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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45 views

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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28 views

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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15 views

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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31 views

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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32 views

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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21 views

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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47 views

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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Doing Quantile Regression on Classification [closed]

By some google search, it seems like we can do classification (say, only 0,1) with quantile regression (How binary quantile regression divides the dependent variable into quantiles). So I create 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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39 views

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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59 views

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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23 views

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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120 views

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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1answer
61 views

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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25 views

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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39 views

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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55 views

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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43 views

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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42 views

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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39 views

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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103 views

Quantile regression and linear regression coefficient comparison

I am trying to understand the concept of quantile regression by modelling the monthly expenditure on insurance on several variables. The R package ...
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122 views

How to check that quantile regression forests provide valid predictions?

I am using quantile regression forests to predict the distribution of a measure of performance in a medical context. I am using the ranger R package for that purpose. I would like to have advices ...
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250 views

What is the quantile covariance?

Suppose that $X$ is a p-dimensional random vector and $Y$ is a random scalar. Then, Dodge and Whittaker (2009) indicate that the covariance of these two variables can be formulated as a minimization ...
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175 views

How to find a value that ensures 70% of population is above it

i'm trying to solve this statistics problem. i have a certain number of samples that are randomly chosen to represent a population. (yellow dots in the picture) over those samples are run tests to ...
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Quantile regression ANOVA and ANCOVA [duplicate]

ANOVA posits that the mean of a particular group is equal to the overall mean plus some amount. If we find that amount to be significant, then we decide that the groups don't all have the same mean. ...
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427 views

Time series quantile regression

I have time series where at each time step I have a bunch of real-valued points (e.g. individual purchases on a given day), and would like to produce a forecast of several quantiles. One approach I'm ...
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55 views

which quantile select when doing quantile regression

I want to know how strongly a variable restricts the maximum values another variable can reach. I asume there will be some degree of error in my estimates of both variables. Also, the availability of ...
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239 views

Pooling across quantile regression analyses from multiple imputed datasets (quantreg, MICE)

We have a dataset looking at predictors of reading comprehension ability, with a few missing data points here and there. After lots of going round in circles I think that multiple imputation is the ...
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Is survival analysis is a time series models

I would like to apply a quantile regression model on lung cancer (survival). My question is, does survival analysis is a time series models. Or can I fit linear quantile regression models to this data?...
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65 views

Limitations of unconditional quantile regressions?

I've been reading that conditional quantile regression may yield results that are not interesting or generalizable in a policy context, and that unconditional quantile regressions (UQR) are a better ...
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33 views

How to compare two plots of two different quantile regression models

I am new to the quantile regression. I found an example Here that compare vine copula quantile regression model with a linear quantile regression model. The example provides the plots of the two ...
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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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