Characterization of the Zero Inflated Generalized Poisson (ZIGP) Fisher Information Matrix and Estimation of the ZIGP Model for Data with Missing Values - Manapat, George Ringo S. (Quezon City University of the Philippines, 2023)
ABSTRACT

Count data commonly arise in studies concerning various disciplines. The most common model used to analyze count data is the Poisson distribution. However, many datasets do not conform to the assumption of equidispersion under this model. Heterogeneity in terms of zero inflation and overdispersion are possible source of this problem. Hence, alternative distribution are being considered to analyze data with zero inflation and overdispersion. In addition, missing data is also a common problem in data analysis. In recent years, increasing attention is being given to the Zero Inflated Generalized Poisson (ZIGP) model to analyze zero inflated and overdispersed count data. However, there is no existing methodology yet that incorporates the problem of missingness under the ZIGP context.

In this thesis, we derived the Fisher Information Matrix of the ZIGP distribution and showed that it is positive definite. We also proposed a novel estimation procedure for overdispersed and zero inflated data when some observations are missing. We demonstrated through simulation studies that the proposed procedure is at par with existing practices. In general, the proposed algorithm produces relatively better estimates compared to complete case analysis when zero inflation is large and the location parameter is small. Using the National Demographic and Health Survey (NDHS) 2022 data, we have shown the applicability of the proposed method for estimating the parameters of the ZIGP model when some observations are missing.
Keywords: Count Data; Missing Data; Zero Inflation; Overdispersion; Fisher Information Matrix; Stochastic Expectation-Maximization Algorithm