Structural Adoption Model
v1.1
The Structural Adoption Model formalises behavioural uptake as a bounded probability derived from a latent behavioural index. Incentives exhibit diminishing marginal impact through a concave transformation.
Structural Form
Adoption probability is computed by transforming a nonlinear behavioural index through a logistic function.
P(Y = 1 | X) = 1 / (1 + e^{-Z})
Z = β₀ + β₁·log(1 + Incentive) − β₂·Friction + β₃·Default + β₄·Norm
Positive coefficients increase latent adoption propensity. Incentives exhibit diminishing marginal returns.
Assumptions
- • Independent agents
- • Static equilibrium
- • Additive behavioural effects
- • Diminishing marginal impact of incentives
- • Homogeneous population response
Outputs
- • Adoption probability
- • Expected adopters (N × P)
- • Latent behavioural index (Z)