Value-based choice model comparison

To assess evidence for this theoretical model, we compared the following statistical models. As stated in our preregistration, if VB1—which specifies terms for dlPFC and VS to represent subjective value of relevant choice attributes and vmPFC as the value integrator—is the best fitting model and the neural predictors are significantly associated with bid value, we will interpret this as evidence for the value-based choice model. To mirror the model comparison for the dual-process models, we also planned to test whether adding the balance score (dlPFC—VS) to the model (VB2) would improve model fit. However, this model did not converge because the balance score is a linear combination of dlPFC and VS and was therefore inestimable.

First level equations:Base model: Y_ij (Bid value of trial i by person j) = β_0j + β_1j Food Type_ij + ε_ijVB1: Y_ij (Bid value of trial i by person j) = β_0j + β_1j Food Type_ij + β_2jdlPFC_ij + β_3jVS_ij + β_4jvmPFC_ij + ε_ijVB2: Y_ij (Bid value of trial i by person j) = β_0j + β_1j Food Type_ij + β_2jdlPFC_ij + β_3jVS_ij + β_4jvmPFC_ij + β_5j(dlPFC_ij − VS_ij) + ε_ij

Second level equations: β_0j = γ₀₀ + μ_0j β_1j = γ₁₀ (In VB1 and VB2): β_2j = γ₂₀ (In VB1 and VB2): β_3j = γ₃₀ (In VB1 and VB2): β_4j = γ₄₀ (In VB2): β_5j = γ₅₀