In this two-part article series we present a framework for understanding the role of models in science, and show how it can help to sharpen our understanding of models in marketing research.
Part 1 presents a definition of a “good” scientific model, with applications to brand loyalty models in marketing.
Part 2 makes the case for the value of “multi-model thinking” in marketing research.
“All models are wrong, but some are useful.”
The renowned statistician George Box (1919-2013) famously asserted that “all models are wrong, but some are useful.”[1] The expression has become an aphorism in statistics, and is widely viewed as asserting an important truth about the role of models in scientific reasoning. However,there’s continuing debate over how to best characterize that truth, and what it implies for the nature of science.
The framework that we present here expands on George Box’s approach of treating models as tools for reasoning about the world.
Models as tools for reasoning about the world
Models are used in many ways in science: predicting system behavior, testing hypotheses, making an idea precise, exploring logical possibilities, etc.
When used as tools for reasoning about some domain of reality—the “target system”— models are treated as abstract representations of the target system. We construct models so that there are relevant structural similarities between the model and the target system. These structural similarities allow us to reason with the model’s features and then draw inferences about corresponding features of the real-world target system—a form of reasoning by analogy.
A good model of a target system allows us to give useful answers to interesting questions about the target system. “Good” is always relative to the context of usage and the specific questions we want answered.
Case study: maps as models
To illustrate these principles it’s helpful to think of maps as prototypical models, and how we reason with maps to answer questions about the terrain they represent.
Figure 1: Different maps for different purposes. (Left) Aeronautical weather map. (Center) Road map. (Right) Orienteering map.
In Figure 1:
- The map on the left is an aeronautical map with information about high- and low-pressure areas, wind direction, and areas of rain
- The map in the middle is a road map with information about spatial relationships between place locations along traffic routes
- The map on the right is an orienteering map that identifies topographical objects such as rivers, rock outcroppings, and land elevation
All three maps abstract from reality—they only show the portions of reality that are of interest to the map user. The pilot can identify areas of high and low pressure. The driver can locate roads leading to a family’s destination. The orienteer can locate terrain features as directions to some designated endpoint.
Abstraction and simplification are essential to modelling in science. One needs to simplify reality to focus attention on those parts of the world which are most relevant to our concerns. A street map of a city is designed to answer questions about how to identify and navigate between different spatial locations across the city. It doesn’t represent all the city’s features—there are no buildings, sidewalks, gas lines or sewer networks on the map. This isbecause those features aren’t why a street map is intended.
A street map is “wrong” in the sense that it gives an incomplete description of the target domain (most features of the city aren’t in the map) and often rely on idealizations of the features they do represent (e.g. with the widths of streets are not represented). But it’sthis very incompleteness and idealization that makes a street map useful—that makes it a good street map.
The point is true for models in general. All models are wrong in the sense of being abstract, incomplete and idealized representations of the world. But it is precisely these features of abstraction, incompleteness and idealization that make a model useful as a representation of the world. When a scientific model is good,it’s good in virtue of these features, not in spite of them.
What is a good model?
Within this framework the concept of a “good model” is analysed in terms of the quality and utility of the answers that it enables, relative to questions of interest. It makes no sense to ask of a model whether it is true or false, accurate or inaccurate, good or bad, without specifying the intended domain of applicability and the inquiry’s context.
A street map can be a very good model for purposes of navigation through a city, but a very bad model for purposes of diagnosing a power grid failure.
Put another way, the “modeling relation” in science is actually a three-way relation between the:
- model system
- target system under consideration
- users of the model within a particular context of inquiry
It is the third leg of this relation, the human context of inquiry, that specifies the criteria for success or failure of a model.
A simple model of consumer behavior
Quantitative marketing research models come in various forms—conjoint, regression, structural equations, etc.—and are all useful within varying domains of applicability.
A simple “brand loyalty” model, for instance, can be a multiple regression equation that relates a measure of brand loyalty Y (e.g. “intention to purchase from a given brand in the future”) to a set of stipulated predictors of brand loyalty Xi—perceived brand quality, perceived brand price competitiveness, etc.
Y = a + b1X1 + b2X2 + … + bnXn + error
Estimates for Xi and Y can be derived from survey data. The size of the bi coefficients represents the relative influence of each variable Xi on the dependent variable Y—the larger the bi the greater the influence.
The resulting equation is a model of the factors that influence brand loyalty, allowing us to ask questions and reason about this domain. If it turns out that perceived brand quality is the largest factor, we can infer that (holding all other factors constant) improving a brand’s perceived quality will have the largest positive impact on this measure of brand loyalty.
This simple model strips away nearly all of the complex reality of consumer behavior, and is an incomplete description of the factors that can influence brand loyalty. But these facts don’t make it a bad model. On the contrary, if the model proves to be useful it is precisely because it offers a simplified, incomplete, idealized representation of consumer behavior.
[1] Box, George, E. P. 1976. Science and Statistics. Journal of the American Statistical Association, Vol. 71, No. 356. pp. 791-799. https://www.jstor.org/stable/2286841.
