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Zero-inflated count data models are widely used in various fields such as ecology, epidemiology, and transportation, where count data with a large proportion of zeros is prevalent. Despite their widespread use, their theoretical properties have not been extensively studied. This study aims to investigate the impact of ignoring heterogeneity in event count intensity and susceptibility probability on zero-inflated count data analysis within the zero-inflated Poisson framework. To address this issue, we propose a novel conditional likelihood approach that uses positive count data only to estimate event count intensity parameters and develop a consistent estimator for estimating the average susceptibility probability. Our approach is compared with the maximum likelihood approach, and we demonstrate our findings through a comprehensive simulation study and real data analysis. The results can also be extended to zero-inflated binomial and geometric models with similar conclusions. These findings contribute to the understanding of the theoretical properties of zero-inflated count data models and provide a practical approach to handling heterogeneity in such models. [ABSTRACT FROM AUTHOR]

Spatial or temporal clustering commonly arises in various biological and ecological applications, for example, species or communities may cluster in groups. In this paper, we develop a new clustered occurrence data model where presence–absence data are modeled under a multivariate negative binomial framework. We account for spatial or temporal clustering by introducing a community parameter in the model that controls the strength of dependence between observations thereby enhancing the estimation of the mean and dispersion parameters. We provide conditions to show the existence of maximum likelihood estimates when cluster sizes are homogeneous and equal to 2 or 3 and consider a composite likelihood approach that allows for additional robustness and flexibility in fitting for clustered occurrence data. The proposed method is evaluated in a simulation study and demonstrated using forest plot data from the Center for Tropical Forest Science. Finally, we present several examples using multiple visit occupancy data to illustrate the difference between the proposed model and those of N‐mixture models. [ABSTRACT FROM AUTHOR]

In capture{recapture experiments, covariates collected on individuals, such as body weight and length, are often measured imprecisely or are missing at random. Furthermore, the number of recorded covariate measurements collected on each observed individual is usually equal to or less than the individual's capture frequency. Correcting for multiple error-prone covariates is seldom seen in capture{ recapture models and even fewer researchers have considered cases where individ- ual's have no measurements at all. In this paper, we develop an unbiased estimating equation using the conditional score within the capture{recapture framework. We then extend this approach to simultaneously account for both measurement error and missing data using two well-known missing data methods: (1) inverse proba- bility weighting; and (2) multiple imputation. These new methods are shown to yield consistent and asymptotically normal estimators, and the two approaches are shown to be asymptotically equivalent. We evaluated these methods on simulated and real capture{recapture data. Our results show improvements in both precision and efficiency when using the proposed methods. [ABSTRACT FROM AUTHOR]