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Binary response data arise naturally in applications. In general, the well-
known logistic and probit regression models form the basis for analyzing binary data
in practice. These regression models make use of symmetric link functions (logit and
probit links). However, many authors have emphasized the need of asymmetric links in
modeling binary response data. In this paper, we consider a broad class of parametric
link functions that contains as special cases both symmetric as well as asymmetric
links. Furthermore, this class of links is quite flexible and simple, and may be an
interesting alternative to the usual regression models for binary data. We consider a
frequentist approach to perform inferences, and the maximum likelihood method is
employed to estimate the model parameters. We also propose residuals for the link
models to assess departures from model assumptions as well as to detect outlying
observations. Additionally, the local influence method is discussed, and the normal
curvatures for studying local influence are derived under two specific perturbation
schemes. Finally, an application to the coca leaf cultivation in Peru is considered to
show the usefulness of the proposed link models in practice.