National Food Security Modeling Using the Zero-Inflated Ordered Probit with Correlated Errors (ZIOPC) Approach - Vita Ratnasari; Nidya Putri Yudhani; I Nyoman Budiantara; Ismaini Zain (Journal of Multidisciplinary Applied Natural Science, 2026)
Zero-inflated ordinal data often emerge when the response variable displays both an ordered structure and an excessive number of zero outcomes. Such characteristics are not adequately captured by standard ordinal probit models. To address this limitation, this study employs a zero-inflated ordered probit with correlated errors (ZIOPC) model, which extends the conventional zero-inflated ordered probit (ZIOP) framework by explicitly modeling the dependence between the binary (inflation) and ordinal processes. From a modeling perspective, this study underscores the role of correlated latent errors in enhancing the representation of zero-inflated ordinal data. Parameter estimation was conducted using maximum likelihood estimation (MLE) implemented through the limited-memory BFGS with bound constraint (L-BFGS-B) algorithm to efficiently handle constrained optimization involving bivariate normal distributions. Statistical inference was performed using the maximum likelihood ratio test (MLRT) for simultaneous parameter testing, likelihood ratio test (LRT) for assessing the correlation parameter, and Wald test for partial significance of individual parameters. An empirical application using national food security data in Indonesia revealed substantial zero inflation. The results indicated that the correlation parameter was positive and statistically significant, confirming the presence of dependence between the two latent processes. Model comparison further demonstrates that the ZIOPC model provides a significantly better fit than the standard ZIOP model, as evidenced by the substantially lower AIC value of 1082.192 compared with 1187.468 for the ZIOP model. These findings emphasize the importance of incorporating correlated errors in modeling zero-inflated ordinal outcomes.