High infant mortality rate is still a worldwide problem and the situation is even worse in some developing countries or regions with political instability, low economic levels and epidemic diseases. In addition, some studies have shown that infant mortality rate affects fertility rate, so it is important to reduce the infant mortality rate when China's population has already started to grow negatively in 2022. Infant mortality rate is a discrete count data. This kind of data usually does not follow the basic assumption of normality, so the use of ordinary linear regression models on it may produce inconsistent or biased estimates. Double hierarchical generalized linear model (DHGLM) are a class of models that exist specifically for count data. They can model the mean and proportion parameters hierarchically and specify random effects for the mean and dispersion which is a good solution to the problem of underestimating standard errors due to overdispersion of the data. This paper proposes a double hierarchical generalized linear model combined with the integrated nested laplace approximation within markov chain monte carlo (MCMCINLA) to analyze the data of infant mortality rate in China. At the same time, a spatial lag term is added to the model to analyze the spatial correlation of the data. Finally, the influence of economic or medical factors on infant mortality rate is analyzed and some policy suggestions are given to reduce infant mortality rate according to the analysis results.
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