A new alternative quantile regression model for the bounded response with educational measurements applications of OECD countries. (English) Zbl 07634377
Summary: This article introduces a new distribution with two tuning parameters specified on the unit interval. It follows from a ‘hyperbolic secant transformation’ of a random variable following the Weibull distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions over the unit interval is a motivation for the study. The main distributional structural properties of the new distribution are established. The different estimation methods and two simulation works have been derived for model parameters. Subsequently, we develop a related quantile regression model for further statistical perspectives. We consider two real data applications based on the educational measurements of both OECD and some non-members of OECD countries. Our regression model aims to relate the desire to get top grades on certain young students in the OECD countries with some of their Education and School Life Index such as reading performance, work environment at home, and paid work experience. It is shown that the elaborated quantile regression model has a better fitting power than famous regression models when the unit response variable possesses skewed distribution as well as two independent variables are significant in the statistical sense at any standard significance level for the median response.
MSC:
| 62-XX | Statistics |
Keywords:
educational measurements; Weibull distribution; quantile regression; residuals; education and school life index; OECD data setReferences:
| [1] | Aarset, M. V., How to identify a bathtub hazard rate, IEEE Trans. Reliab., 36, 106-108 (1987) · Zbl 0625.62092 |
| [2] | Altun, E., The log-weighted exponential regression model: Alternative to the beta regression model, Commun. Stat. - Theory Methods (2021) · Zbl 07533668 · doi:10.1080/03610926.2019.1664586 |
| [3] | Altun, E.; Cordeiro, G. M., The unit-improved second-degree Lindley distribution: Inference and regression modeling, Comput. Stat., 35, 259-279 (2020) · Zbl 1505.62027 |
| [4] | Altun, E.; Hamedani, G. G., The log-xgamma distribution with inference and application, J. Soc. Française Stat., 159, 40-55 (2018) · Zbl 1410.62021 |
| [5] | Bayes, C. L.; Bazán, J. L.; De Castro, M., A quantile parametric mixed regression model for bounded response variables, Stat. Interface, 10, 483-493 (2017) · Zbl 1388.62200 |
| [6] | Bayes, C. L.; Bazán, J. L.; García, C., A new robust regression model for proportions, Bayesian Anal., 7, 841-866 (2012) · Zbl 1330.62272 |
| [7] | Butler, R. J.; McDonald, J. B., Using incomplete moments to measure inequality, J. Econom., 42, 109-119 (1989) |
| [8] | Cheng, R.C.H. and Amin, N.A.K., Maximum product of spacings estimation with application to the lognormal distribution, Math Report 791 (1979). University of Wales, Cardiff, Deptartment of Mathematics. |
| [9] | Cox, D. R.; Snell, E. J., A general definition of residuals, J. R. Stat. Soc. B (Methodol.), 30, 248-265 (1968) · Zbl 0164.48903 |
| [10] | Creed, P. A.; Patton, W., Differences in career attitude and career knowledge for high school students with and without paid work experience, Int. J. Educ. Vocat. Guid., 3, 21-33 (2003) |
| [11] | David, H. A.; Nagaraja, H., Order Statistics (2003), John Wiley and Sons: John Wiley and Sons, New York · Zbl 1053.62060 |
| [12] | Dunn, P. K.; Smyth, G. K., Randomized quantile residuals, J. Comput. Graphical Statist., 5, 236-244 (1996) |
| [13] | Eide, E.; Showalter, M. H., The effect of school quality on student performance: A quantile regression approach, Econom. Lett., 58, 345-350 (1998) · Zbl 0901.90082 |
| [14] | Ferrari, S.; Cribari-Neto, F., Beta regression for modelling rates and proportions, J. Appl. Stat., 31, 799-815 (2004) · Zbl 1121.62367 |
| [15] | Fischer, M. J., Generalized Hyperbolic Secant Distributions: With Applications to Finance (2013), Springer Science & Business Media, Springer |
| [16] | Ghitany, M. E.; Mazucheli, J.; Menezes, A. F.B.; Alqallaf, F., The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval, Commun. Stat. Theory Methods, 48, 3423-3438 (2019) · Zbl 07539723 |
| [17] | Gómez-Déniz, E.; Sordo, M. A.; Calderín-Ojeda, E., The log-Lindley distribution as an alternative to the beta regression model with applications in insurance, Insur. Math. Econom., 54, 49-57 (2014) · Zbl 1294.60016 |
| [18] | Gündüz, S.; Korkmaz, M.Ç., A new unit distribution based on the unbounded Johnson distribution rule: The unit Johnson SU distribution, Pak. J. Stat. Oper. Res., 16, 471-490 (2020) |
| [19] | Gursakal, S.; Murat, D.; Gursakal, N., Assessment of PISA 2012 results with quantile regression analysis within the context of inequality in educational opportunity, Alphanumeric J., 4, 41-54 (2016) |
| [20] | Hahn, E. D., Mixture densities for project management activity times: A robust approach to PERT, Eur. J. Oper. Res., 188, 450-459 (2008) · Zbl 1149.90351 |
| [21] | Henningsen, A.; Toomet, O., maxLik: A package for maximum likelihood estimation in R, Comput. Stat., 26, 443-458 (2011) · Zbl 1304.65039 |
| [22] | Jodra, P.; Jiménez-Gamero, M. D., A quantile regression model for bounded responses based on the exponential-geometric distribution, Revstat, 18, 415-436 (2020) · Zbl 1455.62047 |
| [23] | Johnson, N. L., Systems of frequency curves generated by methods of translation, Biometrika, 36, 149-176 (1949) · Zbl 0033.07204 |
| [24] | Kieschnick, R.; McCullough, B. D., Regression analysis of variates observed on \(####\): Percentages, proportions and fractions, Stat. Modell., 3, 193-213 (2003) · Zbl 1070.62056 |
| [25] | Koenker, R.; Bassett Jr., G., Regression quantiles, Econometrica, 46, 33-50 (1978) · Zbl 0373.62038 |
| [26] | Korkmaz, M.Ç., A new heavy-tailed distribution defined on the bounded interval: The logit slash distribution and its application, J. Appl. Stat., 47, 2097-2119 (2020) · Zbl 1521.62376 |
| [27] | Korkmaz, M.Ç., The unit generalized half normal distribution: A new bounded distribution with inference and application, UPB Sci. Bull. A: Appl. Math. Phys., 82, 133-140 (2020) · Zbl 1513.62025 |
| [28] | Korkmaz, M.Ç.; Chesneau, C., On the unit Burr-XII distribution with the quantile regression modeling and applications, Comput. Appl. Math., 40, 1-26 (2021) · Zbl 1481.60024 |
| [29] | Korkmaz, M.Ç.; Chesneau, C.; Korkmaz, Z. S., On the arcsecant hyperbolic normal distribution. Properties, quantile regression modeling and applications, Symmetry, 13, 117 (2021) |
| [30] | Korkmaz, M.Ç.; Chesneau, C.; Korkmaz, Z. S., Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models, UPB Sci. Bull. A: Appl. Math. Phys., 83, 149-158 (2021) · Zbl 1524.62070 |
| [31] | Kumaraswamy, P., A generalized probability density function for double-bounded random processes, J. Hydrol., 46, 79-88 (1980) |
| [32] | Kundu, D.; Gupta, R. D., Estimation of \(####\) for Weibull distribution, IEEE Trans. Reliab., 55, 270-280 (2006) |
| [33] | Martins, P. S.; Pereira, P. T., Does education reduce wage inequality? Quantile regression evidence from 16 countries, Labour Econom., 11, 355-371 (2004) |
| [34] | Mazucheli, J.; Menezes, A. F.B.; Chakraborty, S., On the one parameter unit-Lindley distribution and its associated regression model for proportion data, J. Appl. Stat., 46, 700-714 (2019) · Zbl 1516.62470 |
| [35] | Mazucheli, J.; Menezes, A. F.; Dey, S., Unit-Gompertz distribution with applications, Statistica, 79, 25-43 (2019) · Zbl 07690371 |
| [36] | Mazucheli, J.; Menezes, A. F.B.; Fernandes, L. B.; de Oliveira, R. P.; Ghitany, M. E., The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, J. Appl. Stat., 47, 954-974 (2020) · Zbl 1521.62406 |
| [37] | Mazucheli, J.; Menezes, A. F.B.; Ghitany, M. E., The unit-Weibull distribution and associated inference, J. Appl. Probab. Stat., 13, 1-22 (2018) |
| [38] | McCool, J. I., Inference on \(####\) in the Weibull case, Commun. Stat. Simul. Comput., 20, 129-148 (1991) · Zbl 0850.62310 |
| [39] | Mitnik, P. A.; Baek, S., The Kumaraswamy distribution: Median-dispersion re-parameteriza-tions for regression modeling and simulation-based estimation, Stat. Pap., 54, 177-192 (2013) · Zbl 1257.62013 |
| [40] | Nakamura, L. R.; Cerqueira, P. H.R.; Ramires, T. G.; Pescim, R. R.; Rigby, R. A.; Stasinopoulos, D. M., A new continuous distribution on the unit interval applied to modelling the points ratio of football teams, J. Appl. Stat., 46, 1-16 (2018) · Zbl 1516.62501 · doi:10.1080/02664763.2018.1495699 |
| [41] | OECD, PISA 2015 Results (Volume III): Students’ Well-Being, PISA, OECD Publishing, Paris, 2017. doi: |
| [42] | Rangvid, B.S., School composition effects in Denmark: Quantile regression evidence from PISA 2000, in C. Dustmann, B. Fitzenberger, and S. Machin. (Eds.), The Economics of Education and Training, Physica-Verlag HD, 2008, pp. 179-208. doi: |
| [43] | Shafiq, M. N., Gender gaps in mathematics, science and reading achievements in Muslim countries: A quantile regression approach, Edu. Econom., 21, 343-359 (2013) |
| [44] | Shaked, M.; Shanthikumar, J. G., Stochastic Orders (2007), Wiley: Wiley, New York, NY · Zbl 1111.62016 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
