--- date: 2020-11-20 description: 'Choice-based conjoint analysis (discrete choice modelling): estimating which product attributes actually drive consumer choice in a marketplace-like setting.' kategoria: Statystyka i analiza danych slug: choice-based-conjoint-analysis title: 'Conjoint analysis: Discrete choice modelling in market research' --- # Conjoint analysis: Discrete choice modelling in market research ### Choice-Based Conjoint Analysis In choice-based conjoint analysis, a set of products is presented to consumers in a similar manner to the real marketplace situation. They decide which one is the most attractive for them. (fig. by author) In the [previous article](https://towardsdatascience.com/how-to-develop-perfect-product-using-conjoint-analysis-1c2d9e4beb5d), I introduced a conjoint analysis and provided some examples of how useful the market research method is. I recommend you to read it first. Choice-based conjoint analysis (CBC, or: discrete choice modelling, discrete choice experiment, experimental choice analysis, quantal choice models) uses discrete choice models to collect consumer preferences. The main difference distinguishing choice-based conjoint analysis from [the traditional full-profile approach](https://netlabe.com/how-to-develop-perfect-product-using-conjoint-analysis-1c2d9e4beb5d) is that the respondent expresses preferences by choosing a profile from a set of profiles, rather than by just rating or ranking them. The basic idea of choice-based conjoint analysis is to simulate a situation of real market choice. After reading this article, you will know: - what are the uses of choice-based conjoint analysis, - how to design experiment, - how to analyse collected data. ## Design of experiment ![*The choice between different products. Products are described as sets of different combinations of attribute levels — profiles. (fig. by author)*](img/choice-based-conjoint-analysis/078060797635.png) In this method, a set of profiles is presented to respondents and they decide which one is, for various reasons, the most attractive for them. You simply ask respondents to choose the most attractive (preferred) profile from a set of alternatives. A nice example of a well-designed choice-based conjoint survey you find [here](https://websitedemos.sawtoothsoftware.com/cbc-baseball/). Authors, Sawtooth Software, provide professional software tools for conjoint analysis. ## Applications So, when you want to develop a new or modify an already existing product, choice-based approach flexibility of configuration is preferred over other conjoint methods. In general, choice-based conjoint analysis is used to measure preferences (e.g. attribute importance), and the willingness to pay for products and services. By asking respondents to choose the most preferred profile, CBC forces them to make trade-off decisions between different products in a competitive, similar to the real market, environment. This approach enables you to find out how to purchase likelihood is influenced by various product attributes and their levels (values). ### Pricing For example, you can find what is the optimal price for a new product. \![\[fig-amp-price.png\|*In this scenario, the optimal price for the energy drink AMP is \$1.39, where the purchase probability is highest at 15%. ([source](https://www.quantilope.com/en/method-choice-based-conjoint-analysis))*\]\] Or what attributes have the greatest influence on consumers willingness to pay a premium price? \![\[fig-glass-bottle.png\|*Between a can, glass bottle, and plastic bottle, consumers are willing to pay more for a glass bottle when purchasing an energy drink. ([source](https://www.quantilope.com/en/method-choice-based-conjoint-analysis))*\]\] ### Product optimization You can also, as in most conjoints, find out which product features have the greatest impact on consumers’ purchase decisions. \![\[fig-attribute-importance.png\|*Product price (42%) and brand (33%) have the greatest impact, accounting for 75% of a consumer’s purchase decision of energy drinks. ([source](https://www.quantilope.com/en/method-choice-based-conjoint-analysis))*\]\] \![\[fig-sample-task.png\|*Sample Choice-Based Conjoint Analysis Task ([source](https://www.quantilope.com/en/method-choice-based-conjoint-analysis))*\]\] Other problems that can be studied using CBC: - How to combine features to create the best product? - Which products alternatives could be sold for the best price? - How important is each attribute in the matter of purchasing decision? - How do different features compare to others? - How sensitive is the price to changes in levels of attributes? As you can see, you can use CBC in multi-attribute studies or in complex scenarios of purchasing paths for a better representation of real situations. ## Advantages So, choice-based conjoint analysis is a great tool for market simulation. By selecting one of the proposed variants of the product, respondents simultaneously and unknowingly evaluate the attributes that characterize the profiles. Indeed, respondents make a simultaneous assessment of all attributes, as in the case with actual market decisions. In traditional conjoint analysis methods respondent assesses the attributes in pairs in isolation from other parameters. This leads to the under- or overestimation of the importance of certain attributes, especially such specific attributes as the price or brand. In contrast, the choice-based conjoint analysis gives you the ability to obtain more realistic estimates of the value (significance) of individual attributes that respondents are associated with their chosen attribute levels. Another advantage of a choice-based approach over traditional conjoints is the ability to learn which attribute values or their combinations may discourage the consumer from buying any of the products available on the market. Depending on the problem studied, respondents have or not a possibility to refrain from choosing, e.g. by selecting “none” when no profile meets their expectations. When you will have to decide whether to give that possibility to the respondent or not, you should take into consideration the best resemblance to the situation on the real marketplace. ![*Things like laptops or cars are more serious and thoughtful purchases than groceries. (fig. by author)*](img/choice-based-conjoint-analysis/9ee880457a59.png) Consumers in case of lack of perfect alternative more likely would refrain from purchasing smartphone (e.g. because they have still working old device) than wine (e.g. because they invited friends for dinner). The utility of a combination of attributes that is not chosen is a threshold value that should be taken into account when defining a new profile that is acceptable to the potential buyer. CBC can also measure the main effects and interactions between them. CBC is more effective than full-profile in profile assessment because it requires less effort from respondents. This requires a smaller number of decisions from respondents than the traditional conjoint analysis method. ## Disadvantages But like any method, the CBC has limitations. The choice procedure results in less informative data than the ranking or rating assessment procedures. A choice-based experiment requires the collection of a large number of observations in order to obtain reliable parameter estimators. Therefore, the costs of such an experiment may be higher than the costs of an experiment carried out for traditional conjoint analysis. ![*CBC requires the collection of a large number of observations in order to obtain reliable parameter estimators. (fig. by author)*](img/choice-based-conjoint-analysis/2b57877d244d.png) Algorithms required to analyse collected data are also more sophisticated. Depending on the design of a particular experiment, it may be difficult to achieve a reliable utility function in the continuous field of attribute levels. Another disadvantage of this type of conjoint analysis is that standard estimation methods only allow for modelling at the aggregate level. The data collected as a result of a choice-based experiment does not allow the estimation of separate utility models (part-worth utilities) for each of the respondents on an individual level. However, as we will show later in the case study, you can segment the market and estimate part-worth utilities for each segment of consumers at least. Discrete choice procedure in comparison with a ranking or positional assessment procedure leads to the collection of data of lesser informative value. Especially, if you include too many parameters displayed at the same time, the respondent will have to mentally process a large amount of information. This leads to an effort that is disproportionate to the added value and higher costs of conducting the study. So remember, you should only include a limited number of attributes and their levels to avoid respondents’ information overload. Choice-based conjoint analysis is not adaptive by design. In the case of a large number of attributes or their values, a correspondingly larger sample must be collected. Then you should consider using adaptive methods such as adaptive choice-based conjoint analysis or hybrid methods. Note: CBC tests products that are fixed. If the consumer can customize the product, consider creating a menu-based study. ## Data analysis The process of choosing between profiles is probabilistic, as consumers do not always act in a predictable and consistent manner. This means that the consumer, under the same conditions and from the same set of profiles, can make different choices at different times. That’s why choice-based conjoint analysis shares assumptions with random utility theory. In random utility theory, we assume that people generally choose what they prefer, and when they do not, this can be explained by random factors. So, let’s propose a random utility function with deterministic and random components. ![](img/choice-based-conjoint-analysis/26a133796f3f.png) ![](img/choice-based-conjoint-analysis/cc64b8ccd9c2.png) The random component has a very precise meaning. It is a source of inconsistencies in the choices of the consumer over time and must not be explainable by other factors. It could be the result of the actual emotional state of the consumer, his or her special needs at this particular time. However, if you could propose a model for these needs, this won’t be a random phenomenon. Next, we can propose a linear model for random utility: ![](img/choice-based-conjoint-analysis/910821b27c78.png) ![](img/choice-based-conjoint-analysis/947e8339349e.png) An assumption in aggregate-level models is the homogeneity of parameters. The parameters representing the average value for the population. For the estimation of model parameters, a specific distribution of the random component is assumed, which leads to different probabilistic models. Most often it is assumed that the random component has a normal or Gumbel distribution. Therefore a binary probit model or a polynomial logit model is obtained accordingly. Although the possibility of heterogeneous preferences among the population is ignored in aggregate-level models, there are methods for using choice-based conjoint analysis to segment consumers using additional data. For example, sympathy for anchovy is not normally bell-shaped distributed. Rather than that, distribution has two “humps”, reflecting the overlapping of two very different populations: people who like anchovy and who don’t. As you will see in the example study, you can split consumers into segments that have different part-worth utilities. ### Hierarchical Bayes estimation Although aggregate-level estimation of preferences is sufficient in forecasting the market share of a new product, in many situations, it is still desirable to obtain estimates of every individual consumer’s preference structure. From data collected by choice-based conjoint experiment part-worths at the individual level cannot directly be estimated. It’s because the dataset is too sparse. But you can Hierarchical Bayes methods in post-processing to recover individual preference heterogeneity even with insufficient degrees of freedom. [More about HB.](https://sawtoothsoftware.com/resources/technical-papers/hierarchical-bayes-why-all-the-attention) ## Case study Let’s analyze the example study from “[Using cluster analysis and choice-based conjoint in research on consumers preferences towards animal origin food products. Theoretical review, results and recommendations](http://www.ighz.edu.pl/uploaded/FSiBundleContentBlockBundleEntityTranslatableBlockTranslatableFilesElement/filePath/1129/str171-184.pdf)”. ### The business problem Consumers are becoming more aware of food of animal origin. They shift their interests towards products that are safe, nutritious, produced through ethical and environment-friendly methods. The aim of the study is to determine which characteristics of the product (eggs) are of most importance to the consumer. Note: in the original study, there is also an important analysis of methods of market segmentation. Market segmentation is beyond the scope of this article, but I recommend that you familiarize yourself with the methods described in the source study. ### Attributes Attributes selected to further research are a farming method, hen breed, nutrition claims, egg size, package size and price. Their levels (values) are described in the table below. \![\[fig-egg-attributes.png\|*Attributes and levels used in the conjoint survey design. ([source](http://www.ighz.edu.pl/uploaded/FSiBundleContentBlockBundleEntityTranslatableBlockTranslatableFilesElement/filePath/1129/str171-184.pdf))*\]\] Attributes and levels were selected after reviewing previous studies on consumer preferences and by direct assessment of their importance by the research team. ### Experiment design Each respondent saw similar screens (with 3 different products at a time) with all the attributes defined in accordance with the established levels (presented in Tab. 1) and had to choose one of them. Each respondent saw a dozen screens with the question “Which product would you choose?”. ![*Respondents choose from 3 different alternatives of product. (fig. by author)*](img/choice-based-conjoint-analysis/83369ab22e51.png) Every screen contains 3 different profiles and respondents had to choose one of them. Importantly, there was no “none of those” option. As the authors of the study argue, this is similar to the real situation, when a person goes shopping and wants to buy eggs. Usually, he or she is forced to choose from what is available on the shelf and rather buy anything, than refrain from buying eggs. The questionnaire contained choice-based questions, socio-demographic questions and questions about food selection habits, nutritional beliefs and preferences. Examples of additional questions: - How often do you buy organic eggs? - Information on the packaging is very important to me. - I need to know what the product contains. - Organic eggs are better than non-organic eggs. The scale was 1–7, where 1 means “I strongly disagree…” and 7 means “I strongly agree…”. ### Data collecting Answers from nearly 1000 respondents aged 21+ were collected using Computer Assisted Personal Interviewing (CAPI). The sample was selected to be representative of the polish population for region, age and gender. ### Analysis After collecting data, [Hierarchical Bayesian networks](http://www.aurelielemmens.com/wp-content/uploads/2019/04/Conjoint_HB_2018_shortened.pdf) are used to analyze it. > K-means clustering algorithm. The aim of the K-means algorithm is to divide M-points in N-dimensions into K-clusters in order to minimize the within-cluster sum of squares. We seek “local” optima solutions so that no movement of a point from one cluster to another will reduce the within-cluster sum of squares. A detailed statistical algorithm is described e.g. [here](https://en.wikipedia.org/wiki/K-means_clustering) and [here](https://towardsdatascience.com/understanding-k-means-clustering-in-machine-learning-6a6e67336aa1). \![\[fig-kmeans-clusters.png\|*K-means clustering algorithm: the part-worth utilities with the relative importance of attributes for 4 identified clusters. ([source](http://www.ighz.edu.pl/uploaded/FSiBundleContentBlockBundleEntityTranslatableBlockTranslatableFilesElement/filePath/1129/str171-184.pdf))*\]\] ### Results The most important attributes were “price” and “farming method”. Other (“breed”, “nutrition claims”, “size”, and “package”) were defined as less important but were taken into consideration later on. Regarding mean relative importance, there are two clusters focused on price (Cluster 1 — RI — 59% and Cluster 3 — RI — 53%) whereas Cluster 4 does not perceive the price as the only important egg attribute (RI — 39%). It can be seen that segments that consider “price” as extremely important pay less attention to attributes related to animal welfare. ## Takeaways As you can see, choice-based conjoint analysis is a useful tool. Furthermore, in combination with other methods, like clustering algorithms, it can circumvent some of its limits. ## References - https://www.slideshare.net/surveyanalytics/webinar-a-beginners-guide-to-choicebased-conjoint-analysis - https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=2685&context=gradschool_dissertations - https://help.xlstat.com/s/article/choice-based-conjoint-cbc-in-excel-tutorial?language=en_US - https://www.quantilope.com/en/method-choice-based-conjoint-analysis - https://www.researchgate.net/publication/23505678_A_HIERARCHICAL_BAYES_APPROACH_TO_MODELING_CHOICE_DATA_A_STUDY_OF_WETLAND_RESTORATION_PROGRAMS - https://docs.displayr.com/wiki/Random_Utility_Theory