Logistic regression with covariate-dependent probability of misclassification

We propose a model that generalizes the logistic model with misclassification in the outcome. While the previous model assumed constant probabilities of false positivity and false negativity of the observed outcome, in our model one of these probabilities can be covariate-dependent. Our model can be applied in cases where the presence of a feature depends on some covariates and its detection probability (given it is present) depends on other covariates. It may also have applications in social science studies where respondents are reluctant to answer honestly some sensitive survey questions, and the degree of honesty depends on certain covariates. In such cases, the model makes it possible to simultaneously estimate the dependence of the true response on independent variables and the degree of response distortion conditional on its covariates. Sub-models of the proposed model are tested using likelihood ratio tests. We illustrate the properties of the model through simulations and applications to real data.