Quantile Regression

8Heterogeneous Quantile Regressions Based on Experimental Data

8.1 Introduction

It is well known that an experiment is conducted with the main objective of studying the treatment factors, either nominal or ordinal, on the response or objective variables by taking into account the effects of covariates. In general, the covariates also are the cause factors or variables of the response variables, so we can study the differential effects of covariates on the objective variables by the factors. We do this using heterogeneous quantile regressions (HQRs) of an objective variable by the factors considered.

The applications of quantile regressions (QRs) presented in previous chapters have been based on experimental data in Data‐Faad.wf1 containing four numerical variables, two covariates X1 and X2, two response variables Y1 and Y2, and two dichotomous factors A and B, as presented in Figure 1.1. In addition, to present various alternative QRs, four ordinal variables G2, G4, H2, and H4 were generated based on the covariates X1 and X2, respectively, as presented in Chapter 1. The following examples present illustrations based on selected HQRs.

8.2 HQRs of Y1 on X1 by a Cell‐Factor

8.2.1 The Simplest HQR

The name Cell‐Factor (CF) is used to represent one or more factors that can be generated based on either numerical or categorical variables. Hence, the simplest HQR of Y1 on X1 by CF is the heterogeneous linear QR (HLQR) with the following alternative general equation specification ...