A growing number of researchers have advocated for the advancement of cognitive neuroscience by blending cognitive models with neurophysiology. The recently proposed joint modeling framework is one way to bridge the gap between the abstractions assumed by cognitive models and the neurophysiology obtained by modern methods in neuroscience. Despite this advancement, the current method for linking the two domains is hindered by the dimensionality of the neural data. In this article, we present a new linking function based on factor analysis that allows joint models to grow linearly in complexity with increases in the number of neural features. The new linking function is then evaluated in two simulation studies. The first simulation study shows how the model parameters can be accurately recovered when there are many neural features, that mimics real-world applications. The second simulation shows how the new linking function can (1) properly recover a representation of the data generating model, even in the case of model misspecification, and (2) outperform the previous linking function in a cross-validation test. We close by applying a model equipped with the new linking function to real-world data from a perceptual decision making task. The model allows us to understand how differences in the model parameters emerge as a function of differences in brain function across speed and accuracy instruction.