Q 232. Quantile Regression estimates the median (or a particular quantile) whereas Linear Regression estimates the mean. What are some of the business scenarios where quantile regression would yield better results as compared to linear regression?

 

 

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Quantile regression methodology is a  method  of regression that incorporates relationships between variables, beyond the mean of data and  is quite useful in evaluating non linear relationship between variables. Quantile regression  is a valuable  alternative to linear- ordinary least squares (OLS) regression and  other related methods, which are based on the concept that there is some kind of association between independent and dependent variables.

 

Quantile regression (QR) was developed as an alternative to mean based regression and largely used in various fields such as financial and risk management, healthcare, tourism etc.. Quantile regression can be widely used because of suitability in nonnominal , longitudinal and data with heterogenous conditional distributions. QR  can tackle outliers much more efficiently compared to  mean-based regression.

 Applications of Quantile regression:

1)    Financial Risk Management:

There are usually a number of variables , that determine  a farm’s equity growth. Mean based regression is not the ideal way to study the interaction of  multiple dependent and independent variables. The  equity analysis of a farm employs quantile regression method to investigative the heterogenicity of different components of equity. Farms adopt multiple strategies for business growth. Many of the strategies are complementary to each other. The important strategies are:

-       Asset Management strategy

-       Financial management strategies

-       Minimising the borrowing cost or interest paid, through refinancing

-       Cost reduction strategies

-By  prudent use of quantile regression, important insight is obtained on ways to use different strategies to  enhance farm net worth/equity and building of ideal portfolio  of investments.

2)  Measure racial and ethnic differences across the distribution of health care expenditures:

 Identification of racial or ethnic differences in health care expenditures is carried out using  multivariate linear regression or quantile regression.  Racial or ethnic differences in health care expenditures are computed, using  a multivariate regression equation of health care spendings, which are  conditional on a number of covariates.  In order to analyse  the difference at the upper and lower ends of the distribution, we use quantile regression models. Log of total health expenditure is used to use the nonlinear data and investigate the multiplicative effects of different predictor variables, in case of  heavy spenders on healthcare.

 

 

3. QR finds  lots of applications in health  and behavior related sciences. Some of the examples are- evaluation of effect of physical activity, dietary intake, on different quantile level of variables such as- Body mass index(BMI), waste circumference, socioeconomic status, , various health related scores and biomarker data. QR can also be used  to evaluate and improve various behavioral interventions and sustaining the behavioral change, by separately implementing measures in  two extreme ends of population distribution. Many similar applications are there, including  various determinants of weight in obese versus only  slightly overweight,  various dietary predictors of HbA1c levels among non-diabetics and  Type I or II diabetics, and those with high levels of glucose levels

Quantile Regression: -

Linear regression evaluates the mean response of the dependent variable dependent on the independent variables. There are many cases where data is skewed and have outliers when mean do not show the complete pattern of data.

 Quantile Regression is good alternative of linear regression in the case of skewed data. We can study of distributional relations of variables, heteroscedasticity, dealing with censored variables.

We can use Quantile regression to analyze to Major League Base ball salary data at 10%,25%,50%,75% and 90% quantiles.

In (Salary) =   β°+ β1AtBats+ β2Hits+ β3HmRun+ β4 Walk+ β5Year+ β6Putout

Example of using the Quantile regression

1. Health care services during the expenditure analysis

2. Ranking Exam Performance

3. Financial Risk management

4. Prediction close rates of retail store

Summary: -

1. Approach of Quantile Regression modeling is multipurpose. It uses linear model to conditional quantiles of the response without considering of parametric distribution.

2. Quantile process regression evaluates the complete conditional distribution of the response allows the shape of the distribution to depend on the predictor.

3. Quantile Regression can predict the quantile levels of observations with adjusting for the effect of the covariates.

Benchmark Six Sigma Expert View by Venugopal R

Linear regression fits a relationship model between the response variable and predictor variable(s) using the method of least sum of squares. The linear regression model will provide a good estimate with the assumption that the variation of the response variable across its range (i.e. at different quantiles) is fairly uniform. If this assumption is not true and the variation of the response is different across different quantiles of the response variable, then linear regression would not be the best model and one may consider using the Quantile regression.

 

Quantile regressions are applicable when the extreme observations of the dependent variable are important and expected to vary. While Linear regression estimates the conditional mean of the dependent variable, Quantile regression estimates the conditional median (or other quantiles) of the dependent variable.

 

Quantile regressions are more robust and not influenced by outliers as compared to the linear regression. However, the other important advantage of Quantile regression is when we are interested in the regression relationship with respect to various quantiles of the response function.

 

Quantile regression scores over linear regression in situations where the relationship between the mean of the predictor and the response variables are weak. Below are examples of likely scenarios where Quantile regression would apply:

 

• Predictive relationships pertaining to ecology has been one of the prominent areas where Quantile regression has emerged advantageous
• Expenditure for a given population of people with respect a set of predictor variables, it would make sense to break the expenses into different quantiles viz. Groups with High, Medium and Low expenditures.
• Relationship between the quantum of sales vs input factors such as Promotional spend, demographic and other factors, it would help to identify predictors that are more significant for different quantiles of the sales volume and their corresponding relationships.
• ‘Close rates’ for a department stores – Effect of predictive factors on ‘High close rates’ and ‘Low close rates’
• For climate related studies for eg. the factors influencing the intensity of a hurricane, Quantile regression has found application due to the varied relationship of factors for different quantiles of the hurricane intensity
• Corporate liquidity levels for property insurers have been found to be influenced differently by same factors are different quantiles.

 

While the calculation for Quantile regression is more complex compared to the OLS (Ordinary Least Square) approach, with the advancements in computation technologies, application of Quantile regression is gaining more popularity

Both Shashikant Adlakha and Sudheer Chauhan are winners for this questions. Congratulations to both!

 

Please go through the answer by Benchmark Expert Venugopal as well.