Models are studied where the response Y and covariates X, T are assumed to fulfill E(Y ; T) = G{XT ud8 + ubb + m1(T1) + … + md(Td)}. Here G is a known (link) function, ud8 is an unknown parameter, and m1, …, md are unknown functions. In particular, we consider additive binary response models where the response Y is binary. In these models, given X and T, the response Y has a Bernoulli distribution with parameter G{XT ud8 + ubb + m1(T1) + … + md(Td)}. The paper discusses estimation of ud8 and m1, …, md. Procedures are proposed for testing linearity of the additive components m1, …, md. Furthermore, bootstrap uniform confidence intervals for the additive components are introduced. The practical performance of the proposed methods is discussed in simulations and in two economic applications.
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