Going one better

Editor's note: Steve Cohen is partner and co-founder of in4mation insights.

For many of us, daily life has changed beyond all expectation during the pandemic. Consumers are finding that they need to reassess their spending in response to changes in personal circumstances and the rising cost of goods. There's greater focus on the way we budget and get the most for our money. By necessity, we make trade-offs that drive our buying behavior in a search for greater value. 

Of course, it's not just price that affects what we purchase. Many factors influence consumer behavior and the way we budget. As researchers, how can we help our clients optimize the value that a consumer places on a product or service? How do we help steer their innovation and product strategies so that they can prioritize the features and options offered in products and price them accordingly?

There are tried-and-true research methodologies that have enabled analysts to yield highly impactful results for years. But one size does not fit all. There are new tools and technologies that improve upon standard choice models and if we aren’t leveraging the new tools to our advantage, if we aren’t building on existing tools with new thinking, are we not missing the opportunity to do better? To know more? To create greater value for our customers and our companies?

How do people make decisions?

To start with, let's consider how people make decisions. If you gave someone three or four different purchase options, with varied features and prices, we could assume they would go through some mental math to evaluate each of the choice alternatives. As noted above, we're expecting them to make trade-offs between the benefits that the features offer and the price that must be paid. Marketing scientists use this principle to work out what the most probable choice would be for each item in a set of alternatives.

Choice models have been a very important tool in market research for the past 40 years. I built my reputation on the use of choice-based conjoint (CBC) and I am proud that my pioneering work on CBC, including introducing MaxDiff and menu-based conjoint, has been recognized by the American Marketing Association, the Institute of Management Science and the Market Research Council as being worthy of lifetime achievement awards. 

Too often we see CBC deployed at a very basic level by less-savvy practitioners using software tools that enable programming of complex studies with only the most simplistic understanding of the assumptions and math of the analytic tools and how to interpret the results in a reliable, predictive way. I caution against relying on an analyst whose only training in CBC was to “read the manual.”

For those unfamiliar with CBC, at its most basic level respondents express their preferences by choosing a product from a set of alternatives, rather than by rating or ranking them.

We identify how respondents value different features by asking them to compare several options and to select the one that they prefer most. These product profiles are generally limited to sets of a few alternatives, so as to not overwhelm or confuse respondents with a larger number of options.

In essence, we're asking people to choose a product by comparing – or trading off – the features and benefits of a small range of products that are relative substitutes for each other. More on this in a moment.

By exposing enough of the product options to a large enough sample of people, we can apply complex math to reveal an optimal path for product development and pricing strategies that a brand should pursue.

How to understand a multinomial logit model

The standard multinomial logit (MNL) model at the core of choice modelling is simple in theory but the math behind it is a bit complicated if you're not a data scientist. Let’s examine this equation.

This is the formula used in the standard multinomial logit model, the workhorse model of choice. To put it in words, the probability (Pr) of choosing item i from set of items S is equal to the result of a fraction. B_i is the weight that is placed on the product features X_i. We assume that the features offer benefits to the chooser and each feature has its own positive weight or importance (B_i).

Counterbalancing the feature’s benefits is the disutility or price penalty that must be paid to gain those benefits, shown as B_pP_i. To complete the fraction, two additional operations must be executed.

In the numerator of the fraction, we calculate the benefits minus the disutility, as shown in parentheses, and then it is exponentiated as exp (). We perform the same calculation for all items in set S, subtracting the disutility from the benefits, exponentiating each of these and then taking their sum.

In short, multinomial logit is a share of preference model that tells us, for each person and for each item in the set, how they would allocate their “choice shares” across the alternatives that they can pick from.

In practice we're putting a value to the trade-offs between something a consumer really likes, such as more features or better performance, and the price they are prepared to pay.

How to get more stable results

The standard multinomial logit model (MNL) has its limits. For starters, people only choose one thing from a small set of choice alternatives. This provides the analyst with some basic information but it’s not enough to generate stable results for each person. To get more stable results, we must ask repeated questions in CBC so that we see how people respond under different offerings and conditions. This gives us more information from each person and is more likely to get good results.

As stated earlier, a major assumption behind CBC is that the offerings shown are relative substitutes for one another. This works well when the choice alternatives are similarly featured and similarly priced. However, in some situations we may want to compare choice alternatives that differ greatly by price or other factors. For example, the prices of different iPhones are very different, with more expensive phones being two or three times the price of less expensive phones. Similarly, many CPG products come in different sizes. A large container of laundry detergent may cost three to four times as much as the small size.

If you wish to investigate the choice between two different sizes, how should price be treated in an analytic model? Let’s say that a six-pack of beer costs $10 and a 30-pack costs $25. If we ask beer buyers which they would choose and we use the actual prices, then, all else equal, people should choose the six-pack because $10 is less than $25. However, if we were to show the cost per liquid volume, then the 30-pack is a better choice because its cost per volume is less than the six-pack.

But what if the buyer doesn't have $25 to spend on beer or didn’t want to spend $25 because it’s beyond their budget? Now we're in a situation that standard MNL cannot handle. It can't understand or quantify the fact that the buyer is constrained because they're unable or unwilling to spend $25 for the case. So why are people not buying the $25 case? Is it that they don’t want to spend that much money or that they don’t want that much beer? Perhaps they don’t have enough room to store a case of beer or can't carry it home. It’s impossible to tell with standard tools.

In other words, the budget is one of several constraints on purchasing that is not considered in choice modeling – that is, until now. 

Incorporating constraints into the equation

If we are going to take the standard multinomial logit model and make it more effective in choice modelling, what exactly does it mean to incorporate constraints like a budget into the equation? Why is that important?

At a basic level, we look at our income and expenditures and we apportion what we have accordingly to cover our living costs. But a money budget is just one of many constraints that have an impact on what we buy. Other constraints include product availability, the time it takes to purchase and receive an item, whether I'd pay to ship a product that is heavy versus carry it home from the store, how much storage space I have for buying bulk-priced options (as in our example above), the calories, sugar or gluten content and if it is a novel or a repeating purchase.

In short, people make choices under constraints. This is a fundamental tenet of human behavior.

A budget can be impacted by more than strictly the consumer’s available discretionary income. As behavioral economics instructs us, the occasion or context can also influence a purchase. Picking up a quick-service dinner for the family on a work night may include a budget consideration. Buying the food and beverages for your eight-year-old’s birthday party introduces a budget consideration that is totally different.

As shown above, the traditional MNL model investigates the trade-off between benefits and price and quantifies the extent of price sensitivity. The downside of this approach is that, even if you were to raise the price of a product to astronomical levels, this standard approach predicts that someone, even if it’s a very small percent of people, will still purchase this very expensive item. A very unlikely event indeed.

In contrast, a new CBC approach estimates an individual-specific constraint, in this case a money budget. This constraint assumes that each person has a fixed budget for their purchases. If a purchase option costs more than their budget, the consumer will just not buy the product. Each person’s budget is estimated through some statistical magic and is part of the modeling output. 

With each person’s budget in place, the price-demand curve is much steeper because when each person’s budget is surpassed, they drop out of the market. The graph in Figure 1 illustrates this.

It is taken from a prior analysis that we did concerning the purchase of digital cameras. The range of prices shown to consumers went from $199 (lowest price) to $499 (highest price). The green line represents the price-demand relationship that the standard MNL model produced. The orange line is the equivalent relationship from a constrained hierarchical Bayesian discrete choice model (CHBDCM).

In this graph, note that, as the price of Brand N increases (shown on the x-axis), the standard MNL model has a nice, smooth-sloping line of choice shares, while the budget model is much steeper. Essentially, we see that people are likely to drop out of the market as the price is increased and their budget limit is exceeded.

To show more dramatically what happens when the budget is exceeded, at the highest price tested, the standard MNL model predicts 2.5x the share of choices (about 26%) than does the budget model (about 10%).

Further, note the location of the lines in the lower-right portion of the graph at a price of $1,000, which is double the highest price tested. The standard MNL still predicts that about 10% of people will buy at that high price, while the budget model predicts no one (0%) will do so.

In short, the budget choice model yields more plausible price-demand relationships than does standard MNL, which will typically suggest higher prices than are likely to be accepted by consumers.

Our work with the new budget-constrained choice model has been exciting. CHBDCM can provide a superior fit to the raw choice data compared to results from a standard MNL choice model. It has lower estimation error. It also identifies which people have lower and higher budgets and higher and lower price sensitivity.

The benefit of budget

Over the years, skilled analysts have noticed that standard MNL produces estimates of price sensitivity that are too large. The budget-constrained choice model produces price sensitivity estimates that are smaller (less negative) than MNL and less variable than MNL.

This concept of “budget” brings real benefit in the new world that we're in. This is particularly useful for certain fast-moving consumer goods or more expensive items that we typically budget for – liquor, durables and luxury goods, etc. It can reveal more realistic variations across people and budgets.

The budget model enables us to do something that the standard multinomial logit model cannot. In the hands of skilled partners who understand the math and science, it can uncover constraints on purchasing, including a money budget, in all its beautiful complexity, from the sole criteria of price sensitivity, giving us more sophisticated insight into the why behind the what as well as the how. 

Identify new microsegments

By adding in the consideration of the budget in CBC, you get more than just price sensitivity. You get insight into the power of the brand and factors beyond price that influence what consumers are more likely to buy. Done right, you can even identify new microsegments to which you can advertise your products and build new streams of revenue. 

Newer discrete choice models are emerging that reflect the realities of consumers’ lives. The predictions that result from their application are much more effective for brands trying to make decisions about features and benefits to add into products and what the price tolerance will be for consumers who will buy them. 

If you are not challenging your research partners to embrace more sophisticated choice models, you are likely to miss the rich insights that can refine your pricing and product development most effectively. We see “budget” in its broadest sense as a vital part of a new and nuanced mathematical approach to choice modelling and right now that's not something that is built into standard approaches.