Steps Involved in Conjoint Analysis

Many conjoint theorists and researchers have suggested the use of a process flow diagram in carrying out a practical conjoint analysis (Green and Srinivasan, 1978).

Step Alternative Methods

Selection o f a model o f preferenee

The following models can be used depending on attribute sealing: Partial benefit value model, vector model, ideal-point model, part-worth function model, mixed model

Fractional factorial design, full profile design, random sampling from multivariate distribution

Selection o f the way stimuli arc presented

Verbal description (multiple cue, stimulus card), paragraph description, visual, pictorial or three-dimensional model representation

• Metric scales • Non-metrie scales

o Rating scales, o Paired profile

o Constant-sufcBfibale comparisons,

Estimation o f benefit values method

Estimation method for metric; Estimation method for

non-T . c metric:

• Least Squares

. • MONANOVA PREFMAP,

• Multiple Regression LINMAP,

• LOGIT, PROBIT

• Johnson’s numeric trade-off analysis

Table 5.1: Steps involved in conjoint analysis (Green and Srinivasan, 1978).

Green and Srinivasan, 1990; Hausmckinger and Herker, 1992; Vriens, 1995;

Schweikl, 1985; Schubert 1991). Green and Srinivasan (1978) argue that by focusing attention on the steps themselves, better overall combinations may emerge. One the other hand, Gustafsson et al. (2003) noted that although each step is suitable for revealing findings and future development of the research areas, no one should think that individual steps could be carried out one after the other, and that decision could be made independently. Table 5.1 outlines the steps involved in a carrying out a conjoint analysis.

The preference function is the basis for determining partial benefit values for the respective attributes that reflect the preferences of the persons interviewed (Gutsche, 1995;

Green and Srinivasan, 1978; Schweikl, 1985; Gustafsson et al., 2003), and is often the first step in the selection of the preference function based on which the influence i.e. that the defined attributes have on respondents’ preferences, shall be determined (Gustafsson et al., 2003). Other authors have emphasised the importance of selecting attributes and their levels as the first step (Vriens, 1995).

Nevertheless, most authors seem to agree that the most frequently used models are the: ideal vector model, ideal point model, and the partial benefit or part-worth function model (Srinivasan and Shocker, 1973; Parker and Srinivasan, 1976; Green and Srinivasan,

1978; Schweikl, 1985; Vriens, 1995). The three models are further described below.

First, let

= 1, 2, ..., t ...Equation 5.2

denote the set of t attributes or factors that have been chosen. Next let yjp denote the level of the ^th attribute for theyth stimulus. Consider the case where is a continuous variable.

The ideal vector model of preference states that the preference Sj for the yth stimulus is given by:

^ W p y j p ...Equation 5.3

Where the {wp} are the individual’s weights for t attributes. Gustafsson et al. (2003) noted that the weights {wp} will, in general, be different for different individuals in the sample.

Geometrically, the preference sj can be represented as the projection of the, stimulus point {yjp} on the vector {wp} in the t-dimensional attribute space.

When using the ideal vector model, a proportional relationship is assumed between a partial benefit value and the manifestation of an attribute. This means that benefit increases ( Wp > 0) or decreases (wp < 0) with an increasing or decreasing manifestation of the attribute (Vriens, 1995; Srinivasan et al., 1983; Allenby et al., 1995).

The ideal point model is used when the researcher assumes the existence of an ideal manifestation. The benefit value of a manifestation drops as soon as it falls below or exceeds the ideal point (Green and Tull, 1982).

The ideal-point model st; s that the preference is negatively related to the squared (weighted) distance dj^ of the location {yjp} of the yth stimulus from the individual's ideal point {Xp}, where dj^ is defined as:

2 2

d j — ^ W p ( y jp - X p ) ... Equation 5.4 p = \

Thus, stimuli which are closer to the ideal point will be the more preferred ones.

5.5.1 The Part-Worth Function Model

This is also known as the partial benefit model and can be stated as follows:

f p ( y j p ) Equation 5.5

Where fp is the function denoting the path worth of different levels of yjp for the pth attribute.

In practice,^ (yjp) is only estimated for a select set of levels for typically three or four. The part worth for intermediate yjp and yjp that fall outside the range of estimation can therefore be interpolated or extrapolated respectively. However, the validity of the latter is questionable. In this regard, Green and Srinivasan (1978) advise the researcher to try to employ the full range of attributes, wherever practical.

Nonetheless, the part-worth function approach has received wide acceptance partly due to the ready interpretability of the graphically displayed attribute part-worth function.

In addition, the path-worth model is the most flexible of all the 3 models in the sense that it allows different shapes for the preference function along each of the attributes (Green and Srinivasan, 1978) or better still includes the ideal vector and the ideal point models as special cases (Carroll, 1972).

Green and Srinivasan (1978) however noted that although the part-worth model seems to be the most attractive in terms of being compatible with an arbitrary shape for the preference function, this benefit comes at a cost of having to estimate additional parameters thereby lowering their reliability. Consequently, as we go from the ideal vector to the ideal point and to the part-worth function models, the reliability of the estimated parameters is likely to decrease. As a result, the relative desirability of the three models is not clear.

On the other hand, if the attribute is categorical (e.g. mode of travel - auto versus carpool versus public transit or type of educational institution- junior college, private university, state university), the researcher is forced to use the part-worth function model (Green and Srinivasan, 1978). This particular scenario is analogous to the three levels of critical display of information systems which would later be adopted in this study- critical, important, and desirable. Based on these considerations, the type of preference model to be used in this study would the part-worth function model. Figure 5.1 displays in graphical format the three alternative models of preference.

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i A

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Figure 5.1: Alternative models o f preference (green and Srinivasan, 1978).