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Site occupancy models have been developed that allow for imperfect species detection or \"false negative\" observations. Such models have become widely adopted in surveys of many taxa. The most fundamental assumption underlying these models is that \"false positive\" errors are not possible. That is, one cannot detect a species where it does not occur. However, such errors are possible in many sampling situations for a number of reasons, and even low false positive error rates can induce extreme bias in estimates of site occupancy when they are not accounted for. In this paper, we develop a model for site occupancy that allows for both false negative and false positive error rates. This model can be represented as a two-component finite mixture model and can be easily fitted using freely available software. We provide an analysis of avian survey data using the proposed model and present results of a brief simulation study evaluating the performance of the maximum-likelihood estimator and the naive estimator in the presence of false positive errors.

For assessing the precision of measurement systems that classify items dichotomically with the possibility of repeated ratings, the maximum likelihood method is commonly used to evaluate misclassification probabilities. However, a computationally simpler and more intuitive approach is the method of simple majority. In this approach, each item is labelled as conforming if the majority of repeated classification outcomes are conforming. A previous study has indicated that this technique yields estimators that have a lower mean squared error than but the same asymptotic properties as the corresponding maximum likelihood estimators. However, there are circumstances in which the use of measurement systems with a wider scale of responses is necessary. In this paper, we propose estimators based on simple majority results for evaluating the classification errors of measurement systems that rate items in a trichotomous domain. We investigate their properties and compare their performance with that of maximum likelihood estimators. We focus on the context in which the true quality states of the objects cannot be determined. The simple majority procedure is modelled using a mixture of three multinomial distributions. The proposed estimators are shown to be a competitive alternative because they offer closed-form expressions and demonstrate a performance similar to that of maximum likelihood estimators.

Classification error can lead to substantial biases in the estimation of gross flows from longitudinal data. We propose a method to adjust flow estimates for bias, based on fitting separate multinomial logistic models to the true state transition probabilities using values of auxiliary variables. Our approach has the advantages that it does not require external information on misclassification rates, it permits the identification of factors that are related to misclassification and true transitions and it does not assume independence between classification errors at successive points in time. Constraining the prediction of the stocks to agree with the observed stocks protects against model misspecification. We apply the approach to data on women from the Panel Study of Income Dynamics with three categories of labour force status. The model fitted is shown to have interpretable coefficient estimates and to provide a good fit. Simulation results indicate good performance of the model in predicting the true flows and robustness against departures from the model postulated.