# Conjoint analysis

Conjoint analysis (also conjoint measurement , German composite analysis or composite measurement ) is a multivariate method that was developed in psychology . Today, conjoint analysis is understood to be any decompositional method that estimates the structure of the preferences of consumers by making use of their overall judgments about a set of alternatives ( stimuli ) that are specified by expressing various properties (including features). In practice, a stimulus is usually a product that is made up of (product) properties, each with a specific expression.

## history

Conjoint analysis was first mentioned in the work of Robert Luce and John Tukey in 1964 . Paul E. Green and V. Seenu Srinivasan introduced it as a method to market research in the 1970s . This original method is now known as traditional or classic conjoint analysis or profile method. Various other methods were developed in the 80s and 90s, such as B. the adaptive conjoint analysis and the selection-based conjoint analysis. Today, the conjoint analysis is one of the most widely used analytical methods for collecting the preferences of consumers.

## Procedural principle

The so-called decomposition principle of this procedure is essential for understanding the conjoint analysis : A product (stimulus) is interpreted as a combination (or “composition”) of the manifestations of its properties. The goal is now to use the benefit judgments of consumers for holistic products in order to infer the following relative benefit contributions:

• The utility contributions of the properties to the overall utility
• The benefit contributions of the individual characteristics of the properties to the overall benefit

In order to ascertain the benefit judgments, the consumers are presented exclusively with holistic products, which they put in a ranking order or from which they make certain predefined selection decisions. The benefits of the properties and characteristics are then calculated according to the respective method of conjoint analysis.

The great advantage of this approach is that the decisions of the consumers come very close to a real decision-making situation (usually a purchase situation), since, as in reality, only complete products have to be assessed. The assessment of the properties and characteristics takes place implicitly, without the consumer having to make explicit statements about this. This relation to reality is the reason why conjoint analysis is so important in practice.

### example

A company wants to introduce a new product. The product can be composed of different characteristics of different properties. The properties and their possible characteristics can be represented as follows:

properties Characteristics
Product design Design A, Design B, Design C
Product name K2R, GLORY, BISSELL
price $1.19,$ 1.39, $1.59 seal of approval Yes No Money back guarantee Yes No So there are 5 properties available, 3 of them with 3 characteristics each, 2 of them with 2 characteristics. In total there are 3 × 3 × 3 × 2 × 2 = 108 different products. Products are now defined as combinations of characteristics, e.g. B. So: • “K2R” in Design A for$ 1.19, with a seal of approval and with a money-back guarantee
• “GLORY” in design B for \$ 1.39, with a seal of approval and no money-back guarantee
• Etc.

These holistic products are now presented to consumers for assessment.

## Areas of application

The three most important areas of application of conjoint analysis in market research are the areas of product development , pricing policy and market segmentation .

### Product development

In the area of ​​product development, conjoint analyzes play a major role , especially in the market launch of new products or the relaunch of existing products that are to be modified. A typical question in this context could be: “Which properties and characteristics of my product are it that provide the buyer with the maximum benefit ?” The aim is not only to increase sales of the products, but also to save costs Conjoint analysis Under certain circumstances, those product features identified as being irrelevant for the buyer which are associated with high manufacturing costs.

An example would be examining the influence of children on their mothers' product preferences when purchasing bicycles.

### Pricing policy

In the area of ​​price policy, conjoint analyzes are often used to provide the database for calculating the expected price-sales function for a product in a given market or in a competitive environment. With the data of the conjoint analysis, a simulation can be carried out, which can be used to calculate the price for a given product that brings the manufacturer the optimum profit.

An example would be the analysis of the acceptance of different price levels for different service strategies for technical consumer goods.

### Market segmentation

Market segmentations based on conjoint analyzes can For example, predict how competitors will react to market launches or what market shares can be expected for certain products. It is also possible to estimate the reaction of the market (or parts of the market, i.e. certain goals) to variations in certain properties, such as: B. Innovations or changes in brand strategy.

An example would be checking the size of the expansion potential of an umbrella brand in different target groups.

## Traditional profile method

The profile method got its name because each product (stimulus) is presented as a complete profile of its properties. In this respect, the profile method is based on the definition of the properties and their characteristics. Based on this, the test plan is determined, i.e. those stimuli are selected that are included in the assessment by the test persons. The evaluation then takes place using a form of ranking, so that ordinally scaled ranking values ​​are available for the stimuli as a result . On the basis of these ranking values, the utility values ​​are finally estimated and aggregated in the last step.

### Properties and their characteristics

Every conjoint analysis begins with the definition of the properties and characteristics of which the products are then composed. The following requirements should be met as best as possible:

• The properties and characteristics should be relevant for the consumer, as well as influenceable and realizable by the manufacturer.
• The selected properties should be independent, which means that the perceived benefit of one property value is not influenced by the values ​​of other properties.
• The properties and characteristics should be in a compensatory relationship to one another and should not contain any exclusion criteria (“KO criteria”). This means that the (high) benefit of the expression of one property can compensate for the (low) benefit of the expression of another property.
• The number of properties and characteristics should be limited. Since all combinations of the characteristics are taken into account as stimuli in the profile method, the survey effort increases exponentially with an increasing number of characteristics and characteristics.

Example:

Taking into account the above requirements, a margarine manufacturer specifies that the properties to be examined are “use”, “calorie content” and “packaging”. It provides 3 ways of use: As a spread, for cooking / baking / roasting, universal (i.e. both). The possible packaging is: cups, paper or portion sizes. The calorie content can be normal or low. In summary, the following overview results:

properties Characteristics
(A) usage (1) spread, (2) cooking / baking / roasting, (3) universal
(B) packaging (1) cups, (2) paper, (3) portion sizes
(C) calorie content (1) normal, (2) low

### Experimental design

The survey of the profile method is about the evaluation of stimuli (products), whereby a stimulus is a combination of exactly one characteristic expression for each characteristic. This gives the total number of possible stimuli as the product of the numbers of property values ​​for each property. Here, 20 stimuli are considered the upper limit for a suitable test plan . A stimulus is presented in the test plan as a complete product, in the simplest form as a map on which all properties and their respective characteristics can be recognized. In order to increase the reliability of the assessment, the aim should be to present the stimuli as realistically as possible instead of in the form of maps. B. as product samples, samples, final artwork, digital animations, etc.

#### Complete design

A complete design includes all possible stimuli. In a test plan with 3 properties, each with 2 values, there is a total of 2 × 2 × 2 = 8 possible stimuli. Since this meets the requirement for a maximum of 20 stimuli, a complete test plan would be used in this example, that is, all 8 stimuli would be presented to the test subjects for evaluation. In a test plan with 3 properties, each with 3 characteristics, a total of 3 × 3 × 3 = 27 stimuli would be obtained. In this case, you should use a reduced design.

#### Reduced design

If more than 20 stimuli would have to be included in the complete survey, the number of stimuli can basically be reduced in two ways:

1. By a corresponding random selection
2. By constructing an orthogonal design

The random selection of 20 stimuli should only be used in one of the following cases:

• When an orthogonal design is not available.
• If you still have more than 20 stimuli even after you have constructed an orthogonal design.

If the special case applies that you are dealing with exactly 3 properties, all of which have the same number of manifestations, you get the (symmetrical) reduced test plan with the help of a Latin square . This ensures that every expression of a property occurs exactly once with every expression of another property. So you get z. B. for a (3 × 3 × 3) design with 27 stimuli, a reduced design with 9 stimuli.

The normal case is accordingly the construction of an asymmetrical reduced test design. To do this, an existing orthogonal test plan is initially used .

If possible, a test plan is used that corresponds exactly to the number of properties and values ​​per property. In this case the construction has already been completed.

If an exactly matching test plan is not available, one selects a test plan that has the correct number of properties and provides at least as many values ​​for each property as there are in the study. The characteristics that do not exist in the investigation are now converted into existing characteristics by means of a clear transformation. This condition of proportional frequencies is sufficient for obtaining uncorrelated estimates and is therefore permissible for conjoint analysis.

If the result (with or without transformation) still has more than 20 stimuli, a random selection is made from the already reduced number of stimuli in order to complete the test plan.

Example:

For a (3 × 3 × 2 × 2) design with 4 properties (A), (B), (C), and (D), a reduced design is required. There is an orthogonal plan for a (3 × 3 × 3 × 3) design that is used as a basis. Since the properties (C) and (D) each only have 2 values, i.e. the 3rd value of the two properties must be eliminated according to the orthogonal plan, value 3 is transformed into value 1, i.e. 3 ⇒ 1.

The result is the following reduced (orthogonal) test plan:

stimulus (A) (B) (C) (D)
1 1 1 1 1
2 1 2 2 3 ⇒ 1
3 1 3 3 ⇒ 1 2
4th 2 1 2 2
5 2 2 3 ⇒ 1 1
6th 2 3 1 3 ⇒ 1
7th 3 1 3 ⇒ 1 3 ⇒ 1
8th 3 2 1 2
9 3 3 2 1

The 9 stimuli that will be included in the survey are now established. The stimuli can be read directly from the orthogonal test plan, with the columns corresponding to the properties with their respective characteristics for the 9 stimuli in the rows.

### Evaluation of the stimuli

For the estimation of the part worth utility of properties and property values, one needs ordinally scaled evaluations of the stimuli in the profile method. For this, a ranking of the stimuli is the traditional approach. However, ranking them makes high cognitive demands on the test subjects, especially if the number of stimuli increases. The results of a ranking therefore often do not correspond to the actual preference structure of the test persons. To improve the mapping of the actual preference structure, there are therefore alternative evaluation methods such as pair comparisons and choicing, in which the ranking is achieved through realistic, repeated selection.

#### Ranking

A ranking is established by presenting all the stimuli in the test plan to a test person. The test person now puts all stimuli in a sequence, with each ranking position representing the ordinally scaled rank of the individual stimulus. Missing or split ranks are permitted, but should be minimized if possible in the interest of valid results.

In order to mitigate the high demands that ranking places on the test person, it can be useful to let the test persons first make a rough classification. The test persons are asked to form groups according to their rough preference (e.g. 3 groups for the preferences "low", "medium" and "high") before a ranking is made within each group.

Rating scales are also often used as an aid. Here are monadic , since in this case each stimulus is judged in isolation especially rating scales in which for each stimulus a rating is given off as bad indicators. Common rating scales are therefore preferable, in which all stimuli are arranged together on one axis, with the option of adjusting the positions again and again in the course of the evaluation. As a result, this represents a ranking that is simplified in terms of content for the test person.

#### Pair comparisons and choicing

In order to arrive at ordinally scaled ratings for all stimuli without having to carry out a complex ranking, the test subjects can be asked to make pair comparisons for all stimuli. Here, the test person only needs to select the stimulus that is preferred over the other stimulus from each possible pair of stimuli. Although this procedure usually leads to a better mapping of the preference structure, it has the two major disadvantages that the survey is very time-consuming on the one hand, and inconsistencies often arise on the other, if z. For example, a test person indicates that he prefers stimulus A over B, and B over C, but then at a later point in time C over A, so that a clear ranking cannot be determined.

In order to counter these two problems of pair comparisons, a choice of 2 or 3 stimuli is allowed for the choicing survey method. The next selection set of stimuli is always formed based on the currently known preference structure, with strict preference relationships being taken into account. In addition, the currently most preferred stimuli are preferred when creating the selection sets. The selection is still very easy for the test person, but the result (the ranking) is available much faster and is always consistent in itself. Another advantage is that the survey can be limited in time, whereby the current ranking correctly maps the most preferred stimuli when the program is canceled.

### Estimation and Aggregation

On the basis of the empirically determined rank data of the stimuli, the partial utility values ​​are now first determined for all property values. The total utility values ​​of all stimuli, as well as the relative importance of the individual properties, can be derived from these partial utility values. Basically, the utility values ​​are determined for each individual test person. In order to arrive at an overall result, the individual results are first normalized so that they can then be aggregated. Alternatively, a common estimate is also possible for all test persons at the same time, but this should be avoided if possible, as this is associated with a loss of information.

#### Mathematical model

The profile method is based on an additive model, which means that the sum of the partial utility values ​​of the characteristic values ​​results in the total utility value of a stimulus. This can be formulated mathematically as follows:

${\ displaystyle y_ {s} = \ sum _ {e = 1} ^ {E} \ sum _ {a = 1} ^ {A} \ beta _ {ea} \ cdot d_ {ea}}$

With:

${\ displaystyle y_ {s}}$: Overall Estimated Utility Value for Stimulus p
${\ displaystyle \ beta _ {ea}}$: Part worth utility for value a of property e
${\ displaystyle d_ {ea}}$: Dummy variable , which is 1 if the property e for stimulus s is a, and 0 otherwise

#### Solution method

The ranking values ​​are now arranged in such a way that the highest ranking value is assigned to the stimulus for which there is the highest preference. It is also assumed that the test subjects consider the distances between the ranks to be the same (equidistant). With this assumption one can fall back on a solution with the KQ method . Here one minimizes the squared distance between the empirical rank data r and the utility values ​​y, i.e.:

${\ displaystyle \ min _ {b} \ sum _ {s = 1} ^ {S} (r_ {s} -y_ {s}) ^ {2}}$

The same solution can be reached with a regression analysis of the rank values ​​r on the dummy variables d. This is the most common method of calculation that can be used with simple standard software such as B. Excel is feasible.

If you want to drop the assumption of equidistant ranks, you switch to the monotonic analysis of variance . Here, in an iterative procedure, based on the KQ or regression solution, an adapted monotonic rank value is determined for the empirical rank values, whereby the procedure is terminated when the deviation between adapted rank values ​​and estimated utility values ​​cannot be further reduced (i.e. the " Stress ”measure of the monotonous analysis of variance was minimized).

#### Aggregation of utility values

After performing the estimates of all part-worth utilities of all test persons, these individual preference structures have to be normalized to an overall result of the conjoint analysis and then aggregated.

To this end, in each individual result for each property that part utility value is set to zero (normalized) that provides the lowest utility contribution. Now you put each (new) part worth worth in relation to the sum of the maximum part worth worth of each property. This achieves that

• all part-worth utilities normalized between 0 and 1 and thus comparable between the test persons,
• the maximum benefit of a stimulus for each test person is exactly 1,
• the maximum part-worth utilities of each property correspond to the relative importance of the property.

Example:

For a property (A) the part worth utilities -2, 0 and 2 are available for the 3 values ​​of A, and for a property (B) the part worth utility values ​​0.1667 and -0.1667 for the 2 values ​​of B. By the normalization we get 0, 2 and 4 for (A) and 0.3334 and 0 for (B). The sum of the maximum part-worth utilities thus corresponds to 4.3334. If you put the part-worth utilities in relation to this, you finally get 0, 0.462 and 0.923 for (A) and 0 and 0.077 for (B). Accordingly, the relative importance of (A) is 92.3% and that of (B) 7.7%.

## Two standard methods of conjoint analysis

The basic form of conjoint analysis has been converted into numerous variants over the years, which are intended to overcome certain weaknesses of the traditional method. Above all, two disadvantages should be mentioned: On the one hand, the number of features that can be queried is very limited in the original version. On the other hand, rating and ranking questions as they are used there do not provide any direct conclusions about the actual product selection of a respondent, which is the basis of a market simulation. Among the conjoint methods that have developed over the years through modifications and specialization of the existing methods, two methods have become established that allow a better handling of these problems: adaptive conjoint analysis (ACA) and selection-based conjoint analysis. Analysis ( English Choice Based Conjoint Analysis , short: CBCA ).

### The adaptive conjoint analysis

In contrast to the “classic” conjoint methods, the adaptive conjoint analysis is a process that can only be carried out with the aid of a computer. This procedure is called adaptive because the respondent's input is processed by the computer during the interview and used to develop the next page of the questionnaire. The interview adapts to the individual preference structure of the individual user in order to obtain the most meaningful information possible from the interviews. For the respondent, the adaptive conjoint analysis is a very varied type of survey, since an ACA consists of a total of five survey phases that he has to go through. The computer gets to know the preference structure of the test person better from phase to phase and designs the questionnaire pages in such a way that they provide the maximum information value.

In contrast to the classic conjoint analysis, the ACA is not a full profile method, which means that the respondent never has to evaluate product combinations that are made up of ALL characteristics during the interview. Rather, each of the products to be evaluated consists of only a small number of features, although information about the respondent's preference structure with regard to all features is nevertheless obtained in the course of the interview. The length of the interview increases with a higher number of characteristics, since more preferential judgments are required of the test person. The interview lengths, however, are moderate, even with large test plans. In practice, ACA studies are usually carried out with 8–15 characteristics and about five values ​​each. In theory, it is possible to include up to 30 characteristics in the survey design. Since it is difficult for the respondent to give consistent assessments for a complex issue, the effect can be observed with the ACA that characteristics that are "actually" unimportant for the respondent tend to be overestimated, while important characteristics tend to be underestimated. This is particularly problematic if price determination or market simulations are a key objective of the study.

### The choice-based conjoint analysis

The second advance in the field of conjoint procedures is the choice-based conjoint analysis , known as the so-called choice-based conjoint analysis ( English Choice-Based Conjoint Analysis , abbreviated as: CBCA ). In contrast to traditional conjoint analysis, the CBC is a procedure based on the findings of economic decision theory . By mapping the decision-making situation of consumers, two improvements are achieved in particular: firstly, the forecasts are more precise due to the greater realism, and secondly, they are behavioral and thus directly sales-oriented. The purchase probabilities obtained in the course of the selection-based conjoint analysis can be converted directly into expected contribution margins, profits and market shares.

In contrast to the ACA, the CBC is a full-profile procedure, so the test person evaluates products that, as in the real purchase situation, are always composed of all possible features. Another difference to the ACA is that the user cannot grade his evaluation of the presented products. Rather, the user is presented with a number of products per survey page, from which he can only select one as the one he prefers, i. H. "acquire" can.

Since, in such a situation, the test person has to weigh up four products, each with all their characteristics, against each other, the CBC places much higher demands on the participant's attention than an ACA. In return, the answers obtained in this way can be used to determine the trade-off between the individual characteristics more precisely. Implicit decision-making criteria that the respondent is not necessarily aware of also become more obvious.

In the case of longer interviews, however, a learning process can take place with the respondent in which he no longer perceives the products in their entirety, but only decides on the basis of features that are less relevant to him (e.g. brand, price). The task imitates the buying process, in which the buyer hides unimportant features and focuses on relevant criteria. However, as long as the information reduction corresponds to that of the real buying process, which is often observed, this is not a problem.

The selection-based conjoint analysis is currently the “golden standard” in the industry.

The choice- based conjoint analysis is also used in other areas under the name of Choice Experiment , including health and environmental economics .

## Further developments

### The limit conjoint analysis (LCA)

The limit conjoint analysis (LCA) extends the traditional conjoint approaches by a further procedural step. In the first step, the subjects are presented with a certain number of stimuli, which have to be evaluated according to the test plan and ranked. A stimulus here is a combination of different characteristics.

In the second step, the individual willingness to buy is determined by dividing the stimuli into alternatives that are worth buying and not worth buying. This is done by placing a limit card (LC) behind the last place that is still worth buying. The LC cannot only be placed between two stimuli, but rather also before the first or after the last position. In this way, the test person can express that he is not willing to buy any or all of the stimuli.

The LC is interpreted as utility zero. Stimuli worth buying assume positive, not worth buying negative utility values. This approach makes it necessary to assume that the test persons judge the benefit differences between the ranks to be constant. The groups of stimuli classified as “worth buying” and “not worth buying” must also be assumed to be scaled equally. In this way, in contrast to the classic conjoint analysis, absolute utility values ​​are determined instead of mere changes in utility.

This eliminates a central weakness of traditional conjoint analysis - namely that it is hardly possible to forecast purchase decisions, since only preference information is collected here, which does not allow the mapping of non-purchases, but the LCA also only allows recording a small number of features.

### The hierarchical individualized limit conjoint analysis (HILCA)

On the one hand, HILCA improves the ability to forecast purchase decisions by taking into account the idea of ​​limit conjoint analysis. In order to be able to map a larger number of features within the procedure, HILCA uses cognitive theories. These assume that, in order to avoid cognitive overload in complex assessment tasks, individuals undertake a hierarchization and subsequent successive processing of the information to be processed. The HILCA can be characterized by a hierarchical assessment approach for characteristics, which undertakes a different type of hierarchization compared to hierarchical conjoint analysis, and the basic idea of ​​limit conjoint analysis, which allows both the inclusion of a theoretically unlimited number of characteristics and the Intended to improve purchase decision prognosis.

### The Multi-Rule-Conjoint-Analysis (MRC)

The Multi-Rule-Conjoint-Procedure (MRC) takes into account several ( English multi ) psychological decision rules ( English rule ) of the respondents. As a result, in contrast to the classic conjoint analyzes, this method can map not only rational , but also irrational decisions. Since the irrational as well as the rational decision-making behavior has a certain systematics, it can be statistically calculated and predicted.

The rational decision-maker in traditional conjoint calculation models evaluates and weights the characteristics of a good individually and makes his decision by adding up the part-worths to an overall benefit . An irrational decision maker, on the other hand, orients himself to certain reference values, such as price discounts, and compares the various offers directly on the basis of these properties. For him, the decisive factor is which alternative represents the better option for most properties with regard to the respective reference value and not which, rationally speaking, actually has the greater overall benefit.

By combining the statistical algorithms for forecasting rational and irrational decision-making behavior, the forecast quality can then be increased considerably.

### Selection-based conjoint analysis with hierarchical Bayes estimation (CBCHB)

With the help of hierarchical Bayesian (HB) models, the preferences of individual persons within a data set can be estimated. It should be noted here that the hierarchical Bayesian estimation is a special statistical estimation method and must not be confused with the hierarchical structuring of an evaluation task. Where there is not enough information about the evaluation of individual characteristics, this is derived from the preference distribution of the total population within the framework of the HB estimation, which leads to very robust results. The distribution of preferences in the overall population is of particular interest here, as it reflects the heterogeneity of customers. From the heterogeneity of the customer population z. For example, it can be derived which percentage of customers has sufficiently strong preferences to be able to offer them the product profitably. Furthermore, the hierarchical Bayesian method avoids distortions in the application in the simulation of profits and contribution margins, which inevitably occur in the aggregated method due to Jensen's inequality as soon as the population distribution shows any heterogeneity. A new variant of the process is the adaptive selection-based conjoint analysis (ACBCA).

## literature

• RD Luce, JW Tukey: Simultaneous conjoint measurement . In: Journal of Mathematical Psychology . tape 1 , 1964, pp. 1-27 .
• Paul E. Green, V. Srinivasan: Conjoint Analysis in Consumer Research: Issues and Outlook . In: The Journal of Consumer Research . tape 5 , 1978, p. 103-122 .
• B. Erhardt: Conjoint Analysis: A Comparison of the Classical Profile Method and Selection-Based Analysis . beingoo, Spiegelberg 2009, ISBN 978-3-940525-02-4 , pp. 260 .
• Anders Gustafsson, Andreas Herrmann, Frank Huber (Eds.): Conjoint Measurement. Methods and Applications. 3. Edition. Springer-Verlag, Berlin / Heidelberg 2003, ISBN 3-540-40479-1 .
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• M. Brocke: Preference measurement by the discrete choice analysis. German University Publishing House, Wiesbaden 2006.
• Daniel Baier, Michael Brusch: Conjoint analysis: methods - applications - practical examples. Springer, Berlin 2009, ISBN 978-3-642-00753-8 .
• T. Melles: Framing Effects in Conjoint Analysis. An example of problems with the feature definition. Aachen 2001.
• Thorsten Teichert : Conjoint Analysis. In: Andreas Herrmann, Christian Homburg (ed.): Market research: methods, applications, practical examples. Gabler, Wiesbaden 1999, pp. 472-511.
• R. Boutellier, R. Völker: Success through innovative products. Carl Hanser Verlag, Munich / Vienna 1997.
• Christian von Thaden: Conjoint analysis with many features. Peter Lang Verlag, 2001.
• Markus Voeth : Benefit measurement in purchasing behavior research: The hierarchical individualized limit conjoint analysis (HILCA). German Univ-Verlag, 2000.
• Sönke Albers among others: Measurement of willingness to pay and their commitment to price bundling. In: Marketing ZFP. 29th year, 2007, pp. 7-23.
• Florian Bauer: Defragment the consumer. Three ways to unleash the predictive power of market research. In: ESOMAR Congress 2006 - Foresight - The Predictive Power of Research. 2006, ISBN 92-831-0197-9 , pp. 82-95. (www.esomar.org) ( Memento from December 1, 2007 in the Internet Archive )
• Joel Huber: Conjoint Analysis: How we got here and where we are. (PDF; 101 kB). Sawtooth Software, Research Paper series, 2005.
• P. Wiliams, D. Kilroy: Calibrating Price in ACA: The Price Effect and How to Manage it. Sawtooth Software Research Paper Series, 2000.

## Individual evidence

1. For the discussion of terms cf. H. Schweikl: Computer-aided preference analysis with individually important product features . Berlin 1985.
2. Green / Srinivasan, 1978, p. 104.
3. Luce / Tukey, 1964, pp. 1-27.
4. Green / Srinivasan, 1978.
5. Erhardt, 2009, p. 27.
6. ^ Richard M. Johnson: History of ACA . In: Proceedings of the Sawtooth Software Conference ., Pp. 205-212.
7. JJ Louviere, G. Woodworth: Design and Analysis of Simulated Consumer Choice or allocation experiment: An Approach Based on aggregate data . In: Journal of Marketing Research . tape 20 , no. 4 , 1983, p. 350-367 .
8. ^ J. Büschken: Conjoint Analysis. In: T. Tomczak, S. Reinecke (Ed.): Market research. St. Gallen 1994, p. 73.
9. The example is taken from: PE Green, Y. Wind: New way to measure consumers' judgments . In: Harvard Business Review . 1975, p. 107-177 .
10. A. Mengen, G. Tacke: Method-based automobile pricing with conjoint measurement. In: H. Bauer, E. Dichtl, A. Hermann (eds.): Automotive market research: Benefit orientation of car manufacturers. Munich 1996, pp. 33-52.
11. Thomas, L .: The influence of children on the product preference of their mothers . Duncker & Humblot, Berlin.
12. L. Theuerkauf: customer benefit measurement with conjoint . In: Journal for Business Administration . tape 59 , no. 11 , 1983, pp. 1179-1192 .
13. R. Weiber, P. Billen: The brand span portfolio for determining the expansion potential of an umbrella brand: Theoretical analysis and empirical evidence. In: D.-M. Boltz, W. Leven (Ed.): Efficiency in brand management. Hamburg, pp. 72-91.
14. The presentation of the profile method is based on K. Backhaus, B. Erichson, W. Plinke, R. Weiber: Multivariate Analysis Methods . Springer, Berlin / Heidelberg 2008, p. 543-604 .
15. Example: With margarine, the low benefit of high calorie content is offset by the high benefit of better taste.
16. Example: With 3 properties with 4 values ​​each and 2 properties with 3 values ​​each, the total number is 4 × 4 × 4 × 3 × 3 = 576 stimuli.
17. Green / Srinivasan, 1978, pp. 104ff.
18. See Backhaus / Erichson / Plinke / Weiber, 2008, p. 553.
19. Orthogonal test plans can be found e.g. B. in S. Addelman: Orthogonal Main-Effect Plans for Asymmetrical Factorial Experiments . In: Technometrics . tape 4 , no. 1 , 1962, pp. 21-46 . More test plans can be found here: Orthogonal Arrays (Taguchi Designs). Retrieved November 17, 2017 .
20. For proof cf. S. Addelman: Orthogonal Main-Effect Plans for Asymmetrical Factorial Experiments . In: Technometrics . tape 4 , no. 1 , 1962, pp. 21st ff .
21. See Orthogonal Array L9 (Taguchi Design): Four three-level factors. Retrieved November 17, 2017 .
22. The transformation 2 ⇒ 1 is just as permissible.
23. ^ I. Fenwick: A user's guide to conjoint measurement in marketing . In: European Journal of Marketing . 1978, p. 203-2011 .
24. KJ Clancy, R. Garsen: Why some scales predict better . In: Journal of Advertising Research . tape 5 , 1970, p. 33-38 .
25. G. Hausruckinger, A. Herker: The construction of estimation designs for conjoint analyzes on the basis of pair comparisons . In: Marketing ZFP . tape 2 , 1992, p. 99-110 .
26. ^ H. Schweikl: Computer-aided preference analysis with individually important product features . Berlin 1985, p. 56 ff .
27. See Backhaus / Erichson / Plinke / Weiber, 2008, p. 568.
28. See Backhaus / Erichson / Plinke / Weiber, 2008, p. 595ff.
29. P. Wiliams, D. Kilroy: Calibrating Price in ACA: The ACA Price Effect and How to Manage It. (PDF; 223 kB). Sawtooth Software Research Paper Series, 2000.
30. In Sawtooth Solution Newsletter (2006) it was published that 75% of their customers use CBC, 16% ACA and 9% use the traditional conjoint method.
31. Albers, Becker, Clement, Papies, Schneider: Measurement of willingness to pay and their use for price bundling. In: Marketing ZFP. 29th year, 2007, pp. 7-23.
32. ^ Conjoint Analysis: How we got here and where we are. (PDF; 101 kB). Sawtooth Software, Research Paper series, 2005.