In my last post, I explained the defining characteristics of cognitive models and the main steps to developing a cognitive model. In this post, I’ll discuss the advantages of cognitive modeling over alternative approaches to studying human cognition and behavior, and a precaution to be taken about interpreting modeling results. As in my last post, I will illustrate my points in the context of two competing models of human categorization mechanisms. According to the prototype model of categorization, learners abstract and memorize a single summary representation, namely the prototype for each category from all examples already learned in that category. When a new probe item is presented, the similarity of this probe to each category prototype is evaluated, and the category with the most similar prototype is chosen. For example, a prototype-based view on how people categorize a novel-looking pet as a cat or dog would be that the learner first abstracts the mental images of typical dog and cat faces by morphing all the salient features for both types of the pets. Then the learner makes the categorization decision by evaluating the relative similarity of the face of the new pet to the two typical faces. In contrast, the exemplar model of categorization specifies that learned examples from all categories were memorized, and the new probe item is classified into the category whose constituent examples are, in sum, most similar to the probe. So, in the example of dog vs. cat categorization, the exemplar-based view would be that the learner makes the categorization decision by comparing the overall similarity of the new pet face to the individual faces for both dogs and cats one has seen.
The main advantage of quantitative cognitive models over verbal accounts is that, by using mathematical languages, they are guaranteed to produce logically valid predictions. Predictions may often defy or evade our own intuitions. For example, to argue for the superiority of the prototype model over the exemplar model of categorization, prototype theorists often cite evidence from an experimental finding which showed that the category prototypes, even if not explicitly learned by participants, were categorized with higher accuracy than many of the category examples actually learned. Surprisingly, once the exemplar model was mathematically developed and tested, it was shown that this logic was incorrect. The exemplar model could account for a better classification of the prototype. In this case, reasoning from a conceptual framework led to incorrect conclusions regarding how human categorization occurs.
On the other hand, many cognitive models have the advantage of interpretability and generalizability over statistical models. Going back to the example of category learning, a classification algorithm named k-nearest neighbor can well approximate the kind of classification behaviors exemplar models tend to predict, especially when the category examples are fairly discriminable from one another. Although the k-nearest neighbor algorithm can model classification behavior with high accuracy, it operates based on hard-and-fast mathematical rules and tells us nothing about cognitive processes. In contrast, the exemplar model gives a clear psychological interpretation of how the classification decisions arise: namely, by comparing the similarity of a target stimulus to individual examples of each category. The rich details on the cognitive processes explained by the exemplar model facilitates researchers’ ability to derive new predictions that go beyond their original design. For example, researchers have extended this work to account for the psychological phenomenon in which more recently experienced category examples exert more influence on categorization. Importantly, such cognitive complexities pose serious challenges to the predictions made by algorithms such as k-nearest neighbor, but may be easily incorporated into baseline exemplar models.
As much as cognitive modeling is superior to alternative approaches to cognitive research, it is also important to bear in mind that cognitive models by no means provide exact accounts of the cognitive processes underlying the behavior being studied. For the sake of computational convenience, auxiliary assumptions introduced when creating cognitive models are often criticized as being too simplistic to be psychologically realistic. For example, for both exemplar and prototype models, researchers make detailed assumptions about what features should be used to represent the stimuli that are later categorized. In experimental settings, it seems intuitive to simply pick out a small number of salient features designed to be important for classification (e.g. color and size of an object), but when it comes to the classification of real-life objects, the number of potential features that classification decisions can be based on suddenly becomes intractable, and different subjects may shift their attention between different sets of features in a given object at any point of the categorization process. Nevertheless, all models are deliberately constructed to be simple representations that only capture the essentials of the cognitive system. As such, we know that all models are wrong in some details and a sufficient amount of data will always prove that a model is not true. However, the question we need to ask is the following: which model provides a better (or, more accurate) representation of the cognitive system we are trying to represent? For example, we know that the prototype and the exemplar model have their respective limitations, but we are most interested in knowing which of these two models provide a better explanation of how we categorize objects, while keeping our assumptions (such as feature representation) in mind. Given the brain’s complexity, we can only attempt to solve the puzzle of the human mind piece by piece. In the case of categorization research, cognitive modeling can explore how simplistic features can contribute to human category learning–a step that is necessary before we fully understand what and how relevant features are categorized in the real world.
Beyond the realm of cognitive psychology, cognitive modeling has many practical uses in various fields of psychology. To give a few examples, clinical psychologists use cognitive models to assess individual differences in cognitive processing between healthy individuals and clinical patients, cognitive neuroscientists use cognitive models to understand the psychological function of different brain regions, and social psychologists use cognitive models to simulate agent behaviors in the context of social dynamics. On the whole, cognitive modeling plays a vital role in extending and refining our knowledge in all fields of psychology. In order to wield the full potential of cognitive modeling, it is important that psychology students acquire the basic mathematical literacy that is necessary to successfully apply these techniques to their research.