  A variety of recent papers discuss the application of Shapley values, a
concept for explaining coalitional games, for feature attribution in machine
learning. However, the correct way to connect a machine learning model to a
coalitional game has been a source of controversy. The two main approaches that
have been proposed differ in the way that they condition on known features,
using either (1) an interventional or (2) an observational conditional
expectation. While previous work has argued that one of the two approaches is
preferable in general, we argue that the choice is application dependent.
Furthermore, we argue that the choice comes down to whether it is desirable to
be true to the model or true to the data. We use linear models to investigate
this choice. After deriving an efficient method for calculating observational
conditional expectation Shapley values for linear models, we investigate how
correlation in simulated data impacts the convergence of observational
conditional expectation Shapley values. Finally, we present two real data
examples that we consider to be representative of possible use cases for
feature attribution -- (1) credit risk modeling and (2) biological discovery.
We show how a different choice of value function performs better in each
scenario, and how possible attributions are impacted by modeling choices.
