  In empirical science, many variables of interest are categorical. Like any
model, models for categorical responses can be misspecified, leading to
possibly large biases in estimation. One particularly troublesome source of
misspecification is inattentive responding in questionnaires, which is
well-known to jeopardize the validity of structural equation models (SEMs) and
other survey-based analyses. I propose a general estimator that is designed to
be robust to misspecification of models for categorical responses. Unlike
hitherto approaches, the estimator makes no assumption whatsoever on the
degree, magnitude, or type of misspecification. The proposed estimator
generalizes maximum likelihood estimation, is strongly consistent,
asymptotically Gaussian, has the same time complexity as maximum likelihood,
and can be applied to any model for categorical responses. In addition, I
develop a novel test that tests whether a given response can be fitted well by
the assumed model, which allows one to trace back possible sources of
misspecification. I verify the attractive theoretical properties of the
proposed methodology in Monte Carlo experiments, and demonstrate its practical
usefulness in an empirical application on a SEM of personality traits, where I
find compelling evidence for the presence of inattentive responding whose
adverse effects the proposed estimator can withstand, unlike maximum
likelihood.
