Journal of Multidisciplinary Applied Natural Science
Periódico de Acesso Aberto
Scopus CiteScore 2025
2.1
Calculated on 05 May, 2025
SJR 2025
0.25
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Periódico de Acesso Aberto
2.1
Calculated on 05 May, 2025
0.25
Powered by scimagojr.com
https://doi.org/10.47352/jmans.2774-3047.444
Vita Ratnasari
Nidya Putri Yudhani
I Nyoman Budiantara
Ismaini Zain
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.
[1] M. N. Harris and X. Zhao. (2007). "A Zero-Inflated Ordered Probit Model, with an Application to Modelling Tobacco Consumption". Journal of Econometrics. 141 (2): 1073-1099. 10.1016/j.jeconom.2007.01.002.
DOI: https://doi.org/10.1016/j.jeconom.2007.01.002[2] D. Dale and A. Sirchenko. (2021). "Estimation of Nested and Zero-Inflated Ordered Probit Models". The Stata Journal. 21 (1): 3-38. 10.1177/1536867X211000002.
DOI: https://doi.org/10.1177/1536867X211000002[3] D. Lambert. (1992). "Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing". Technometrics. 34 (1): 1-14. 10.2307/1269547.
DOI: https://doi.org/10.2307/1269547[4] Y. Min and A. Agresti. (2005). "Random Effect Models for Repeated Measures of Zero-Inflated Count Data". Statistical Modelling. 5 (1): 1-19. 10.1191/1471082X05st084oa.
DOI: https://doi.org/10.1191/1471082X05st084oa[5] A. Ghanbarnejad, A. Homayuni, Z. Hosseini, and A. Madani. (2022). "Smoking Behavior Among Students: Using Health Belief Model and Zero-Inflated Ordered Probit Model". Tobacco and Health. 1 (2): 74-82. 10.34172/thj.2022.12.
DOI: https://doi.org/10.34172/thj.2022.12[6] H. Wang, Z. Liu, X. Wang, D. Huang, L. Cao, and J. Wang. (2022). "Analysis of the Injury-Severity Outcomes of Maritime Accidents Using a Zero-Inflated Ordered Probit Model". Ocean Engineering. 258 : 111796. 10.1016/j.oceaneng.2022.111796.
DOI: https://doi.org/10.1016/j.oceaneng.2022.111796[7] J. Wu, W. Fan, and W. Wang. (2020). "A Zero-Inflated Ordered Probit Model to Analyze Hazmat Truck Drivers' Violation Behavior and Associated Risk Factors". IEEE Access. 8 : 110974-110985. 10.1109/ACCESS.2020.3001165.
DOI: https://doi.org/10.1109/ACCESS.2020.3001165[8] B. Neelon and D. Chung. (2017). "The LZIP: A Bayesian Latent Factor Model for Correlated Zero-Inflated Counts". Biometrics. 73 (1): 185-196. 10.1111/biom.12558.
DOI: https://doi.org/10.1111/biom.12558[9] B. E. Bagozzi, D. W. Hill, W. H. Moore, and B. Mukherjee. (2015). "Modeling Two Types of Peace: The Zero-Inflated Ordered Probit (ZiOP) Model in Conflict Research". Journal of Conflict Resolution. 59 (4): 728-752. 10.1177/0022002713520530.
DOI: https://doi.org/10.1177/0022002713520530[10] C. Xu, S. Xu, C. Wang, and J. Li. (2019). "Investigating the Factors Affecting Secondary Crash Frequency Caused by One Primary Crash Using Zero-Inflated Ordered Probit Regression". Physica A: Statistical Mechanics and Its Applications. 524 : 121-129. 10.1016/j.physa.2019.03.036.
DOI: https://doi.org/10.1016/j.physa.2019.03.036[11] R. Liesenfeld and J. F. Richard. (2010). "Efficient Estimation of Probit Models with Correlated Errors". Journal of Econometrics. 156 (2): 367-376. 10.1016/j.jeconom.2009.11.006.
DOI: https://doi.org/10.1016/j.jeconom.2009.11.006[12] L. Cappellari and S. P. Jenkins. (2003). "Multivariate Probit Regression Using Simulated Maximum Likelihood". The Stata Journal. 3 (3): 278-294. 10.1177/1536867X0300300305.
DOI: https://doi.org/10.1177/1536867X0300300305[13] M. Zulfadhli, I. N. Budiantara, and V. Ratnasari. (2024). "Nonparametric Regression Estimator of Multivariable Fourier Series for Categorical Data". MethodsX. 13 : 102983. 10.1016/j.mex.2024.102983.
DOI: https://doi.org/10.1016/j.mex.2024.102983[14] M. Rifada, V. Ratnasari, and Purhadi. (2023). "Parameter Estimation and Hypothesis Testing of the Bivariate Polynomial Ordinal Logistic Regression Model". Mathematics. 11 (3): 579. 10.3390/math11030579.
DOI: https://doi.org/10.3390/math11030579[15] R. Guo, J. Zhu, X. Jiang, and F. Qu. (2025). "Fast and Efficient Implementation of the Maximum Likelihood Estimation for the Linear Regression with Gaussian Model Uncertainty". Signal Processing. 110403. 10.1016/j.sigpro.2025.110403.
DOI: https://doi.org/10.1016/j.sigpro.2025.110403[16] R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu. (1995). "A Limited Memory Algorithm for Bound Constrained Optimization". SIAM Journal on Scientific Computing. 16 (5): 1190-1208. 10.1137/0916069.
DOI: https://doi.org/10.1137/0916069[17] P. Venkataraman. (2009). "Applied Optimization with MATLAB Programming". John Wiley & Sons, New York.
[18] N. Andrei. (2018). "A Double Parameter Scaled BFGS Method for Unconstrained Optimization". Journal of Computational and Applied Mathematics. 332 : 26-44. 10.1016/j.cam.2017.10.009.
DOI: https://doi.org/10.1016/j.cam.2017.10.009[19] V. Ratnasari, Purhadi, M. Rifada, and A. T. R. Dani. (2025). "Explore Poverty with Statistical Modeling: The Bivariate Polynomial Binary Logit Regression (BPBLR)". MethodsX. 14 : 103099. 10.1016/j.mex.2024.103099.
DOI: https://doi.org/10.1016/j.mex.2024.103099[20] H. Fransiska, A. M. Soleh, K. A. Notodiputro, and E. Erfiani. (2025). "Evaluation and Comparison of Three Mixed-Effect Models for Household Food Insecurity Classification in West Java". Journal of Multidisciplinary Applied Natural Science. 6 (1): 466-480. 10.47352/jmans.2774-3047.334.
DOI: https://doi.org/10.47352/jmans.2774-3047.334[21] W. H. Greene.(2020)." Econometric Analysis". Prentice Hall, New Jersey.
[22] C. B. Barrett. (2010). "Measuring Food Insecurity". Science. 327 (5967): 825-828. 10.1126/science.1182768.
DOI: https://doi.org/10.1126/science.1182768[23] FAO, IFAD, UNICEF, WFP and WHO. (2023). “Urbanization, agrifood systems transformation and healthy diets across the rural–urban continuum”. Rome, FAO. 10.4060/cc3017en
DOI: https://doi.org/10.4060/cc3017en[24] C. Béné, D. Bakker, M. J. Chavarro, B. Even, J. Melo, and A. Sonneveld. (2021). "Global Assessment of the Impacts of COVID-19 on Food Security". Global Food Security. 31 : 100575. 10.1016/j.gfs.2021.100575.
DOI: https://doi.org/10.1016/j.gfs.2021.100575[25] D. Laborde, W. Martin, J. Swinnen, and R. Vos. (2020). "COVID-19 Risks to Global Food Security". Science. 369 (6503): 500-502. 10.1126/science.abc4765.
DOI: https://doi.org/10.1126/science.abc4765[26] C. R. Bhat and S. K. Dubey. (2014). "A New Estimation Approach to Integrate Latent Psychological Constructs in Choice Modeling". Transportation Research Part B: Methodological. 67 : 68-85. 10.1016/j.trb.2014.04.011.
DOI: https://doi.org/10.1016/j.trb.2014.04.011[27] Q. H. Vuong. (1989). "Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses". Econometrica. 57 (2): 307-333. 10.2307/1912557.
DOI: https://doi.org/10.2307/1912557