Table 1

Model selection criteria for nested and non-nested models

  • Likelihood ratio (LR) test:

  • LR=2(LL1–LL2) follows χ2(1)

  • where LLi is the log-likelihood for the ith model

A significant LR test suggests that unobserved heterogeneity accounts for dispersion
  • Vuong test 18:

  • Embedded Image

  • where Embedded Image and Embedded Image 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+k*ln(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