With the current outbreak of coronavirus disease 2019 (COVID-19), countries have been on rising preparedness to detect and isolate any imported and locally transmitted cases of the disease. It is observed that mode of transmission of the disease varies from one country to the other. Recent studies have shown that COVID-19 cases are not influenced by race and weather conditions. In this study, effect of modes of transmission of COVID-19 is considered with respect to prevalence and mortality counts in World Health Organisation (WHO) regions. Also, a negative binomial model is formulated for new death cases in all WHO regions as a function of confirmed cases, confirmed new cases, total deaths and modes of transmission, with the goal of identifying a model that predicts the total new death cases the best. Results from this study show that there is strong linear relationship among the COVID-19 confirmed cases, total new deaths and mode of transmission in all WHO regions. Findings highlight the significant roles of modes of transmission on total new death cases over WHO regions. Mode of transmission based on community transmission and clusters of cases significantly affects the number of new deaths in WHO regions. Vuong test shows that the formulated negative binomial model fits the data better than the null model.
COVID-19 has remained and continued to be a severe pandemic threatening the present and future health stability of all the countries, the West African Countries inclusive. The challenge to avert the threat by modeling the reported cases in each of these West African Countries becomes needful for future planning and a K. Ayinde (B) •
This research extends design optimization to model involving count data. A two-variable Poisson regression model was investigated for A-optimality on a constrained design space and the weights of the optimal design points were obtained. The constructed designs were verified to be A-optimal at 4-point design through the general equivalence theorem. The efficiency of the constructed optimal design was found to be 100% A-efficient. The concept of weighted optimal designs for Poisson regression model was applied to fertility studies. Approximate A-optimal design weights of educational level of women were obtained for each marriage duration period with respect to their places of residence. The study revealed that the numbers of women with secondary education and above were found to be consistently more than that of women with no education, lower primary education and upper primary education, respectively for all the marriage duration periods considered and at each place of residence. The only exclusion is the marriage duration of 0–4 years at Suva where the proportion of women with no education was more than other educational levels.
Keywords: A-optimality; Design Point; Fisher Information Matrix; Imperialist Competitive Algorithm; Poisson Regression Model
One of the basic assumptions of Seemingly Unrelated Regression Equations (SURE) is the normality of error terms in the regressions model. This paper thus considers estimating SUR model when the normality assumption of the error term is violated. Small and asymptotic properties are examined using Ordinary Least Squares (OLS) and Feasible Generalized Least Squares (FGLS) estimators. The results revealed that the SUR estimator (FGLS) was diminishingly efficient as sample size increases with their standard errors converging at large sample size of 1000.
In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focussed on optimal experimental designs with concentration on D-optimality. In this research, two- and three-variable Poisson regression models were considered for E-optimization on restricted design space [0, 1]. The two-variable Poisson regression model was not optimal at 3-design points, but was found to be E-optimal at 4-design points (1, 1), (0, 0), (0, 1) and (1, 0) with equal design weights of 0.25. The three-variable Poisson regression model was E-optimal at 4-design points (0, 0, 1), (0, 1, 0), (1, 1, 1) and (1, 0, 0) with each design point having design weights of 0.25. The prediction error variance (PEV) for the two-variable Poisson regression model is 0.35 and that of the three-variable Poisson regression model is 0.68. From this research, the two-variable Poisson regression model is preferred to the three-variable Poisson regression model because of smaller PEV.
Keywords: E-optimality; Fisher Information Matrix; Poisson Regression Model; Prediction Error Variance
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