Estimating detailed distributions from grouped sociodemographic data: 'get me started in' curve fitting using nonlinear models
Estimating detailed distributions from grouped sociodemographic data: 'get me started in' curve fitting using nonlinear models
复制标题
从分组的社会人口统计数据估计详细分布：使用非线性模型“让我开始”曲线拟合
DOI：
10.1007/s12546-012-9082-9
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发表时间：
2012
影响因子：
2
通讯作者：
Norman P
中科院分区：
文献类型：
--
作者：
Norman P
在许多人口统计分析中，重要的是要知道发生暴露率或转变概率如何随年龄或时间连续变化。我们经常有粗略或波动的数据，因此可能需要进行估计和平滑。由于比率或计数在年龄或其他变量上的分布通常是曲线型的，所以非线性模型可能是合适的。本文的主要重点是从分组数据中估计详细信息，如年龄和收入范围；然而，我们概述的方法也可以应用于其他设置，如原始数据参差不齐的平滑率。对于人口地理学家和人口学家来说，进行曲线拟合的能力是一项非常有用的技能。统计教科书中没有很好地介绍曲线拟合，尽管期刊上有大量文献详细讨论了定义曲线的函数的细节，但非数学专家的研究人员很可能无法接触到这些文本。我们在这里的目标是使非线性建模尽可能容易实现。我们演示了如何使用SPSS进行非线性回归，并给出了逐步的假设和研究实例。我们注意到其他可以进行非线性回归的软件，并概述了曲线拟合的替代方法。
In much demographic analysis, it is important to know how occurrence-exposure rates or transition probabilities vary continuously by age or by time. Often we have coarse or fluctuating data so there can be a need for estimation and smoothing. Since the distributions of rates or counts across age or another variable are often curved, a nonlinear model is likely to be appropriate. The main focus of this paper is on the estimation of detailed information from grouped data such as age and income bands; however, the methods we outline could also be applied to other settings such as smoothing rates where the original data are ragged. The ability to carry out curve fitting is a very useful skill for population geographers and demographers. Curve fitting is not well covered in statistics textbooks, and whilst there is a large literature in journals thoroughly discussing the detail of functions which define curves, these texts are likely to be inaccessible to researchers who are not specialists in mathematics. We aim here to make nonlinear modelling as accessible as possible. We demonstrate how to carry out nonlinear regression using SPSS, giving stepped-through hypothetical and research examples. We note other software in which nonlinear regression can be carried out, and outline alternative methods of curve fitting.