Misclassification means the observed category is different from the underlying one and it is a form of measurement error in categorical data. The measurement error in continuous, especially normally distributed, data is well known and studied in the literature. But the misclassification in a binary outcome variable has not yet drawn much attention in psychology. In this study, we show through a Monte Carlo simulation study that there are non-ignorable biases in parameter estimates if the misclassification is ignored. To deal with the influence of misclassification, we introduce a model with false positive and false negative misclassification parameters. Such a model can not only estimate the underlying association between the dependent and the independent variables but also provide the information on the extent of misclassification. To estimate the model, the maximum likelihood estimation method based on a Newton-type algorithm is utilized. Simulation studies are conducted to evaluate the performance and a real data example is used to demonstrate the usefulness of the new model. An R package is also developed to aid the application of the model. [This paper was published in "Behaviormetrika" v44 n2 p447-476 2017.]