Table 1

Model selection criteria for nested and non-nested models

Models	Tests	Decision
Nested	Likelihood ratio (LR) test: LR=2(LL1–LL2) follows χ²(1) where LL_i is the log-likelihood for the ith model	A significant LR test suggests that unobserved heterogeneity accounts for dispersion
Non-nested	Vuong test 18: where and are predicted probabilities of the two competing non-nested models	If V >1.96 the Vuong test favours model 1, while the test favours model 2 if V <−1.96
Nested or non-nested	Information criteria: Akaike Information Criterion (AIC)=−2LL+2k Bayesian Information Criterion (BIC) =−2LL+kln(n)* where k is the number of independent model parameters and n is the number of observations19	Competing models are indistinguishable if the difference in AIC or BIC is <2 while a difference >10 suggests strong evidence in favour of the model with the smallest criterion