We develop a least squares regression theory for the empirical study of models of preference and individual decision-making. Our approach utilizes common invariance properties of various models to obtain cardinal measurements of preference intensity. Our theory is widely applicable, and provides richer, more granular insights into the drivers of a model’s predictive success or failure than traditional revealed preference methods, while simultaneously remaining computationally simple. We illustrate our methodology on common models of preferences over consumption bundles, dated rewards, lotteries, consumption streams, and Anscombe-Aumann acts.