Volume 42 - Article 38 | Pages 1097–1146 Editor's Choice Author has provided data and code for replicating results

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

By Hal Caswell

Print this page  Facebook  Twitter


Date received:02 Mar 2020
Date published:19 Jun 2020
Word count:9000
Keywords:kinship, matrix models, multistate models, parity, sibship, Slovakia, vec-permutation matrices
Additional files:readme.42-38 (text file, 2 kB)
 42-38_supplement (pdf file, 756 kB)
 demographic-research.42-38 (zip file, 258 MB)


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.

Author's Affiliation

Hal Caswell - Universiteit van Amsterdam, the Netherlands [Email]

Other articles by the same author/authors in Demographic Research

» The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16

» Healthy longevity from incidence-based models: More kinds of health than stars in the sky
Volume 45 - Article 13

» The formal demography of kinship: A matrix formulation
Volume 41 - Article 24

» The sensitivity analysis of population projections
Volume 33 - Article 28

» Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
Volume 33 - Article 20

» Demography and the statistics of lifetime economic transfers under individual stochasticity
Volume 32 - Article 19

» A matrix approach to the statistics of longevity in heterogeneous frailty models
Volume 31 - Article 19

» Why do lifespan variability trends for the young and old diverge? A perturbation analysis
Volume 30 - Article 48

» Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
Volume 23 - Article 19

» Perturbation analysis of nonlinear matrix population models
Volume 18 - Article 3

Most recent similar articles in Demographic Research

» “One hand does not bring up a child:” Child fostering among single mothers in Nairobi slums
Volume 46 - Article 30    | Keywords: kinship

» National estimates of kinship size and composition among adults with activity limitations in the United States
Volume 45 - Article 36    | Keywords: kinship

» The formal demography of kinship III: Kinship dynamics with time-varying demographic rates
Volume 45 - Article 16    | Keywords: kinship

» Socioeconomic differentials in fertility in South Korea
Volume 44 - Article 39    | Keywords: parity

» The decline of patrilineal kin propinquity in the United States, 1790–1940
Volume 43 - Article 18    | Keywords: kinship


»Volume 42





Similar Articles



Jump to Article

Volume Page
Volume Article ID