Visualizing Rate of Change: An Application to Age-specific Fertility Rates
本文利用相平面图可视化年龄别生育率的变化率，能识别生育率最大正负变化速度的年龄，并比较不同年份变化幅度，对人口学者分析生育率动态变化有参考价值。
Summary Visualization methods help in the discovery of characteristics that might not have been apparent by using mathematical models and summary statistics. However, visualization methods have not received much attention in demography, with the exceptions of scatter plots and Lexis surfaces. We utilize a phase plane plot to visualize the rate of change, obtained from derivatives of a continuous function. The phase plane plot bears a resemblance to hysteresis loops, isogrowth curves and solutions to differential equations. Using Australian and Chilean fertility, we present phase plane plots. Similarly to the scatter plot and Lexis surface, the phase plane plot identifies the age with maximum fertility rate and displays skewness of the fertility distribution. Unlike the scatter plot and Lexis surface, the phase plane plot identifies the age with maximum positive or negative velocity (i.e. the trend) and can compare the magnitude of the rate of change between any two years on the basis of the size of the radius of circles. The phase plane plot enables visualization of dynamic changes in fertility for a given age over the years and is potentially useful for visualizing dynamic changes in birth cohort fertility. Via the animate package in LATEX, a dynamic phase plane plot is also proposed to visualize changes in fertility over age or year.