Short answer: Yes, it is entirely possible. There are a lot of formal models in psychology, and some of it has been fairly successful. I would recommend you to check out SUSTAIN, ALCOVE, EXIT, CAL.
Also note that it is currently unclear what you mean by formal computational models. I assume that you mean: A formal computational model unambiguously describes how the independent variable(s) is translated by different psychological processes into the dependent variable(s). This would probably exclude statistical models, regardless of how insightful they are. For example, there are attempts to use random sampling to capture some results concerning recall memory and some irrational biases (Costello and Watts, 2019). They are statistical models and what they claim is that people literally randomly sample from stored information, even though that there is no direct evidence for it.
Long answer: In principle, it is possible. In reality, it is incredibly hard.
For example, a problem with your question is that it is unclear what you are trying to model. Reading articles and retaining information from said article is a hard problem, and currently there isn't even a formal theory of language processing that could do it. For now let as assume that this is nonetheless the problem you are facing, even though you should probably also develop some tests to see what they remembered (e.g. recognition task, recall tasks).
Even when we assume this scenario and we only want to model this scenario, there are way too many questions we have to deal with, and the first should be what input is available to the model. Also, people don't remember every word from the article, and they compress what they read into simpler sets of information. These are very hard problems, as they might remember some sentences verbatim but nothing else, even though they remember what the article was about. It is also possible that what words people remember will be moderated by syntax. If that is the case, is it also true for non-native speakers? These are all governed by psychological processes that you need to specify in the model. Also, the concepts that underlie words can vary tremendously between individuals: how do you represent it in the model and how do you know what are the concept that you need to represent in the model?
These questions all come up regarding trying to model and most of it should be addressed experimentally. In fact, it has been argued that the problem of modelling is intractable (Rich, de Haan, Wareham and van Rooij, 2021) - which simply put means that finding the right theory/model is so hard that even if every atom in the universe would be a computer, we would still likely not be able to find that model.
I would recommend these readings here:
Guest, O., & Martin, A. E. (2021). How Computational Modeling Can Force Theory Building in Psychological Science. Perspectives on Psychological Science. https://doi.org/10.1177/1745691620970585
Pitt, M. A., Kim, W., Navarro, D. J., & Myung, J. I. (2006). Global model analysis by parameter space partitioning. Psychological Review, 113(1), 57.
Wills, A. J., & Pothos, E. M. (2012). On the adequacy of current empirical evaluations of formal models of categorization. Psychological bulletin, 138(1), 102.
Jones, M., & Love, B. C. (2011). Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behavioral and brain sciences, 34(4), 169.
Rich, P., de Haan, R., Wareham, T., & van Rooij, I. (2021, April 23). How hard is cognitive science?. https://doi.org/10.31234/osf.io/k79nv