where I is investment expense/cost,

where I is investment expense/cost, X(s) are exploratory variables, α, β and γ are coefficients, and ε is the error term for firm i. Then, without losing any information, one can always write the “binary” version of the above model with investment expense/cost now being an exploratory variable, as:
Pðϕ ¼ 1Þ ¼ f ðα′ þ β′X1i þ γ′X2i þ θIi þ ψiÞ; ð2Þ
where α′, β′, γ′ and θ are the coefficient, and ψ is the error term.