Constructing Profiles

The number and composition of the residential profiles that are presented to respon-dents is determined by the chosen experimental design. Basically, three different types of experimental designs can be distinguished: full-factorial designs, frac-tional-factorial designs and compromise designs.

A full-factorial design involves making all the possible combinations of the selected attribute levels that can be made. This design type allows the estimation of all main effects and all possible interaction-effects. A disadvantage of the full-factorial design type is that the number of profiles rapidly increases with increasing numbers of attributes and attribute levels. For example, in the empirical illustration discussed later in this chapter, a single two-level attribute and eight three-level attributes are selected to describe the residential profiles. A full-factorial design in this case would involve 2 * 3⁸ = 13,122 combinations. It may be obvious that this number is too large to handle in practical research. Hence, full-factorial designs are only applied if the number of attributes and number of attribute levels is very limited. As this is not usually the case in residential preference research, fractional-factorial designs are typically applied in practice.

A fractional-factorial design is usually an orthogonal selection of the factorial design. Orthogonal means that the attributes are not correlated across all the profiles. A consequence of this is that all the combinations that can be made

between the levels of two attributes will occur in the resulting residential profiles.

For example, the attribute level ‘detached house’ will typically be paired an equal number of times with high prices as with low prices. The advantage of uncorrelated attributes is that for rating-based experiments the lowest number of observations is required to arrive at statistical significance for the estimated coefficients. For choice-based experiments orthogonal designs provide a good starting point, but efficient design strategies may be even more efficient (see final section).

Another desired property of experimental designs concerns attribute level bal-ance. This involves that all the levels of an attribute appear an equal number of times across all the constructed profiles. If this was not the case, than the estimation of the coefficient for one level of an attribute would be based on more observations than the estimation of another level. Consequently, the coefficient estimated on more observations would have a higher probability of becoming statistically signifi-cant. Providing attribute level balance in practice typically results in choosing an equal number of levels for each attribute or choosing a mix of two- and four-level attributes.

The use of fractional-factorial designs brings back the number of constructed profiles to manageable proportions. For example, the smallest possible orthogonal fractional-factorial design for the application, to be discussed later in the chapter, results in the construction of 27 profiles, which is considerably less than the 13,122 combinations of the full-factorial design. This reduction in the number of profiles comes at a cost. Fractional-factorial designs do not allow the estimation of interac-tion-effects. Hence, to apply this type of design one must assume that none of the interaction-effects for the attributes plays a role in the residential preferences, in other words that their effects are equal to zero.

Basically, a fractional-factorial design is a matrix in which the numbers dictate which attribute levels one should combine to create profiles. Each attribute is assigned to a column that varies a certain quantity of numbers of which the series (0, 1), (0, 1, 2) and (0, 1, 2, 3) are the most common. Hence, a column containing the first series of numbers can be used to vary a second-level attribute, the second series a third-level attribute and the third series a fourth-level attribute. Each row of the matrix represents a profile. To illustrate this, the simplest possible fractional-factorial design for three selected attributes is depicted in the left part of Table 6.3.

This design allows three attributes to be varied with two levels each. The two levels

Table 6.3 Applying an orthogonal fractional factorial design to construct profiles Tenure:

0  owner-occupied 1  rental

Housing type:

0  single family house 1  multi family house

2 0 1 0 Owner-occupied Multi family house 500

3 1 1 1 Rental Multi family house 1,000

4 0 0 1 Owner-occupied Single family house 1,000

of each attribute are then arbitrarily assigned to a level 0 or 1 as presented in the upper part of the table. This results in the four profiles that are provided in the lower right part of the table. Hence, this design requires the assumption that all interaction-effects are equal to zero and allows only three of the main-interaction-effects to be estimated.

Note that this design is included here only for illustrative purposes. To make pro-files of three attributes each varying in two levels it would probably be better to construct a full-factorial design resulting in eight profiles, which has the advantage that it allows the estimation of all the interaction effects.

In order to arrive at an orthogonal fractional-factorial design one can make use of published designs (e.g. Addelman 1962; Steenkamp 1985), or use specialized computer software. For example, SPSS provides a conjoint analysis module that supports the construction of such designs. Another example is the recently intro-duced program Ngene, which is probably the most advanced software package to support the construction of statistical designs. The number of profiles constructed in this way is at least equal to the number of indicator variables one needs to esti-mate. However, because of the attribute level balance requirement explained earlier, the number of profiles is usually larger.

A disadvantage of the smallest fractional-factorial designs most often used in practice is that not all of the main-effects are independent of all the interaction-effects. As a consequence, if interaction-effects that were assumed to be zero are not zero in reality and thus played a role in the decision-making process, some of the main-effects are confounded with these interaction-effects. Hence, the esti-mated main-effects may then be biased. This can be prevented by selecting those designs in which all the main-effects are independent of all the two-way interac-tions. However, this requires selecting larger designs that increase the number of required profiles.

One way to construct such designs is to create the foldover of the selected fractional-factorial design. A foldover design is the mirror image of the original design. For two-level attributes this means that a 0 entry in the design is replaced by a 1 in the foldover design, and a 1 by a 0. For a three-level attribute, the entry 0 is replaced by 2, the entry 1 remains 1 and the entry 2 is replaced by zero. The foldover design created in this way is then added to the original fractional-factorial design. Fractional-factorial designs combined with their foldover have the property that all main-effects are orthogonal to unobserved, two-way interactions.

A drawback of this design strategy is that it doubles the number of profiles to be evaluated.

The third and final experimental design type distinguished here is the compro-mise design. This design allows estimating some selected interaction-effects.

A compromise design consists of a main-effects design, combined with a second design that permits the estimation of selected interaction effects (e.g., Louviere et al. 2000). Although compromise designs still require the assumption that certain interactions are zero, they usually do not extend the number of profiles as much as applying the foldover strategy does. For a further introduction in constructing designs the interested reader is referred to Steenkamp (1985), which also includes several of the most applied fractional designs, and Louviere et al. (2000).

It should be clear that the possibility to deal with interaction-effects needs to be traded-off against the requirement to limit the number of profiles to be evaluated by each respondent to avoid information overload. Decisions regarding design size are typically based on the assessment of how many profiles a respondent can reliably complete in a given response situation. In practice, fractional-factorial designs that only allow the estimation of main-effects are therefore often chosen, because these designs provide the lowest number of profiles and therefore limit the complexity and expense of the data collection effort. Main-effects-only-models often predict preferences for new choice alternatives reasonably well and it has been observed that main effects typically account for most of the variance in the data (Louviere 1988, p. 40). Still, as stated before, one has to be aware of the fact that for some of these designs, main-effects are not independent of interaction-effects, which may result in biased estimates.