Is there a generalized linear mixed-effects model implementation for R that could handle misclassified binary data? Unless I have overlooked something in the documentation, glmer with family=binomial(link="probit") does not handle misclassification. Closest to what I have found was misclass, which implements Hausman et al. 1998, in an old McSpatial package version 1.1.1, but it is no longer available.

The more I think about this, the stranger it seems that there is no obvious solution to overcome noisy binary data. In reality, the data are often noisy so that the probabilities don't approach 1.0, but something like 0.8. There is also the remote possibility that I have misunderstood something

Here's a nice presentation of the problem and a solution using a Bayesian model:

Suggestions for other software packages or approaches are welcome, too.

Hausman, J. A., Abrevaya, J., & Scott-Morton, F. M. (1998). Misclassification of the dependent variable in a discrete-response setting. Journal of Econometrics, 87(2), 239-269.