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**Identifiability of parameters in longitudinal correlated Poisson and inflated beta regression model with non-ignorable missing mechanism.**
*(English)*
Zbl 1440.62289

Summary: The identifiability of a statistical model is an essential and necessary property. When a model is not identifiable, even an infinite number of observations cannot determine the true parameter. Non-identifiablity problem in generalized linear models with and without random effects is very common. Also it can occur in such models when the response variable has non-ignorably missing. Since the structure of the beta regression model is similar to that of the generalized linear models and identifiability of many commonly used models such as the beta regression model has not been investigated in the literature, we establish a study about identifiability of some types of the beta regression models such as beta regression model with non-ignorable missing mechanism, zero and one inflated beta regression model, zero and one inflated beta regression model with non-ignorable missing mechanism, longitudinal beta regression model, longitudinal zero and one inflated beta regression model, longitudinal zero and one inflated beta regression model with non-ignorable missing mechanism, and longitudinal correlated bivariate Poisson and zero and one inflated beta regression model with non-ignorable missing mechanism. We construct estimators for the parameters in all mentioned models based on the EM algorithm and the likelihood-based approach. Simulation results and two applications of the Facebook network and FBI datasets are also presented.

### MSC:

62J12 | Generalized linear models (logistic models) |

62J02 | General nonlinear regression |

62H11 | Directional data; spatial statistics |

62D10 | Missing data |

62P25 | Applications of statistics to social sciences |

### Keywords:

identifiability; inflated beta distributions; joint modelling; missing data; responsiveness rate in social network
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\textit{E. Tabrizi} et al., Statistics 54, No. 3, 524--543 (2020; Zbl 1440.62289)

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