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

Abstract

AbstractEnergy securityis one of the major components of energy sustainability in the world’s energy performance. In this study,energy securityis taken as an ordinal response variable coming from the multinomial distribution with the energy grade levelsA,B,C, andD. Thereafter, the worldenergy securitydata is tried to be statistically modelled by usinggeneralized 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 theGLMapproach 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 theGLMfor the multinomially distributed response variable is highlighted. In terms of energy evaluation, by usingcumulative logitas 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 importsare found to have statistically significant effects onenergy securityin the world’s energy performance.