So the last application we're going to talk about for conjoint analysis is propensity modeling. What does that mean? It really means predicting either the market share of an individual product or the probability that an individual will buy the product, given certain specified attributes of that product. Now what I have in front of me is a big ugly formula that's called a logit model. Now what is this thing? This is actually the model that conjoint analysis estimates in order to get the utilities that you saw in the output from conjoint. Now, you're never really going to have to estimate a multinomial logit model. This will be done by the software. But because the software estimates this kind of model, it means that we can take the estimated utilities and plug it back into this model in order to get those market share forecasts or those probabilities. Now, while this looks ugly, I bet you've all seen parts of this before. In particular, this e that's sitting right here. You probably saw that in high school. That's the base of the natural logarithm. You can find e on your calculator. It's 2.7 something. And that's literally what it is in this model. So your calculator can handle this. But it's e raised to the power of a particular utility. And what is this utility sitting up here in the exponent? Well, it's the utility of the product that you're trying to project. So, in this case, we're trying to project the propensity to buy or the market share of some product called i. And i is just the product specified by the different levels of the different attributes, right? And we'll do an example of this in just a minute. What's in the denominator? The denominator is all the competitive products for product i, including product i itself, okay? So, the use of j is are all the different products that you might think would compete with i in any particular competitive space. I think this is best thought of if we go through an example of it. When you get the utility, what that will do is it'll spit out a number. And that number will between 0 and 1, so this Si will be between 0 and 1. And that will take you to the market share or the forecasted probability. Now, what we can do is just take a golf ball example. And kind of see what that implies given the more abstract material that I showed you. Well, suppose we have two golf balls. One is the High-Flyer, it goes 10 yards further and is $8.99 a pack. The total utility of that is .60. Then we have the Eclipse, 5 yards further and -.08. That is the utility associated with $8.99 per pack, so it's the same price. But the overall utility of that is -.94. Now, does it mean that most people prefer the High-Flyer, this particular product? Yes, it does. But it doesn't mean that they're going to get a 100% of the market. In fact, we can use that logit model. And this is all done automatically in the software. But I want you to know what software is capable of doing in this space. We can take these overall utilities of this product, the software will then plug them back into the logit model. And if I ask, well, what market share will this less desirable product probably get, if we were competing in the market with that product? It's not going to get to zero, because some people are going to prefer it, all right? So what would it get? By plugging this utility back into the logit model, and then dividing it by e to that same utility, plus e to the utility of the competitive product, you get .18. So on average, we would imagine that this would get 18% market share. Or stated in other way, if I took a random person from the population that might buy it, there'll be about 18% chance that that individual would prefer this least desirable product in the space. So that's really what's going on. Now, of course, you can do this at the individual level, as well. These are all utilities. So, for any product combination, I could take these utilities, construct products, plug it back into the logit model and specify the probabilities that each individual would buy whatever product that we want to specify, again, all done in the software. Now, can you do this all the time? All the different things I've done up to this point, you can do in most circumstances with conjoint analysis output. This is a little bit different. We're now doing demand forecasting, and it comes with a certain set of assumptions. What are those? Well, it first of all, assume that you know who your competitors are and it's a stable set of competitors. You have to know who to put in the denominator. If you don't know who you are competing against, or you've not measured the utility for the selling attributes of your competitor, you can't use that kind of forecasting models because you won't know what to plug in the formula. It also assumes that all competitors are evaluated on the same dimensions. So when Singapore Airlines goes and looks at commercial aircraft, they're looking at the Boeing aircraft and the Airbus aircraft, and they're evaluating them on the exact same dimensions. For certain product categories, that's true. For other categories, it may not be true. And if it is not true, then the conjoint analysis will not be able to get the utilities necessary to do the forecasts. And it also assumes, no competitive reaction given the attributes. If you took this model and then said, well, what would happen to my market share if I change price? You could certainly do that. You would change price. Then we could change the utility and look at what the market share reaction would be. But that assumes your competitor does absolutely nothing. In certain markets, that's going to be completely unrealistic. So, I would say in general, this kind of forecasting is better for industries with long product development times where they can't change things very rapidly given maybe certain price and changes that you might make, right? You know what the Airbus aircraft is going to look like, right? They can't change that very rapidly, then these kind of market share forecasts can make sense, but you have to satisfy all of these. So, willingness to pay, you can do in a lot of different situations. Determining what products people prefer and trade offs they're willing to make between attributes, you can do in a lot of situation, market share forecasting more narrow. So recapping, what can we do with this conjoint analysis? We can determine the products people prefer. Look at the trade-offs among the features. We can determine the rank ordering of attributes in terms of importance in the choice process. We can compute willingness-to-pay for design changes. And finally, we can do Propensity Modeling. Now, I have come to the end conjoint analysis and we have gone a long way with conjoint analysis. I hope you understand what conjoint analysis is capable of doing. And recognize that in a lot of pricing situations, doing a conjoint analysis on your product, if it fits, if it has attributes, can really be a valuable tool in you setting price. I would also caution that there are a lot of technical aspects to doing a conjoint analysis. Determining exactly how many questions to ask individuals. Determining which order the pictures appear on the page. Those kinds of things can matter to the utility estimates that you get out on the other side. So if you got a lot of money on the line, if you're making a big decision relative to product pricing, you might want to seriously consider going to a marketing research firm that has done a lot of conjoint analysis and getting them to help you through this process. But by now, through this material, I hope that you know when to go to the marketing research firm and when this kind of analysis can help you.
