Flexible Multi-Index Binary Choice Models

This paper develops a flexible class of binary choice models that relaxes the single-index restriction underlying standard logit and probit specifications. The proposed framework allows multiple component-specific indices to jointly determine the probability of success through a multiplicative structure, accommodating both probit and logit link functions while retaining analytical tractability. We characterise marginal effects and relative marginal effects within this framework and show that, unlike standard single-index models where relative marginal effects are fixed by parameter ratios, the proposed specification allows them to vary with the covariates. This structure gives rise to flexible marginal responses and endogenous interaction effects without requiring explicit interaction terms. The model also admits a useful logarithmic representation that connects it to a structured and interpretable approximation of unknown choice probability functions, analogous to a restricted neural network. Despite its added flexibility, the model can be estimated using standard maximum likelihood methods. Overall, the framework provides a tractable and interpretable extension of conventional binary choice models that captures more complex behavioural responses while preserving the empirical appeal of logit and probit approaches.