Bridging Designs for Conjoint Analysis: The Issue of Attribute Importance

Pierre Francois
Katholieke Universiteit Leuven, Belgium
andDouglas L. MacLachlan
University of Washington, Seattle, USA

September 1997

This is a draft. Please do not quote without the authors’ permission. Contact theauthors at pierre.francois@econ.kuleuven.ac.be or macl@u.washington.edu.

BRIDG97.doc

2Bridging Designs for Conjoint Analysis: The Issue of Attribute Importance(Key words: Market Research; Conjoint Analysis)

Abstract

Conjoint analysis studies involving many attributes and attribute levels often occur inpractice. Because such studies can cause respondent fatigue and lack of cooperation,
it is important to design data collection tasks that reduce those problems. Bridging
designs, incorporating two or more task subsets with overlapping attributes, canpresumably lower task difficulty in such cases. In this paper, we present results of astudy examining the effects on predictive validity of bridging design decisions
involving important or unimportant attributes as links (bridges) between card-sorttasks and the degree of balance and consistency in estimated attribute importanceacross tasks. We also propose a new symmetric procedure, Symbridge, to scale thebridged conjoint solutions.

Introduction

Conjoint analysis has emerged in recent years as being among the most important anduseful methods in marketing research (Cattin & Wittink, 1982; Wittink & Cattin,
1989; Green & Srinivasan, 1990). Its value to marketing decision makers stems fromits ability to provide realistic customer evaluations of the attributes of products,
services, and so forth, as well as to allow the simulation of choice shares inhypothetical competitive scenarios. Academics have explored the usefulness and3applicability of conjoint analysis and sought understanding of its limitations. For
example, Reibstein, Bateson, and Boulding (1988) assessed the reliability of conjoint
analysis under a variety of conditions, finding, among other things, that the type ofdata collection procedure has an impact on the reliability of the results.

Among the limitations of the method is the typically difficult task respondents face inproviding data suitable for conjoint analysis. Frankly speaking, the task is usuallyboring, complex, and frustrating for even the most highly motivated respondents.
Although different data collection methods used in studies (e.g., full-profile, trade-off,and paired-comparisons, with rating or ranking of stimuli) have different degrees oftask difficulty, it is apparent that the task is never easy. Although it is probable thathybrid designs (Green 1984) and adaptive methods employing interactive computers(Johnson 1987) help to reduce the task difficulty and boredom factors, it is likely thatfull-profile designs will continue to be used for some time in marketing applicationsof conjoint analysis. Even with fractional factorial designs, full profile data collection
procedures involve comparing a number of stimuli with multiple attributes and levels.
The respondent's decision problem is exacerbated when the number of attributes andlevels becomes large. Various studies (e.g., Miller 1956 and Wright 1975) haveshown that people have difficulty processing more than a relatively few pieces of
information at one time. Since the conjoint task requests people to keep in mind
multiple attributes and levels simultaneously, their task becomes much more difficult
as the number of attributes/levels (and hence tradeoffs) increases.

4

Possible strategies to reduce the task difficulty in conjoint studies.

Looking at the literature about Conjoint Analysis published in the nineties, thetechnique is still very popular, and many topics are still being addressed today. In thissection we try to give an overview of ways to handle the number of attributes
problem. Some of them have been specifically been designed for this purpose, whileothers were proposed with another objective in mind, but with the potential side
benefit of reducing the information overload for the respondent (typically the numberof stimuli to be evaluated).

1. Ad hoc reduction of the number of attributes and/or levels.

The easiest and most subjective approach, and the one probably used most, is to prune
the set of attributes and levels, until a reasonable number of stimuli (cards) has beenobtained. It is still open to debate what this optimal number could be, but in our own
experience, conjoint designs requiring complete rank ordering of stimuli should notcontain more than 12 to 16 cards.
Obviously this approach entails the risk of eliminating relevant attributes, although agood pretest can reveal which attributes are used more often or are more important torepresentative users (depending on how one measures ‘importance’).
At the same time, one can try to reduce the number of levels for some attributes.
This may not be possible in some cases (think about brand names), and will have theundesirable effect of reducing the importance of attributes with a smaller number oflevels (Wittink et al (1990)).

5Another approach would be to reduce the number of parameters to be estimated, by
imposing certain functional forms (vector, ideal point) on the partial utility functions.
In this way one would gain degrees-of-freedom, and in principle be able to reduce thenumber of stimuli accordingly. This approach to the problem has not been extensively
researched, and known references studied the impact on predictive validity instead(Pekelman and Sen 1979). Although this is an empirical matter, one could argue that
imposing specific forms could lead to misspecifications, and this would explain why
the generalized form is so popular. Also, it would only apply to metrically scaled
attributes (e.g. price).

2. Combination of full-profile and self-explicated data.

These approaches do not try to reduce the number of attributes, but reduce the numberof judgments by respondents, compared to full-profile methods. Among the more
popular methods, one can mention ACA (Johnson (1987)) and hybrid conjoint models(Green (1984)).
An extension of ACA combines unacceptable levels with the basic ACA approach(Mehta et al 1992)
A more recent approach and alternative to ACA is CCA (Srinivasan and Park 1997).
Self-explicated methods have proven to be very popular with practitioners, probably
due to their appealing data collection procedure, ability of handling large problems,and relative mathematical simplicity. Whether they perform as well or better than
traditional full-profile methods, has been the subject of some very involved debates,
and the issue is not resolved yet (Carroll and Green, 1995).

6

The hierarchical integration method (Oppewal et al 1994) also belongs to this class,and tries to define superattributes, which in turn can be conjoint modelled as afunction of attributes only relevant for a particular superattribute. The overall
preference function would then only contain the superattributes, which are smaller innumber than all the attributes that compose them.

3. Adaptation of the design matrix.

These strategies aim to keep the number of attributes, and reduce the number of
judgments by respondent, by trying to adapt the full fledged orthogonal design,
typically by incorporating available information (Huber and Zwerina 1996).

4. Optimal segmentation methods.

This family of techniques is the object of much research lately. From our point ofview, these methods solve the problem by abandoning the idea of estimating
individual utility functions (and reducing the workload of the respondent), but
retaining information about the individual respondents as sources of heterogeneity.
Methods include latent class models (Kamakura et al (1994)), optimal scaling(Hagerty (1985), Green et al (1993), Desarbo et al (1992)), Hierarchical Bayes
methods (Allenby et al (1995),Lenk et al (1996)).
Some of these methods have however not been positioned to reduce therespondents’workload, but more as alternative segmentation models (compared toclustering of individual part-worths).

7This reduction in the number of stimuli comes however at the price of having tointerview more respondents.

5. Bridging

This variant of conjoint, which is the subject of our research, tries to cope with theoverload problem, by splitting the set of attributes in two, and building a scaling‘bridge’ between the two sets of derived utilities.

6. Constrained estimation procedures.

This extension of conjoint has also received some attention lately (Allenby and Ginter1995),Green and Krieger (1995). These researchers do not mention reduction of
number of stimuli as an objective but rather the efficiency of the estimates or qualityof prediction. However, imposing constraints might lead to savings in degrees of
freedom.

Bridging Designs

A way to reduce respondent difficulty handling full-profile designs having large
numbers of attributes/levels is to decompose the data collection into simpler subtasks
that are later linked analytically. Hybrid designs are one type of such design, whereself-explicated attribute weights are combined analytically with data coming fromcard-sort (or other tradeoff) tasks. Another approach is to divide the card-sort (orother stimulus comparison) task into multiple designs containing two or more subsets

8of attributes with one or more attributes common to both subdesigns. In such case,the linking or "bridging" attributes are used to scale the partworths from the two
subdesigns into one overall set of partworths. It is presumed that people will have aneasier time working with these subdesign tasks and therefore be more cooperative andprovide more thoughtful responses. The general class of these latter designs arecalled bridging designs. Although the total number of stimuli needed to be comparedin bridging designs may not be reduced, the task is made simpler for respondents byasking them to evaluate stimuli on fewer attributes within each subdesign. (Anextreme form of bridging design is the pairwise tradeoff grid approach, where only
two attributes are compared at a time.)

Suppose one wished to develop a bridging design. What decisions should be made?
What issues should be considered? The research problem in the current study was toinvestigate the conditions involved in bridging designs that might lead to better orworse estimates of attribute level partworths. Although there is a commerciallyavailable software package for scaling bridging designs (Bretton-Clark's Bridger,
1988), we were unable to uncover any published studies that examined these
conditions or offered advice about how the designs should be developed.

The issues that emerge immediately are:(1) How many bridging attributes should be used?

(2) Which attributes should be used as bridges?

a. How "important" should they be relative to other attributes?

9b. How balanced should the designs be in terms of attribute importance?

(3) What scaling procedure should be used to combine solutions from thesubdesigns into overall partworth estimates?

In the present study we decided to investigate issues (2) and (3). Logically, the more
attributes employed as bridges, the better will be the results ("better" will be describedand operationally defined later). For the present study, we decided to focus on two
bridging attributes, because it creates more stimulating issues than with one bridging
attribute and not much more understanding is gained from using more attributes as
bridges. The more interesting practical problem is deciding which attributes shouldbe employed as bridges and what are the consequences of the choice of bridging
attributes. Our research hypotheses investigate this issue. A secondary issue to beaddressed in this study is how the subdesign solutions should be analyticallycombined.

Research Hypotheses

In the following, we state our hypotheses in the way we anticipate them to be verified.
Obviously, the null hypotheses to be tested in each case will be that of no effect.

Although it will not be possible, in advance of a conjoint study, to know withassurance the level of importance of all attributes for all respondents, there is oftensome a priori information that could be used to develop the designs. Because thebridging attributes are key to the linkage of subdesign partworth estimation into a10single overall solution, it is reasonable to expect that their relative importance will
have an impact on the quality of the estimates. This comes about in a couple of ways.
First, the more important the attributes (i.e., the larger the range of its partworths), themore leverage is given to the estimation. This is analogous to regression, where thewider the range of the independent variable, the more stable is the assessment of slope
and intercept (and the lower is the standard error of estimation). Hence, our first
hypothesis is:

H1: The higher the relative importance of the bridging attributes, the better is theoverall partworth solution.

Secondly, since the nonbridging attributes can be distributed in different ways acrossthe subdesigns, one would expect solutions to be better to the extent that thesubdesigns are "balanced" in terms of their attributes' relative importances. If one
subdesign were to contain most of the important attributes, one would expect thatdesign to have partworth estimates of higher quality than the other subdesign. Thisshould lead to lower overall estimate quality than if the designs are well-balanced interms of attribute importance. Thus the second hypothesis is:

H2: The more balanced the designs are with respect to attribute importance, thebetter is the overall partworth solution.

We will define two kinds of attribute imbalance to test this hypothesis.

11

Thirdly, with respect to the resulting estimates of bridging attribute importances, since
they are separately estimated in each design, it is possible to question the effect onoverall solution quality of the degree of inconsistency in their measured relative
importance. If an attribute is estimated to have low importance in one subdesign andhigh importance in the other design relative to the other bridging attribute, this should
affect the ability of any linking procedure to provide good estimates of overall
partworth across both designs. If bridging attributes are measured to be consistent inimportance, therefore, we hypothesize that the solution will be better. Thus,

H3: The more consistent the bridging attribute relative importance between
subdesigns, the better is the overall partworth solution.

Finally, it seems useful to investigate whether overall attribute importance spreadover the two subdesigns has an impact on the quality of the partworth solution. Thatis, since total attribute importance indicates the extent to which a respondent holds
strong opinions regarding the extent to which different levels of the various attributes
have different utility, we hypothesize that respondents with stronger-held opinions
will provide higher quality data yielding better solutions. This last hypothesis does
not directly depend on which particular attributes are used as bridges (i.e., it is more ahypothesis regarding respondent quality than design quality).

H4: The higher the total attribute importance over subdesigns, the better is theoverall partworth solution.

12

Although these hypotheses could conceivably be addressed with mathematicalanalysis or simulation, practical application of bridging designs involves dealing withpeople, so we decided to examine them with real subjects and realistic situations. We
developed the following study design to test the hypotheses empirically.

Study Design

The study employed a household durable product with a fairly high number ofimportant attributes: vacuum cleaners. A pretest was conducted wherein 240
housewife subjects were interviewed on three separate occasions using different
procedures to elicit conjoint-analysis based importance scores for a subset of theattributes used in the current study. For the present study, some additional attributes
were employed, for which we subjectively assessed relative importance. The
attributes and ranges are shown in Table 1.

[Table 1]

In order to test the hypotheses, we needed to assure ourselves that sufficient ranges ofbridging attribute importance would exist in our sample. In this case, therefore, we
had a priori indications of the relative importance of the attributes (a combination ofpretest results and researcher subjective judgments) that could be used in generating
bridging designs having (on average) different levels of importance in the bridging
attributes. The attributes either had three or two levels. Three conditions were
specified: (1) bridging attributes both important, (2) one important and one
unimportant bridging attribute, and (3) both unimportant bridging attributes. We

13carefully selected the remaining attributes in each design to try to achieve balance inoverall importance across the two subdesigns. Moreover, we set up the subdesigns sothat each half contained the same number of attributes with two and three attributes.
This also meant we could use the same fractional-factorial design in preparing thestimuli for each half and each subdesign would contain the same number of stimuli.
The resulting designs contained attributes as indicated in Table 2. Although we fully
realized that individual respondents might assign quite different relative importances
to the various attributes in each design, it was felt useful to employ the a priori
information in creating the study to assure a wide range of conditions acrossrespondents. The testing of our hypotheses, however, does not depend on the a priori
conditions being confirmed on average.

[Table 2]

Main-effects only stimulus configuration designs were obtained for the subdesigns,
each containing five attributes (using Bretton-Clark's Conjoint Designer, 1987). The
fractional-factorial designs each resulted in a set of 16 stimuli. Attributes and levels
were assigned to the subdesigns in such a way that no stimulus was completely
dominated by (or completely dominated) the others; i.e., no stimulus had the "best" or"worst" values on all attributes.

A sample of 120 housewives in Belgium was selected and randomly assigned to thethree attribute bridge conditions. Student interviewers were employed and the datacollected as part of their thesis projects. Before doing the bridging task, therespondents were asked to rank order a set of six holdout stimuli containing realistic

14

combinations of attribute levels across all eight attributes (these were selected to be
sufficiently different to provide an adequate range of responses). Before or after thebridging task (randomly assigned to half the respondents), respondents were asked tocomplete a complete full-profile task with all eight attributes. This latter task required
sorting 27 cards, a minimum main-effects design. It is important to note that theoverall task for the two halves of the bridging design involved more stimuli than thefull design. It is apparent on its face, though, that the latter task requires more effort
and should be more difficult for the respondent than the former. Each subdesign task
had 16 cards with 5 attributes (requiring subjects to process simultaneously 80 bits of
information), whereas the full design had 27 cards with 8 attributes each (requiring
simultaneous processing of 216 bits of information). As a final task, respondents
were asked to indicate the importance of the attributes in a self-explicated fashion (6point scale).

Measures

Assume that we have five attributes in each of two subdesigns with twooverlapping attributes (bridging attributes). For each subdesign we may estimate
partworths and hence the range of partworths for each attribute. These latter ranges
we define to be the importances Iij for design i (i=1,2) and attribute j. Next, we
define the relative importances RIij corresponding to the Iij divided by the sum of the
Iij within each subdesign.

15

For the example of the current study, we have:

Design 1

RI15
RI14
RI13
RI12
RI11

Design 2

Overall

RI22
RI21
RI26
RI27
RI28

RI5
RI4
RI3
RI2
RI1
RI6
RI7
RI8

] Bridging] attributes

where RIj is the relative importance of attribute j in the final solution (to be discussed
later).

Measures of Solution Quality

Two measures of the general quality of the bridged solutions are used in this study,
solution inconsistency (a measure of the squared differences between original relative
importances and the rescaled relative importances) and correlation (between original
scaled relative importances and rescaled relative importances). Thus:

Solution inconsistency: This measure is not used to test any hypotheses. It is ameasure of solution internal inconsistency, i.e., a measure of inconsistency between
the original bridging estimates and the "bridged" solution.

16

Solution inconsistency = sum(diffj2)(1)

where diffj is (RI1j - RIj) or (RI2j - RIj).

The measure is summed over 10 differences in the above example.

Correlation: This is the simple Pearson product-moment correlation between
the original estimates of relative importance and the rescaled relative importances.

Correlation = Corr(RIij,RIj)(2)

where the replicates are the 10 relative importances derived in each experimental
condition.

Both measures are helpful for determining how well the particular bridging algorithm
works in comparison with other bridging algorithms. Obviously, the lower themeasured value for solution inconsistency and the higher the value for correlation, thehigher is the solution quality.

Independent variables

A total of five independent variables were developed to test the research hypotheses.

Importance: The first independent variable, used to test H1, is the importanceof the bridging variables. This is simply measured as the sum of the relative
importances of the bridging variables across both subdesigns. Thus,

17

Importance = RI11 + RI12 + RI21 + RI22

(3)

Imbalance: Two imbalance measures are developed in this study. The first is ameasure of imbalance across designs where total bridge-attribute importance in one
design is compared with the similar value in the other design. Thus,

Imbalance1 = abs((RI11 + RI12)-(RI21 + RI22))(4)This is really a measure of the extent to which the non-bridging attributes arebalanced in total attribute importance across subdesigns. That is, if the left subdesign
has higher attribute relative importance estimated for bridging attributes than theright, it would imply that the left design had lower importance for the non-bridging
attributes than the right subdesign.

The second measure is imbalance between attributes over the two designs. Thus,

Imbalance2 = abs((RI11 + RI21)-(RI12 + RI22))(5)

Imbalance measure 2 focuses on the relationship between the two bridging attributes,
as opposed to the non-bridging attributes. A solution can be balanced by measure 1
but imbalanced by measure 2. An example would be where, in each subdesign, thefirst bridging attribute was twice as important as the second attribute. We do not
expect this to have as large an effect on predictive validity as measure 1, since so long18

as the sum of bridging attribute importances in a given subdesign is sizeable, thescaling of the overall solution should be stable.

Inconsistency: A measure is defined to indicate the degree to which there isinconsistency in the magnitude of the relative importances estimated for each bridging
attribute across designs. The larger this measure, the more disparity exists in therelative size of the importances for any bridging attribute. Thus,

Inconsistency = abs(RI11*RI22-RI12*RI21)(6)

The measure is used to test H3.

Total Importance: In order to assess the strength of opinion of the respondent
over all attributes and levels, we create a measure that is simply the sum of the rangesof all attributes in both subdesigns. For the above example, this sum is over 10
values. This measure is used to test H4, and we expect it to have a positive influenceon predictive validity.

Dependent variables

The quality of the partworth solutions was investigated using standard measures ofpredictive validity, comparing predicted utility of hold-out stimuli with the reported
ranking of those stimuli.

19

Correlation. The average Spearman rank correlation between predicted andactual ranks of hold-out cards.

Percentage of first-choice hits. Two cases: (1) "hit" only if prediction of card
was first choice, and (2) "hit" if prediction for card was first or second choice.

The above dependent variables are progressively less stringent measures ofsolution quality.

Analysis and Results

The partworth solutions for each subdesign and the full design were obtainedfor each respondent subject. These were unconstrained OLS solutions using dummyvariable regression (i.e., using Bretton-Clark's Conjoint Analyzer, 1987). In order tocombine the solutions for each of the subdesigns into a single vector of partworths for
all attributes, a number of options were available. Since each subdesign task was
performed independently, each provides estimates of the bridging attribute
importances (ranges of partworth levels). Logically, the solution algorithm should
depend on the ratio of attribute importances for the bridging attributes acrosssubdesigns. However, the solution will differ depending on which ratio (1st over 2nd
or 2nd over 1st) is used to rescale which subdesign's partworths (a problem of
nonsymmetry) and how the importances for the two bridging attributes are combined.

To solve the second problem, we experimented with two types of ratio for the bridgealgorithm. The first was a sum of ratios of bridging attribute ranges, i.e., (R11/R21 +20

R12/R22), where Rij is the range of partworths of bridging attribute j in subdesign i.
However, this tended to be unstable, because some of the ranges were near zero. A
more stable alternative was the following:

B = (R11+R12)/(R21+R22)(7)

To solve the nonsymmetry problem, we applied B (a scalar value) to rescale the 2nd
subdesign partworths and B-1 to rescale the 1st subdesign partworths, then added theresulting partworths. Thus, for our study, the algorithm was as follows, where uij
represents a vector of partworths of all levels of attribute j in design i:Stage 1

Stage 2

Final Partworthsu15

B-1*u15

u15+B-1*u15

u14

B-1*u14

u14+B-1*u14

u13

B-1*u13

u13+B-1*u13

B*u22

B-1*u12

B*u22+B-1*u12

B*u21

B-1*u11

B*u21+B-1*u11

B*u26

u26

B*u26+u26

B*u27

u27

B*u27+u27

B*u28

u28

B*u28+u27

We call our method Symbridge, to denote symmetrical bridging. Table 3 shows themeasures of solution quality (defined above) for Symbridge in contrast with thesolutions provided by Bridger. Symbridge provided an average solution

21

inconsistency measure of 0.120 and correlation of 0.90 for the subjects. By contrast,
the commercial package Bridger yielded an average solution inconsistency measure of
0.077 and correlation of 0.877 for the same input data. Thus the two measures show
mixed performance for the two bridging methods. Given the asymmetric nature of
Bridger solutions, we would have expected it to perform worse relative to Symbridge.
Our understanding, from informal conversations with other conjoint-experienced
researchers, is that Bridger uses a least-squares procedure for scaling the twosolutions, which would tend to minimize the criterion we call "solution
inconsistency". Symbridge provides somewhat more stable results (i.e., thedistributions of solution quality measures over subjects are less skewed; e.g.,skewness coefficient for solution inconsistency was 2.2 for Bridger, but only 0.6 for
Symbridge).

[Table 3]

Table 3 also shows the average results for predictive validity for Symbridge andBridger versus the full design on the various criteria. It is not surprising that the full
design outperforms the other methods, on average, since the holdout sample usedstimuli that included all attributes. Symbridge and Bridger performed approximately
equally on all predictive validity criteria (certainly the differences are not statisticallysignificant).

Table 4 shows the average values of attribute importances estimated from the sample
by the different methods, augmented by the self-explicated importances and our apriori assessments of the attribute importances. Notice that our a priori indications for22

attribute importance were not confirmed by the analysis of this sample of respondents.
Symbridge and Bridger yielded a high degree of correlation in their results, although
one can observe some differences. Bridger average importances have a higher
correlation with full-design average importances than does Symbridge. Symbridge
average importances have a higher correlation with self-explicated average
importances than do either Bridger or full design average importances.

[Table 4]

Table 5 shows the basic descriptive statistics and intercorrelations for the independent
variables to be used to test hypotheses H1-H4. Although there is an indication of
skewness for all of the independent variables except for "total importance", there issufficient variability in all variables to provide some explanatory power. There isfairly high correlation between Importance and Imbalance2, which is understandable
given the variable definitions being based on the same subcomponents. Also, there isa moderate correlation between Importance and Inconsistency. Otherwise, thevariables do not exhibit very high intercorrelation.

[Table 5]

Table 6 examines hypotheses H1-H4 using Spearman correlation of predicted versus
actual holdout stimuli ranks as the predictive validity criterion. It is disappointing toobserve that, except for H4, none of the hypotheses was supported (i.e., the null
hypotheses could not be rejected) in all cases. This turns out the same when using"hit ratio" as the "goodness" criterion. H4 was not dependent on the type of design

23and could be tested as well for the full design. Interestingly, we found support for H4
in the bridged designs, but not the full design. It appears that using a bridge design
causes total attribute importance to become more critical to predictive validity thanwhen using a full design.

[Table 6]

At this point we began investigating the data for subjects with particularly weakpredictive validity that might be skewing the results. However, even comparing
highest and lowest quartile respondents on independent variables involved in H1-H3
turned up no significant differences for predictive validity, except for the peculiar
result for both Symbridge and Bridger that high quartile respondents on the measure
Imbalance1 yielded significantly higher predictive validity than low quartile
respondents (two-tailed p-values were .06 and .004, respectively).

Discussion

We began this investigation favorably disposed to bridging as a means of reducing
respondent task difficulty, hopefully yielding higher quality results. Our conclusion ismuch less optimistic for bridging. Nevertheless, this is the way science progresses.

Despite the disappointing results, we feel we have addressed some worthwhile issues
and have described ways of examining them. The method we developed for scaling
bridging design solutions, Symbridge, while seemingly better on logical grounds,
appears not to outperform the one existing commercial method, Bridger (although one

24should be careful in generalizing from a single study with only one product).
Symbridge has face validity, since it does not depend on the order in which thebridging designs are entered into the algorithm. Although somewhat mixed as we saw
in Table 3, the Symbridge did tend to provide more stable (less skewed) distributionsof solution quality than did Bridger in this instance.

Our various hypotheses are reasonable on their face, as well. A finding consistent
with the null hypothesis is not the same as proving it. Although the number ofsubjects in the study would seem to have provided statistical power sufficient todetect even small effects, the particular study conditions may have worked against
rejecting the null hypotheses. For example, having two bridging attributes reduces
the probability that two unimportant attributes will be used as bridges (and presenceof one important attribute may be sufficient for reasonable solution quality andpredictive validity). We continue to be convinced that choice of bridging attributes isa relevant issue for researchers planning to use bridging designs. To the extent it ispossible, researchers using bridge designs should probably try to make the bridging
attributes the most important ones for the majority of their respondents. Also, theyshould try to balance the subdesigns in terms of their overall attribute importance. On
the other hand, we have evidence in this study of the inability of researchers to reallyjudge the importance of attributes on an a priori basis. This would argue for creating
designs "on the fly", so to speak, that would be potentially different for each
respondent. That would be almost like using the adaptive methods (e.g., ACA,
Johnson, 1987).

25

Although our study does not provide evidence for the proposition, it may be that any
bridging design will be troublesome if any of the subdesigns omits an attribute that isextremely important to the choice decision. An example is the price attribute, whichtends to be important in many conjoint analysis studies. There is thus an argument for
using price as a bridging attribute in any bridging study.

One could use our results to support the idea that full designs should be used insteadof bridging designs (i.e., that bridging should never be used). The full design
outperformed bridging in every instance. More stimuli had to be compared in total in
the bridging tasks, and actually took about the same time overall (the full-design task
averaged 11.1 minutes, while the bridging task averaged 11.7 minutes in total). Thisis despite the "easier" tasks of sorting the stimuli in the subdesign conditions. (Wenote parenthetically that there was no significant correlation between predictive
validity and time for the task for any of the solution methods, suggesting that moretime taken has little to do with quality of "effort".) It is possible that subjects are able
to simplify the full-design tasks by simply ignoring the levels of the unimportant
attributes. And the full design stimuli have greater realism (the more complete
description could provide better context for respondent decisions, even if theunimportant attributes are ignored).

Suggestions for Future Research

Given the inability to reject the null hypotheses corresponding to H1-H3, we need toreplicate this study with different products, different situations, and possibly more
motivated subjects, either paying them or developing some other procedures for26

getting them to take the task seriously. We should also examine the impact of using
designs with larger numbers of attributes and attribute levels. Additionally, one could
consider expanding the number of bridging attributes and/or the numbers of bridging
subdesigns.

A different approach would be to attempt a solution to the problem with mathematicalanalysis. The number of variables and the complexity of the situation suggests that
this approach would be very difficult.

Finally, the hypotheses might be investigated with Monte Carlo simulation. Of
course, in such a case, the researcher must be careful to ground the various
assumptions in reality to avoid merely playing games.

Additionally, new hypotheses might be investigated. For example, does bridging
increase the importance of an attribute (i.e., are the relative importances of bridging
attributes higher than they would be under full designs)? What happens if there areshape reversals for utility functions of attributes estimated from bridging subdesigns?
The latter would be particularly upsetting if it occurred for important attributes.

A much more fundamental question, which has not been asked often, and certainly
not answered, is whether we need to estimate individual utility functions at all. It is
this desire that leads to all those problems of information overload. Supposing we
could reduce this overload by submitting to every respondent a set of stimuli too
small to estimate his own individual utility function, and estimate utilities at the grouplevel, what are the positive and negative consequences ?

27

On the positive side, respondents would be less taxed, and perhaps provide data of
better quality, and if the response rate is a function of the number of stimuli, the costof research could decrease.
On the negative side, one would be faced with the potential problem of having only at
best group or segment utility functions, which would be aggregates of individual
preferences. In theory one can expect that the use of segment utility functions should
lead to a decrease in the quality of conjoint results. The size of this decrease could be
reduced by using optimal segmentation methods discussed earlier or any goodclustering algorithm on whatever individual information we have.
Whether these effects will cancel out, is probably again an empirical matter, whichshould be tested with some urgency, because if aggregation is not a major problem, it
opens up new perspectives about the use of conjoint analysis.

Another fundamental question which has not been answered thoroughly is about thesize of the information overload problem in conjoint studies. Does a larger number of
attributes and levels lead to less reliable data and thus to predictions of lower quality ?
We can distinguish between two sources of overload : simultaneous processing oflarge amounts of information (as in a ranking task of 16 or more cards containing 5 ormore attributes) with the result that some information will not be used (properly), or
consecutive processing (comparing a large number of choice sets containing e.g. 2
stimuli) leading to respondent fatigue and a decrease in response quality.
How much do we gain by reducing the information overload in terms of predictive
validity and perhaps also respondent cooperation ?

28

As Carroll and Green (1995) have already pointed out, conjoint researchers and users
are in need of studies comparing the different approaches to the different problems
plaguing conjoint instead of continuing to propose new variants on an old theme.

29

References

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Allenby, G. M. & Ginter, J. L.(1995). Using Extremes to Design Products andSegments Markets. Journal of Marketing Research, vol 32 (november), 392-403.

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Carroll, J. D. & Green, P. E. (1995). Psychometric Methods in Marketing Research :Part I, Conjoint Analysis. Journal of Marketing Research, Vol. 32 (November), 385391.

Cattin, P.& Wittink, D.R. (1982). Commercial Use of Conjoint Analysis: A Survey.
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Conjoint Analyzer (1987), New York: Bretton-Clark.

Desarbo, W. S., Carroll, J.D., Lehmann, D.R. & O’Shaughnessy , J. (1982), “Threeway Multivariate Conjoint Analysis”, Marketing Science, 1 (Fall), 323-50.

Green, P. E. (1984). Hybrid Models for Conjoint Analysis: An Expository Review.
Journal of Marketing Research 21 (May), 155-159.

30

Green, P. E. & Krieger, A.M. (1995). Attribute Importance Weights Modification in
Assessing a Brand’s Competitive Potential. Marketing Science , vol 14, 253-270.

Green, P. E., Krieger, A.M. & Schaffer, C.M. (1993). A Hybrid Conjoint Model with
Individual Level Interaction. Advances in Consumer Research, 20, 1-6.

Green, P. E. & Srinivasan, V. (1990). Conjoint Analysis in Marketing: New
Developments with Implications for Research and Practice. Journal of Marketing 54(October), 3-19.

Hagerty, M. R. (1985). Improving the predictive power of conjoint analysis : the useof factor analysis and cluster analysis. Journal of Marketing Research, 22 (May), 16884.

Huber, J.& Zwerina, K. (1996). The Importance of Utility Balance in Efficient Choice
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Johnson, R. M. (1987). Adaptive Conjoint Analysis. Sawtooth Conference on
Perceptual Mapping, Conjoint Analysis, and Computer Interviewing, Ketchum, ID:
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Kamakura, W., Wedel, M.& Agrawal, J. (1994). Concomitant Variable Latent Class
Models for Conjoint Analysis. International Journal of Research in Marketing, 11,451-64.

31

Lenk, P. J., Desarbo, W.S., Green, P.E. & Young, M.R. (1996). Hierarchical Bayes
Conjoint Analysis : Recovery of Partworth Heterogeneity from Reduced
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Mehta, R., Moore, W.L. & Pavia, T.M. (1992). An Examination of the Use of
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Our Capacity for Processing Information. Psychological Review, 63, 81-97.

Oppewal, H., Louviere, J.J. & Timmermans, H.J.P. (1994). Modeling Hierarchical
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Srinivasan, V. & Park, C.S. (1997). Surprising Robustness of the Self-ExplicatedApproach to Customer Preference Structure Measurement. Journal of Marketing
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32

Wittink, D. R., Krishnamurthi, L. & Reibstein, D.J. (1990). The Effects of Differencesin the Number of Attribute Levels on Conjoint Results. Marketing Letters.

Wittink, D. R. & Cattin, P. (1989). Commercial Use of Conjoint Analysis: An Update.
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33

Table 1Attributes and Levels for Vacuum Cleaners

Attributes

LevelsPower (watt)

700 1000 1300

Price (Belgian francs)

3999 6999 9999

Warranty (years)

1

2

3

Power control (positions)none 24Type of cleaner

drum box

Accessories

yes

no

Indicator Light

yes

no

Cord

yes

no

34

Table 2

Bridging Design for Vacuum Cleaners

Attribute2 important

1 important,2 unimportant

importanceattributes

1 unimportant

attributes

set 1

set 2

set 1

set 2

set 1

set 2

Bridging

price

price

price

price

warr.

warr.

attributes

power power

warr.

warr.

contr.

contr.

Other

warr.

contr.

contr.

power

price

power

attributes

type

indic.

type

indic.

type

indic.

access. cord

access. cord

access.

cord

16

16

16

16

Number of
stimuli

Sample size

16

40

16

40

40

35

Table 3

Measures of Solution Quality and Predictive Validityof the Bridging Methods and Full Design

Symbridge

Bridger

Full Design

Inconsistency {sum(diffj2)}

.120

.077

Correlation

.860

.840

Spearman correlation

.51

.49

.61

1st place hits

38.3%

37.5%

40.0%

1st or 2nd place hits

55.0%

53.3%

60.0%

Solution Quality (means, n=120)

Predictive Validity

Note: Chance criterion for 1st place hits is 16.7% and for 1st or 2nd place hits is
33.3%; all results are significantly above chance (p < .001).

36

Table 4Attribute Relative Importances Estimated by Different Methods

Attribute

SelfExplicatedSymbridge

Bridger

Full A Priori
Design

81
58
57
55
69
24
30
54

72
38
31
32
49
18
19
21

59
26
27
26
49
19
15
16

48
27
22
28
65
9
13
13

Means (SDs)
Power
Price
Warranty
Power control
Type
Accessories
Indicator Light
Cord

(23)
(32)
(33)
(34)
(35)
(28)
(28)
(30)

(36)
(32)
(30)
(28)
(38)
(22)
(23)
(27)

(38)
(28)
(29)
(27)
(42)
(26)
(19)
(23)

(34) 100(29) 50(23) 20(28) 30(44) 50(15) 40(20) 40(19) 30

Correlations
Self-Explicated 1.00
Symbridge

.88

1.00

Bridger

.83

.97

1.00

Full Design

.79

.83

.90

1.00

A priori

.55

.84

.78

.55

1.00

Note: The scales of the relative attribute importances were made equivalent to eachother as nearly as possible. The correlations in the lower half of the table are basedon the averages in the top half of the table.

37

Table 5

Descriptive Statistics and Intercorrelations for Independent Variables

Descriptive Statistics
Mean

Std. Dev.

MedianMin.

Max.

Importance(bridging attrib.)
Imbalance 1

.93

.39

.88

.19

1.88

.16

.13

.14

.00

.59

Imbalance 2

.45

.36

.41

.00

1.24

Inconsistency

.03

.04

.02

.00

.21

62.79

19.00

62.98

30.25

122.44

Import.

Imbal.1

Imbal.2

Incons.

Tot.Imp.

Total Importance(all attrib.)
Correlations (n=120)

Importance

1.00

Imbalance 1

.13

1.00

Imbalance 2

.82

.16

1.00

Inconsistency

.47

.05

.28

1.00

Total Importance

-.24

.32

-.17

-.18

1.00

38

Table 6

Effect of Independent Variables on Predictive Validity

Independent Variable

Symbridge

Bridger

Importance-.05 (.598)-.03 (.718)

Imbalance 1.14 (.140).13 (.158)

Imbalance 2.03 (.709).07 (.471)

Inconsistency-.06 (.510)-.09 (.350)

Total Importance.32 (.000).28 (.002)

Correlations (p-values)

Note: The measure of predictive validity used here is the Spearman correlation
between predicted and actual holdout stimuli rankings. Thus, the tabled values are
Pearson correlations between the importance measure and the Spearman correlations,where the replicates are the 120 respondents. All p-values are for two-tailed tests.

39

Authors’name and affiliation.

Pierre François is Associate Professor of Marketing at Catholic University of Leuven,Naamsestraat 69, B-3000 Leuven, Belgium.
Douglas L. MacLachlan is Professor of Marketing at University of Washington,
Mackenzie Hall, Box 353200, Seattle, WA 98195-3200.

Authors’ vitae

Pierre François holds an MBA and PhD from Catholic University of Leuven,
Department of Applied Economics, where he teaches Marketing Research andIndustrial Marketing. His main areas of research are presently Pricing of industrial
products, Measurement of trade show effects, Geomarketing and Choice and conjoint
modelling.
Douglas L. MacLachlan is Associate Dean for Academic Programs and Professor ofMarketing, University of Washington Business School. He is also Executive
Director of University of Washington’s Center for International Business Education
and Research. His research has focused primarily on methodological issues inmarketing research and he has published in most of the major marketing andmanagement journals. Work on this project was initiated while he was a visiting
professor at Catholic University of Leuven 1991-92.