Srivastava Ujjaval, Singh Kaushalendra Kumar, Pandey Anjali, Narayan Neeraj
Department of Statistics, Banaras Hindu University, Varanasi, India.
Ministry of Tourism, Government of India, New Delhi, India.
Sci Rep. 2021 Mar 23;11(1):6592. doi: 10.1038/s41598-021-85959-z.
Modelling is a well-established concept for understanding the typical shape and pattern of age-specific fertility. The distribution of India's age-specific fertility rate (ASFR) is unimodal and positively skewed and is distinct from the ASFR of the developed countries. The existing models (P-K model, Gompertz model, Skew-normal model and G-P model considered here) that were developed, based on the experiences of the developed countries, failed to fit the single-year age-specific fertility pattern for India as a whole and for the six selected states. Our study has proposed four flexible models, to capture the diverse age pattern of fertility, observed in the Indian states. The proposed models were compared in three ways; among themselves, with the original models and with the popular Hadwiger model. The parameters of these proposed models were estimated through the Non-Linear Least Squares Method. To find the model with best fit, we used the corrected version of Akaike's Information Criterion (AICc). Optimization of the four original models was successfully done. When the model was fitted to the empirical data of the 4th round of the National Family Health Survey conducted in 2015-2016, the results of this study showed that all the four proposed models outperform their corresponding original models and the Hadwiger model. When comparison among the proposed models was done, the Modified Gompertz Model provided the best fit for India, Uttar Pradesh and Gujarat. Whereas, the Modified P-K model gave the best fit for West Bengal, Tripura and Karnataka. The Modified G-P model is the most suitable model for Punjab. Although our proposed models illustrated the fitting of ASFR for India as a whole and the selected six states only, it provides an important tool for the policymakers and the government authorities to project fertility rates and to understand the fertility transitions in India and various other states.
建模是一个成熟的概念，用于理解特定年龄生育率的典型形状和模式。印度特定年龄生育率（ASFR）的分布是单峰且正偏态的，与发达国家的ASFR不同。基于发达国家的经验开发的现有模型（此处考虑的P-K模型、冈珀茨模型、偏态正态模型和G-P模型）未能拟合印度整体以及六个选定邦的单年特定年龄生育率模式。我们的研究提出了四个灵活的模型，以捕捉在印度各邦观察到的不同年龄生育模式。通过三种方式对所提出的模型进行了比较：相互之间比较、与原始模型比较以及与流行的哈德维格模型比较。这些所提出模型的参数通过非线性最小二乘法进行估计。为了找到拟合度最佳的模型，我们使用了赤池信息准则的校正版本（AICc）。四个原始模型的优化成功完成。当将该模型应用于2015 - 2016年进行的第四轮全国家庭健康调查的实证数据时，本研究结果表明，所有四个所提出的模型均优于其相应的原始模型和哈德维格模型。在所提出的模型之间进行比较时，修正的冈珀茨模型对印度、北方邦和古吉拉特邦的拟合度最佳。而修正的P-K模型对西孟加拉邦、特里普拉邦和卡纳塔克邦的拟合度最佳。修正的G-P模型是旁遮普邦最合适的模型。尽管我们所提出的模型仅说明了印度整体以及选定的六个邦的ASFR拟合情况，但它为政策制定者和政府当局预测生育率以及理解印度和其他各邦的生育转变提供了一个重要工具。
