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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Estimate quantiles by mixed model quantile regression

lqmm::lqmm returns a 95th percentile lower than the 90th, using the data and parameterization below. The goal is only to estimate these upper percentiles, accounting for any within-person dependency ...
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115 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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38 views

Doubt on Quantile Regressions in R (quantreg) x Python (statsmodel)

I'm performing some quantile regressions of a response variable (a ranking difference) over 14 predictors that describe each element of our ranking. Initially I succeeded in performing such ...
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Is it possible estimating Conditional Skewness with Quantile Regressions?

I am studying Quantile Regressions (Koenker, R. and Bassett, G. (1978)). But i cant find a work that uses Quantile Regressions to estimate Conditional Skewness. There is some work/article who did ...
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8 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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21 views

How to fit a mixture of quantile regressions?

I am interested in estimating a mixture of quantile regressions. I have checked several opportunities for the one-component-case as well in SAS (proc quantreg) as in R (package quantreg). But I can't ...
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30 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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92 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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17 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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76 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 Simple Question

When i estimate a regression model using OLS, for example: $Y_t = \alpha+ \beta*X_t + \epsilon_t$ $\beta = Cov(X,Y)/Var(X)$ In my job that i working, $X$ is something like: $X_t = g_t - s_t$ so my ...
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23 views

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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127 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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33 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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30 views

Is it valid to instrument endogenous variables one at a time?

I am a Stata user and am attempting to implement the IV Quantile regression method of Chernozhukov and Hansen (2008), for my model, which has two endogenous variables, call them "GD" and "ED". I am ...
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63 views

Fit quantile regression

I have like 30k rows in training set and 60k in test set. Distribution of dependent variable (ascending order) looks like this: I believe I must use quantile regression here, as OLS regressions fit ...
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29 views

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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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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48 views

Detrending daily precipitation and temperature data for quantile regression analysis

I am carrying out a linear quantile regression analysis to detect long term anthropogenic changes in precipitation and temperature data. The regressions are being used to compare the slopes between ...
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102 views

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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30 views

Conditional quantile function - Linear quantile regression model?

For instance, I know that if $Q_\tau (y|x) = \beta (\tau)^{'} x$ then the linear quantile regression can be written as $y_i = \beta^{'}x_i + \epsilon_i$ where $$Q_\tau (\epsilon_i |x_i)=0$$ However,...
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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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76 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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101 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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59 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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37 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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110 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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108 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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47 views

Weighted Quantile Regression

I am currently trying to work through a situation where the dependent variable is on a different time scale than the predictors. The data is such that for each y we may have between 1 and 12 predictor ...
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63 views

How does anova.rq compare estimates from quantile regression in the quantreg package for R

I am using the quantreg package in R to develop quantile estimates at different taus, then using anova to test whether the Beta ...
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55 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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86 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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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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80 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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106 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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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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45 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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288 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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44 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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33 views

Error propagation over percentile confidence intervals for bootstrapped regression coefficients

I apologize if this is extremely simple or I'm going about this the wrong way or it has been asked before. Please point me in the right direction if so as I might just be searching the wrong question. ...
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49 views

How do you do a nonparametric quantile regression in SAS?

I want to do a nonparametric quantile regression in SAS and I can't, for the life of me, figure out how to do it. All the examples I see don't do a good job of explaining the code that is used and why ...
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Quantile or distribution estimation for continuous variable from sparse matrix

I'm not sure where to start and desperatley need help. I've got a somewhat sparse data set and I'm trying to do either a quantile estimation or a distribution estimation for one continuous variable. ...
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995 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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91 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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365 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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42 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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Is it possible to get a prediction interval for logistic regression via a latent variable?

carbocation asked how to compute prediction intervals for logistic regression. The answer was that prediction intervals don't make sense for logistic regression because the response variable only ...
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101 views

Quantile regression prediction in r

When I call predict.rq function, it returns a matrix which stored different predictions when in different quantiles. But I only need exactly one number for each obs....
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About the appropriate regression model

I have a quantitative dependent variable and all my explanatory variables are qualitative (binary or multi-category). I need to analyze the impact of each level on the dependent variable. I also need ...