginner [duplicate]

I'd like to know if the following explanation is a correct way to introduce Quantile regression to someone who just know OLS (the goal is just to give an intuition) Quantile regression minimise MAE ...
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318 views

Testing the equality of Beta Estimates from Multiple (>2) Quantiles in Quantile Regression

I'm trying to determine whether Beta estimates at different quantiles obtained using quantile regression (quantreg package in R) are statistically different from ...
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1answer
895 views

how does predicted median go above 95% prediction interval when using GBM with quantile loss function

I was checking out how to create prediction intervals with Gradient boosted regression trees using Scikit-learn. If you set the alpha at .95 or .05, you can get the 95% prediction interval around the ...
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2answers
371 views

Quantile Regression: follow up methods to have a more fine-grained understanding of what the results really mean?

I recently employed multiple quantile regression in my area of research and found some interesting quantile differences across the distribution of Y, but I don't quite understand what they all really ...
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1answer
561 views

Quantile regression with continuous endogenous variables

First of all, let me apologise if this question has been resolved elsewhere on the site / the net. I have been researching a methodology for IV Quantile regression with continuous endogenous variables,...
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1answer
1k views

How many data points are in a given quantile in Quantile regression?

I hope somebody can help me with a, probably very fundamental, issue of understanding concerning quantile regression. My dataset is very skewed, so I've looking at the data with quantile regression ...
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123 views

Should I convert age as independent variable in my Quantile Regression?

I'm applying quantile regression to a dataset where the dependent variable is a measurement of load (utilization) of a specific technology. The model includes a number of independent variables ...
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1answer
2k views

Quantile regression for Sales forecast in R

Issue: Cannot forecast sales accurately using quantile regression in R. I am using rq function from "quantreg" package which is giving me warning "Result might have Non unique solutions" Aim: I am ...
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110 views

How does one build a quantile regression model?

I'm confused about how to choose variables for a multivariable quantile regression? Do I just choose significant variables (regardless at what quantile they're significant) and add them to the model?
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1answer
4k views

Expected value as a function of quantiles?

I was wondering where there is a general formula to relate the expected value of a continuous random variable as a function of the quantiles of the same r.v. The expected value of r.v. $X$ is defined ...
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1answer
370 views

How are the results of multivariable quantile regression interpreted?

Is multivariable quantile regression interpreted the same way as a multivariable linear regression would be interpreted? For example, would I say something like "the coefficient represents the ...
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2answers
10k views

How does quantile regression "work"?

I am hoping to get an intuitive, accessible explanation of quantile regression. Let's say I have a simple dataset of outcome $Y$, and predictors $X_1, X_2$. If, for example, I run a quantile ...
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2answers
403 views

Can quantile regression be used to pool multiply imputed count data?

I am using the mice package in R to impute missing data in small study. The study investigates the effect of a behavioral intervention on the frequency of a particular behavior, i.e., count data that ...
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0answers
2k views

Empirical Prediction interval for time series forecast based on quantile regression

As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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131 views

Heteroscedastic censored regression

I am dealing with a heteroscedastic censored dataset. I tried to use the survival analysis package in R to estimate a linear model for it. So before doing that, I conducted a simulation study, where I ...

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