Journal
ENTROPY
Volume 24, Issue 10, Pages -Publisher
MDPI
DOI: 10.3390/e24101472
Keywords
best linear unbiased predictors; logistic regression; nonparametric random effects; overdispersion; random cluster sizes; zero inflation
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada [RGPIN-2020-04751, RGPIN-2015-06124]
- Doctoral Research Initiation Project Fund [2019BSXM11]
- Yunnan Philosophy and Social Science Planning Project Fund [QN2019009]
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This paper proposes a new approach to handle longitudinal binomial data with positive association, which can handle both random and zero number of trials and can accommodate overdispersion and zero inflation in the data.
Numerous methods have been developed for longitudinal binomial data in the literature. These traditional methods are reasonable for longitudinal binomial data with a negative association between the number of successes and the number of failures over time; however, a positive association may occur between the number of successes and the number of failures over time in some behaviour, economic, disease aggregation and toxicological studies as the numbers of trials are often random. In this paper, we propose a joint Poisson mixed modelling approach to longitudinal binomial data with a positive association between longitudinal counts of successes and longitudinal counts of failures. This approach can accommodate both a random and zero number of trials. It can also accommodate overdispersion and zero inflation in the number of successes and the number of failures. An optimal estimation method for our model has been developed using the orthodox best linear unbiased predictors. Our approach not only provides robust inference against misspecified random effects distributions, but also consolidates the subject-specific and population-averaged inferences. The usefulness of our approach is illustrated with an analysis of quarterly bivariate count data of stock daily limit-ups and limit-downs.
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