  This paper considers the problem of mismeasured categorical covariates in the
context of regression modeling; if unaccounted for, such misclassification is
known to result in misestimation of model parameters. Here, we exploit the fact
that explicitly modeling covariate misclassification leads to a mixture
representation. Assuming common parametric families for the mixture components,
and assuming that the misclassification occurrence is independent of the
response variable, the mixture representation permits model parameters to be
identified even when misclassification probabilities are unknown. Previous
approaches to covariate misclassification use multiple surrogate covariates
and/or validation data on the magnitude of errors. Based on this mixture
structure, we demonstrate that valid inference can be performed on all the
parameters even when no such additional information is available. Using
Bayesian inference, the method allows for learning from data combined with
external information on the magnitude of errors when such information does
become available. The method is applied to adjust for misclassification on
self-reported cocaine use in the Longitudinal Studies of HIV-Associated Lung
Infections and Complications (Lung HIV). We find a substantial and
statistically significant effect of cocaine use on pulmonary complications
measured by the relative area of emphysema, whereas a regression that does not
adjust for misclassification yields a much smaller estimate.
