# Conjoint Analysis- A detailed overview

Humans face easy to complex choices each day, For Instance, which restaurant should I visit today? or which car should I buy? etc. Hence, Most of these choices are very easy to make and never potentially harm us if we choose this or that. But, when it comes to business, making choices can be trickier. A wrong decision can make a business go bankrupt, whereas a good decision can help a business grow like nothing else. In business, we would love to somehow get inside our customers’ brains, and get a quantitative report.

Well, Conjoint Analysis does this.

WHAT’S IN IT

## What is a Conjoint Analysis?

Conjoint Analysis is a popular research method for predicting how people make complex choices. So, The conjoint analysis or stated preference analysis is a statistical technique that originated in mathematical psychology. Also, It is used in social science and applied science, even marketing product management and operations research.

Paul Green, a marketing professor at the Wharton School at the University of Pennsylvania, developed it further from its basics originated from mathematical psychology. Another person who greatly contributed to the theory at later stages is V. Srinivasan, professor at Stanford University.

Today, well over 10000 studies are being conducted annually on this tool by research firms, government agencies.

## How does it work

### Simple Example

Let’s assume you go to a shop to buy a smartphone or MP3 player. Now the salesperson tells you you can either get the model with the 32 gigabytes off the shelf at that moment or you get a model with 64 gigabytes. But then you have to wait one week for the delivery.

So, Now the question is, what is your preference? Your preference for one of the alternatives will reveal the part-worth utilities of individual attributes. In our example, attribute-1 is the memory size, and attribute 2 is the delivery time.

According to BPMSG, “In a Conjoint analysis, the Part-Worth Utilities of individual attributes are calculated based on the selection or ranking of a defined set of combinations of attribute values.”

When you choose the first model with 32 gigabytes, it will show that you put a high emphasis on the short delivery time. Choosing the second model will reveal your high emphasis on the large memory size.

So in a conjoint analysis, the part-worth utilities of individual attributes in our case memory size and delivery time are calculated based on the selection of all rankings of a defined set of combinations of attribute values.

### Complex Example

Let’s take our example a little more complex. We take into consideration 3 attributes. Then, we look at the color, green or red. Finally, we look at memory size, 16 or 64 gigabytes and we look at the delivery time, one day or one week.

Combining all attributes with that individual values will result in 8 different combinations.

In order to solve this problem with the mathematical methods, we code the values or levels with minus one and plus one each. So, for example, the green is coded as minus one, and the right is coded as plus one.

Here is the list of combinations with their coding. We call it the design metrics. Fork attributes, there are two to the power k possible combinations. Using all possible combinations is called a full factorial design.

We treat the 3 attributes as variables each of them with the value of minus one or plus one.

## Graphical Representation

In a graphical illustration, each combination is represented as a point in a corner of a cube.

One dimension of the cube shows the colour, the second shows the memory size and the third the delivery time.

The next step in a conjoint analysis is to ask the person for a ranking of the possible combinations, for example, to give 1 for the most preferred combination going down to 8 for the least preferred combination.

Then we use a simple linear model function to describe the ranking and to find the part-worth utilities.

The ranking is expressed as part of attribute one, color, multiplied by the level for attribute one minus one or plus one, plus the part-worth of attribute two multiplied by the level for attribute two, plus part-worth of attribute three, multiplied by level for attribute three, plus a constant.

As a mathematical equation is shown here where better are the part-worth utilities. Now we can set up a system of linear equations using the coded combinations and the ranking for each combination given by the person.

This system of linear equations gets a solution with a multi valiant linear regression. For our simple example here we calculate the part-worth utilities in the following way.

### Further

To find the main effect for attribute one, the color, we take the average ranking for all model combinations with X 1 equals +1, which means the red color, and subtract the average ranking for all combinations with X 1 equals -1, that means green color.

In our cube, it corresponds to the sum of ranking values for all points on the right side of the vertical plane minus the sum of ranking values of all points on the left side of the vertical plane.

We divide by 4 as we take the average of 4 points each and set it concerning the total variation of the X value from minus one to plus one so we divide by 2.

As a result, we get a part-worth utility for the colour of -0.5. In the same way, we proceed for the other 2 dimensions.

As a result, we get the wanted part-worth utilities for color, memory, and delivery time. The ranking calculated with the model function fits exactly the actual ranking. To calculate the relative preference for each attribute we have to look at the total range of variations for our level equals to -1 and +1 which is 7 in our example.

So for the attribute color, we get a relative preference of 1 over 7 or 14 percent. For memory, 4 over 7 of 57 percent and for delivery time 2 over 7 or 29 percent.

## Uses of the Conjoint Analysis

Since the development of Conjoint Analysis in the 1970s, it was a bridge between psychology and mathematics. Few of its many uses are,

### Product Testing

Decision-based conjoint analysis is generally for testing the intrigue of items and services.

For instance, a new drink, a new cabin in an aeroplane, or another public transport system(hyperloop).

Hence, by introducing the different characteristics of the other options, it urges individuals to think through the trade-offs. We get a more profound comprehension of why individuals make decisions.

### Understanding Psychology

The decision-based conjoint analysis is used to recognize which traits individuals see as being generally significant, which is helpful to know for knowing what the buyers are looking for and companies can optimize their products and services likewise.

## Conclusion

After over half a century of it, development of this decision-making tool is still widely relevant.

To conclude, conjoint Analysis has linked two completely different streams of science, Psychology, and Mathematics, and helped marketers and companies a lot in placing their products and services more accurately.

Also You can read our blog on Recognition Primed Decision (RPD)-For complex situations

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