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Visualizing rate of change: an application to age‐specific fertility rates

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  • Han Lin Shang

Abstract

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.

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  • Han Lin Shang, 2019. "Visualizing rate of change: an application to age‐specific fertility rates," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(1), pages 249-262, January.
    • Handle: RePEc:bla:jorssa:v:182:y:2019:i:1:p:249-262
    DOI: 10.1111/rssa.12359
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    Cited by:

    1. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Mammen, Enno & Martínez-Miranda, María Dolores & Nielsen, Jens Perch & Vogt, Michael, 2021. "Calendar effect and in-sample forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 31-52.
    3. Tim Riffe & Jose Manuel Aburto, 2020. "Lexis fields," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(24), pages 713-726.
    4. Timothy Riffe & José M. Aburto, 2019. "Lexis fields," MPIDR Working Papers WP-2019-001, Max Planck Institute for Demographic Research, Rostock, Germany.

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