For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

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The multilayer stochastic block model is one of the fundamental models in multilayer networks and is often used to represent multiple types of relations between different individuals. In this paper, we extend the profile‐pseudo likelihood method for the single‐layer stochastic block model to the case of the multilayer stochastic block model. Specifically, by assuming all network layers have identical community membership labels, we investigate the multilayer stochastic block model with a common community structure. In this paper, we develop a profile‐pseudo likelihood algorithm to fit a multilayer stochastic block model and estimate the community label. Meantime, we prove that the algorithm has convergence guarantee and that the estimated community label is strongly consistent. Further, for estimating the number of communities , we extend the corrected Bayesian information criterion to multilayer stochastic block models. We also extend this algorithm to fit the multilayer degree‐corrected stochastic block model. Both simulation studies and real‐world data examples indicate that the proposed method works well.

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