TY  - JOUR
A1  - Caswell, Hal
T1  - The formal demography of kinship II: Multistate models, parity, and sibship
Y1  - 2020/06/19
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 1097
EP  - 1146
DO  - 10.4054/DemRes.2020.42.38
VL  - 42
IS  - 38
UR  - https://www.demographic-research.org/volumes/vol42/38/
L1  - https://www.demographic-research.org/volumes/vol42/38/42-38.pdf
L2  - https://www.demographic-research.org/volumes/vol42/38/42-38.pdf
L3  - https://www.demographic-research.org/volumes/vol42/38/files/readme.42-38.txt
L3  - https://www.demographic-research.org/volumes/vol42/38/files/42-38_supplement.pdf
L3  - https://www.demographic-research.org/volumes/vol42/38/files/demographic-research.42-38.zip
N2  - 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. 

ER  -