8.1. Introduction

The RMM model has three sets of parameters:

• Parameters associated with the linear predictor (LP);

• "Structural" parameters;

• "Error" parameters.

Estimating procedures for all three sets are developed in this chapter.

An initial approximate ML estimating procedure for the RMM model was developed in Shore (2002). The procedure comprised two separate routines: Stepwise linear regression, to estimate the parameters of the linear predictor (LP), and weighted non-linear regression, to estimate the rest of the parameters of the RMM model. Alternating between the two routines, estimates for the RMM model were eventually derived. This estimating procedure was approximate in the sense that certain approximating assumptions were made in order to apply stepwise linear regression to appropriately transformed response values. A more efficient and rigorous estimation procedure is needed.

In developing the new estimation procedure, two variations of the RMM model are addressed. Recall that by pursuing various assumptions regarding the error structure and the definitions of the independent standard normal variables, associated with the errors, eight different variations of the RMM model are obtained (refer for details to Section 7.2.5). Here we address the basic model, as derived axiomatically in Chapter 7, and a certain variation of the basic model. These are, respectively,

(8.1)

(8.2)

Equation (8.2) is a variation of (8.1), which may be more convenient to apply when search routines are employed to identify ML estimates for the parameters. More specifically, the term ( ?+ ? _?1Z ₁) ^? in (8.1) may occasionally deliver...