Quantile Regression

6Quantile Regressions with Multiple Numerical Predictors

6.1 Introduction

As the extension of the quantile regressions (QRs) with two numerical predictors presented in previous chapter, this chapter presents illustrative examples of QRs with multiple numerical predictors, based on selected data sets. Only a few selected interaction QRs having more than three multiple numerical predictors are presented, because there will be many possible two‐way interaction predictors, and three‐way interaction predictors. For instance, having five predictors, there will be 10 possible three‐way interaction, and 10 possible two‐way interaction predictors. Hence, a researcher should develop the best possible path diagram (up‐and‐down or causal relationships) for the set of selected variables, which is acceptable and it is assumed to be true in the theoretical sense, such as presented in Figure 6.1, as the models based on four numerical variables (X1,X2,X3,Y1), and their extension for five numerical variables, as presented in Figures 6.35 and 6.36. Then based on each path diagram an equation specification of the QR, either additive or interaction QR, can easily be developed. Finally, selected additive, two-way interaction (2WI), and three-way interaction (3WI) QRs having more than four numerical IVs are presented.

6.2 Alternative Path Diagrams Based on (X1,X2,X3,Y1)

Figure 6.1 presents four alternative path diagrams, which show the up‐and‐down or causal relationships between a predicted Y1 ...