Models | Tests | Decision |

Nested | Likelihood ratio (LR) test: LR=2(LL1–LL2) follows χ ^{2}(1)where *LL*is the log-likelihood for the_{i}*i*th 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+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 |