Generalized additive models to capture the death rates in Canada COVID-19

Abstract

To capture the death rates and strong weekly, biweekly and probably monthly patterns in the Canada COVID-19, we utilize the generalized additive models in the absence of direct statistically based measurement of infection rates. By examining the death rates of Canada in general and Quebec, Ontario and Alberta in particular, one can easily figured out that there are substantial overdispersion relative to the Poisson so that the negative binomial distribution is an appropriate choice for the analysis. Generalized additive models (GAMs) are one of the main modeling tools for data analysis. GAMs can efficiently combine different types of fixed, random and smooth terms in the linear predictor of a regression model to account for different types of effects. GAMs are a semi-parametric extension of the generalized linear models (GLMs), used often for the case when there is no a priori reason for choosing a particular response function such as linear, quadratic, etc. and need the data to 'speak for themselves'. GAMs do this via the smoothing functions and take each predictor variable in the model and separate it into sections delimited by 'knots', and then fit polynomial functions to each section separately, with the constraint that there are no links at the knots - second derivatives of the separate functions are equal at the knots.