Modelling world energy security data from multinomial distribution by generalized linear model under different cumulative link functions

Energy security is one of the major components of energy sustainability in the world's energy performance. In this study, energy security is taken as an ordinal response variable coming from the multinomial distribution with the energy grade levels A, B, C, and D. Thereafter, the world energy security data is tried to be statistically modelled by using generalized linear model (GLM) approach for the ordinal response variable under different cumulative link functions. The cumulative link functions comparatively used in this study are cumulative logit, cumulative probit, cumulative complementary log-log, cumulative Cauchit, and cumulative negative log-log. In order to avoid a multicollinearity problem in the data structure, principal component analysis (PCA) technique is integrated with the GLM approach for the ordinal response variable. In this study, statistically, the importance of determining the best cumulative link function on the accuracy of parameter estimates, confidence intervals, and hypothesis tests in the GLM for the multinomially distributed response variable is highlighted. In terms of energy evaluation, by using cumulative logit as the best cumulative link function, energy sources consumptions, electricity productions from nuclear energy, natural gas, oil, coal, and hydroelectric, energy use per capita and energy imports are found to have statistically significant effects on energy security in the world's energy performance.