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The formal demography of kinship II: Multistate models, parity, and sibship

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  • Hal Caswell

    (Universiteit van Amsterdam)

Abstract

Background: Recent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem. Objective: The aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, “stages”). Methods: The vec-permutation method is used to create multistate projection matrices including age- and stage-dependent survival, fertility, and transitions. These matrices operate on block-structured population vectors that describe the age×stage structure of each kind of kin, at each age of a focal individual. Results: The new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019a). As an application, a model is derived including age and parity. It provides, for all types of kin, the joint age×parity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. The age×parity distributions provide the distributions of sibship sizes of kin. As an example, the model is applied to Slovakia (1960–2014). The results show a dramatic shift in the parity distribution as the frequency of low-parity kin increased and that of high-parity kin decreased. Contribution: This model extends the formal demographic analysis of kinship to age×stage-classified models. In addition to parity, other stage classifications, including marital status, maternal age effects, and sex are now open to analysis.

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  • Hal Caswell, 2020. "The formal demography of kinship II: Multistate models, parity, and sibship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(38), pages 1097-1146.
    • Handle: RePEc:dem:demres:v:42:y:2020:i:38
    DOI: 10.4054/DemRes.2020.42.38
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    Cited by:

    1. Hal Caswell, 2022. "The formal demography of kinship IV: Two-sex models and their approximations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(13), pages 359-396.
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Hal Caswell & Xi Song, 2021. "The formal demography of kinship III: Kinship dynamics with time-varying demographic rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(16), pages 517-546.
    4. Hal Caswell & Silke van Daalen, 2021. "Healthy longevity from incidence-based models: More kinds of health than stars in the sky," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(13), pages 397-452.
    5. Sha Jiang & Wenyun Zuo & Zhen Guo & Hal Caswell & Shripad Tuljapurkar, 2023. "How does the demographic transition affect kinship networks?," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 48(32), pages 899-930.

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    More about this item

    Keywords

    kinship; multistate models; parity; Slovakia; matrix models; vec-permutation matrices; sibship;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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