# Conjoint Analysis Example to Predict Customer Preference

Conjoint means joined together, united, combined, or associated. Conjoint analysis has been used for the last 30 years. It has been used in mathematical psychology since the mid-60s for business, but market research applications have been created for the last 30 years. Conjoint analysis is generally used to understand and identify how consumers make trade-offs, and how they choose among competing products and services. Conjoint analysis can be used to predict customer choices, which can be further used for understanding future purchases.

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Conjoint analysis provides answers to many critical managerial questions like the following: What is the best possible design for a new product? What is used in new product launches? What is our value compared to our competitors? How can an existing product be improved? How important is our brand name for a customer to choose our product or service? How much market share can a product hold? What is the price sensitivity of the product? If we change the price then what is going to be the impact on the sales? What is the price value of each product feature, and is it worth adding a new feature or is it not worth the cost?

There are different types of conjoint analysis techniques. The first type is known as full profile conjoint analysis. The second one is known as choice based discrete conjoint analysis, or CBC. Then we have adaptive conjoint analysis, or ACA. There is also MaxDiff conjoint analysis, and the last one which is becoming more popular is Hierarchical Bayes conjoint analysis. Bayesian methods are used to do the analyst part. Bayesian methods by nature are efficient and handle improper or incomplete and large amounts of data. Out of all these types, choice based conjoint is the most popular.

Conjoint analysis procedures are generally the same regardless of the type you use. However, the execution differs. The first step is to describe the product or service in terms of its attributes, characteristics, or features. The descriptions you use are called “factors.” Then, you need to select values for each factor. These values are called “levels.” The third step is constructing a set of products or services using these factors and levels. The various factor and level combinations are known as treatments or stimuli. Once you’ve formulated the treatment and stimuli, you present it to respondents who will provide evaluations.

Your customers elicit preferences for your products. For instance, you can ask customers to choose their most preferred product from a list of options. You can also ask customers to rank their preferences among several products. You can also ask customers to rate your products. Rating products gives you a way to weight each product and its strength against other products. You can also simply ask customers for their favorite choice among a list of products. This preference gives you one favorite from your customer. This option or choice is known as the “conjoint” choice.

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Next, you determine the preference structure. You determine the preference structure based on customer feedback. The preference structure determines the influence of each factor and level. This analysis is performed either individually or using a collection of customer data.

For example, let’s use a fictitious product called Zen Detergent. This detergent has three factors. The three factors are ingredients, brand and its form. Each factor has two levels. Ingredient levels include phosphate based of phosphate-free. Form levels include liquid or powder. Brand levels are Zen Detergent or a generic brand.

In total, we have 8 stimuli. This means there are 8 combinations of forms and levels. You then present these 8 stimuli to your customer. Customers are asked to rank each of these stimuli from one to eight and ranks can’t be a tie.

This example is an edited model. An edited model calculates the worth of every level and factor. So let’s say that our customer has chosen level I for factor one, and level J for factor two, and level N for factor N. The total worth of customer choices is equal to the summation of all levels and the factor combinations. So the overall worth is the summation of level I, J and N.

Continue with the Zen Phosphate brand. For instance, choose Zen, phosphate-free, and powdered as the combination. Assign a worth to each part and add them to find a total worth.

You can understand better with an empirical example. In an empirical example, assume that there are two respondents that have ranked these eight stimuli.

Combinations are also known as profiles. You assign profiles identifiable labels. Label the first profile S1. Then label subsequent profiles D1, D2, D3. The “D” usually means “developed.” The profiles contain your list of factors and the corresponding combination. If you remove a factor, you then use negative numbers to denote the combination profiles.

After you’ve organized your profiles, write respondents’ names in columns and then write each respondent’s choice into each column. You use respondent responses to rank each combination profile as you tally which combination was most popular with your customers.

You also need to know how to rank each part’s worth. You can calculate each part’s worth by taking the average of each combination’s popularity. You first add the rank for each part, then you divide by the total number of parts. For instance, what are the ranks given to liquid? Add up the customer’s rank and then divide by the total number of liquid combinations you used.

Now what do we do? Once we have the ranks we’ll calculate the average out of it. Add up all of the ranks and combination totals and average them to find a total score.

For instance, suppose the Zen Detergent brand ranks as one, three, five, and seven. If we sum up one, three, five, and seven and divide it by four we get a four. This is the way we calculate the averages. Once the averages are calculated, we need to attach something known as a “part worth” to them. For instance, choose the factor as ingredient and the phosphate-free as a level. Us an average rank for phosphate-free as 3.75, and 5.25 for the phosphate based. If you find the difference between both of them, then 5.25 minus 3.75 is 1.5. And if you divide this 1.5 by two, you get 0.75. You assign the lower number to your most preferred product. Therefore, if you have a negative number, you assign it to your most popular product. So in this example, 3.75 is the average rank for phosphate-free, and 0.75 is for the phosphate-based (more popular).

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Once we have the part worth, you can predict rankings. You try to find out the part worth using the overall stimuli. To do this, you sum the part worth for each stimuli to find overall utilities. The second step is to predict rankings based on these utilities.

Let’s pick up the example of profile S2, where the form is liquid, ingredient and phosphate-free, and the brand is generic. The respondent utility for R1 is 2.5. How do we get this 2.5? The liquid part is 1, phosphate-free is 2 and the generic part is -.5 (obtained earlier).

Once you have these part worths, you can sum up to get the total part worth. One plus two, minus 0.5, which is equal to 2.5, and this becomes the total part worth for the S2 profile. You can see that whichever combination has the highest value gets the first rank. So 3.5 is the highest number it will get rank one, 2.5 is the second highest number and it will get a rank two, and similarly, minus 3.5 is the lowest number in terms in sum of part worth utility, and that’s a rank of eight. This is the prediction for the customer, and similar prediction can be made for the second respondent. So, respondent wise we can get a calculation of the part worth for stimuli.

This was a very simple example. You typically need software to calculate these numbers, because there is usually several combinations and several factors to calculate. You also have several hundred respondents who participate in your feedback surveys.

Conjoint analysis is useful to value products or improvements for existing products. It’s a very popular technique in market research. It allows you to estimate something known as willingness to pay for a good that does not exist yet. Conjoint analysis can be used for existing products, or it can be used for hypothetical situations. Those hypothetical situations could be products or services you want to introduce to the market, and you want to know potential customers’ willingness to pay.

There’s one more inherent advantage in conjoint analysis. Conjoint analysis automatically increases the total sample size. The requirement of sample size from a statistical perspective is always high. So the advantage in conjoint is that, though you may have lesser number of respondents, you’ll have more observations. Therefore, your total sample size increases.

Applications for product managers are that they can discover products or concepts with optimal qualities. They can establish contribution of each attribute and each level for each utility. They can identify segments of consumers who put differing importance on attributes. Conjoint analysis is generally coupled with clusters to find out preferred segments. They can then be used to explore market potential for future combinations.

Conjoint analysis also lets you create unique models for predicting respondent preferences. Individual results can then be aggregated to find out the group utility or they can be used to have aggregate models. Conjoint analysis handles non-linear and linear relationships.

A conjoint decision framework is a six-step process. We have to define objectives and what we want to achieve. Secondly, we develop a factorial design and develop assumptions. Then you run a conjoint analysis and understand the model and an assessment. Also, the quality of the model has to be assessed. Then, you interpret the result. You also need to validate your results.

You also have to understand how to design a conjoint analysis study. You first select the attributes that determine the good you want to value. The important thing is the attribute should be relative to the good. You can use price as one of the attributes. You can choose attributes that are either qualitative or quantitative. You then determine the levels for your attributes. Once you’ve finalized the attributes, you need to determine the levels for each attribute. Conditionally, that level should be realistic and reasonable. You can’t have impossible levels for each attribute. They must be realistic.

Let’s use an example to understand this concept further. For example, let’s look at an attribute for access. In access, there are two levels. Basic access levels are whether it’s available or not. Of course, when we say “available,” then each condition should be considered. Another example is the number of new jobs created as an attribute. This is a quantitative number, but you can see it defined as three levels, so 150 is the number of jobs created (level one), 250 is the number of jobs created as well (level two), and 350 jobs created can be the third level.

Step three, as every statistical technique requires, is the sample size, which should be large. For example, suppose you use a house and it’s described with three attributes. Square footage could have three levels 1,500, 2,000, and 2,200. Then, the second attribute could be proximity to a city center. You could use less than three miles or greater than three miles as attributes. And the price has four levels, 200K, 250K, 300K, and 350K. If you take all of these combinations together, our full factorial design will consist of three into two into four, or 24 alternatives.

Full factorial design is advisable in this example, because of the reduced number of alternatives. 24 alternatives is a practical choice when you need one person to evaluate your options. But if this number becomes more, let’s say if they are 100 alternatives or more than 100 alternatives, it becomes too difficult to personally evaluate. When the number of alternatives becomes too high, you use factorial designs. Art has a package by the name of ENG design, which can be used for generating fractional factorial designs. What does fractional factorial design software do? It reduces the number of alternatives.

Next, construct the choice set or the product profiles, and you can add up your number of alternatives. In conjoint analysis, there are a certain number of assumptions. One of the assumptions is the alternatives are driven by the respondent’s underlying utility. So you have to calculate your respondent’s utility.

The respondent utility is broken down into two columns of components: A deterministic one, which we can actually determine, and the second one is an added component where the researcher has not been able to estimate. In terms of equation, you can write this component summation as VIJ, which is the utility, and then V which will amount to XIJ into beta. X is a vector of the attributes and levels, and beta is the vector of the weight-ages that the customer assigns to these factors and levels. Epsilon IJ is the additive, because the market researcher had not been able evaluate this part of the choice.

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