Design of Experiments for Eliciting Customer Preferences

Abstract

In this chapter, the survey methods needed to elicit the customer preference data to estimate a DCA or OL model, are introduced. The survey methods are based upon established Design of Experiments methodologies, but adapted for the specific needs of stated preference experiments.

Appendices

Appendix A: Simplified Method of Expressing M

This appendix provides a method for expressing the information matrix, M, and estimating the prediction variance of a given extended design point, f(x), for use in the optimization algorithm. The ordinal data GLM information matrix of Eq. (6.9) can be written in analogous fashion to the GLS formulation of Eq. (6.7) [14]. An H _n matrix is defined as a matrix of derivatives of the logistic CDF as ${\mathbf{H}}_{n} = {\text{diag}}\left( {f_{n1} ,f_{n2} , \ldots f_{{n\left( {P - 1} \right)}} } \right)$. The extended design point f(x _in ) for a given respondent and given configuration is defined as:

$$ {\mathbf{f}}\left( {{\mathbf{x}}_{in} } \right) = \left[ {\begin{array}{*{20}c} 1 & 0 & \cdots & 0 & { - {\mathbf{x}}_{in} } \\ 0 & 1 & \cdots & 0 & { - {\mathbf{x}}_{in} } \\ \vdots & \vdots & \ddots & \vdots & { - {\mathbf{x}}_{in} } \\ 0 & 0 & 0 & 1 & { - {\mathbf{x}}_{in} } \\ \end{array} } \right]. $$

(A.1)

A C _n matrix defined as:

$$ {\mathbf{C}}_{n} = \left[ {\begin{array}{*{20}c} 1 & 0 & \cdots & 0 \\ { - 1} & 1 & \cdots & 0 \\ 0 & { - 1} & \cdots & 0 \\ \vdots & \vdots & \ddots & 1 \\ 0 & 0 & \cdots & { - 1} \\ \end{array} } \right]. $$

(A.2)

With C _n , H _n and f(x) defined, the information matrix can be written as [14]:

$$ {\mathbf{M}} = \sum\limits_{n = 1}^{N} {{\mathbf{F^{\prime}}}_{n} {\mathbf{W}}_{n}^{ - 1} {\mathbf{F}}_{n} } $$

(A.3)

where ${\mathbf{W}}_{n}^{ - 1} = {\mathbf{H}}_{n} {\mathbf{C^{\prime}}}_{n} {\mathbf{V}}_{n}^{ - 1} {\mathbf{C}}_{n} {\mathbf{H}}_{n}$, and F is the extended design matrix composed of the f(x).

Appendix B: Example of Experimental Configuration Blocks

Table B.1 Example of three experimental configuration blocks