Computational versus Linear Modeling
Elijah Galvan
September 1, 2023
7 min read
So why use computational modeling at all? After all, many researchers in the general field of psychology have gotten along quite well using linear modeling techniques to answer their research questions: what is the upside in doing something more complex and (as we will see) much more prone to user error?
Computational Models Generate Hypotheses
Computational Models generate specific, a priori predictions about how people will behave in a given situation.
Linear Models describe changes in dependent variables in terms of independant variables.
We create computational models to generate predictions: a numeric value for every decision in every trial for every person. In other words, computational models have ultra-specific task-relevant hypotheses which map onto the more abstract hypotheses we generated after our research question.
Computational Models Test the Data Generation Process
Adopting a Computational Modeling approach demands that we formulate and test our speculations about the data generation process - the psychological mechanisms underlying behavior. Thus, we take our hypotheses and think hard about what specific predictions that they would make on a given trial, what computations would underlie this behavioral outcome, and then we try to formulate an equation that generates these predictions. Thus, when we compare models what we are doing is determining which of the models best approximates the data generation process. Naturally, in this regard Linear Modeling does not compare: not only are these descriptive models but they take for granted that the data generation process is linear unless it so obviously not linear that you have to apply a transformation to help the model fit the data better.
Individual Differences
In linear mixed effects modeling, individual differences are treated as a nuisance: random effects for the intercept and conditions varied within individuals are accounted for in order to the give better signal to the fixed effects of interest. Computational modeling differs in comparison in terms of how individual differences are accounted for and what it enables us to do with further analyses. In computational models, individual differences are captured in free parameters: these are (generally) meaningful psychological dimensions which relate how the data generation process differs between people. As such, we can explicitly test to determine whether or not people are significantly different in the context of our experiment and we can do things such as relate these free parameters to other psychological constructs or brain data (for instance via Intersubject Representational Similarity Analysis (IS-RSA): https://naturalistic-data.org/content/Intersubject_RSA.html). Thus, it is an informative and intuitive way to reduce the complexity of high-dimensional datasets: you can go from say a hundred trials of raw behavioral data and arrive at a few (think 1 to 3) numbers that meaningfully characterize your subject.
User-Defined Process
Functionally, you need to install one package for parameter recovery but, apart from that, every line of code that determines the result of the analysis can and should be written by the researcher and should reflect:
Computational logic
Relevant theory
Other extant knowledge
As such, the researcher will be able to justify every choice that they have made and have much clearer insights regarding what their results actually tell them. This enables us to also empirically test questions that are simply out of the reach of linear modeling.
Potential Pitfalls
Computational modeling demands correctly accounting for all possible psychological accounts for how people can solve a certain problem and correct mathematical representation. Thus, the same flexibility that this technique offers can also serve to render wrong or uninterpretable results when the researcher does not observe (what should be) commonsense statistical and philosophical principles. It also requires creativity and higher level reasoning - unlike Linear Modeling - where there are right and wrong answers, with Computational Modeling two people can correctly arrive at different answers.