Note(s): Across the four specifications, Model 2 (Invention) provides the best empirical fit: it attains the lowest −2 log likelihood and the smallest values on AIC, AICC, BIC, CAIC and HQIC, indicating the most favourable balance of fit and parsimony. All models show Pearson χ²/DF between 0.83 and 0.93, which implies only mild under dispersion rather than gross misfit. Overall, the four models capture meaningful structure in the data (information criteria and likelihood improve markedly from some alternatives to Model 2), but none exhibits signs of severe lack of fit; substantive inference should proceed after inspection of coefficients and standard diagnostics