Quantile Regression

2One‐ and Two‐way ANOVA Quantile Regressions

2.1 Introduction

The equation specifications (ESs) of the analysis of variance (ANOVA) models presented in Agung (2011a), as well as other books, can be used directly to apply the quantile regressions (QRs) with categorical predictors, namely ANOVA‐QR. Similarly, the specification equations of other mean regressions (MRs) also can be used directly to obtain the outputs of QRs. With EViews, the output of the MR is obtained using the LS – Least Squares (NLS and ARMA) estimation setting method. Another estimation setting method, QREG – Quantile Regression (including LAD), is used for the quantile regression analysis. The basic estimation process of the QR and its more advanced statistical analysis are presented in Appendix A, Section A.3, for the readers who never do the regression analysis using EViews.

In addition, it is well known that the error terms of MR are assumed to have independent identical normal distribution (IID) ∼N(0, σ²). But, QR, its error terms are assumed to have IID of zero means only. So, they don't need the normal distribution assumption. The ANOVA‐QR, in fact, is nonparametric quantile regression (NP‐QR), and the QR with numerical predictors of independent variables (IVs) is called semiparametric quantile regression (SP‐QR). Agung (2011a) has presented alternative ANOVA models based on selected data sets, including Data_Faad.wf1, which is presented in Figure 1.2 with additional ordinal variables that will be used ...