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

BackgroundRecent 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. ObjectivesOur aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, "stages"). MethodsWe use the vec-permutation method 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 agexstage structure of each kind of kin, at each age of a focal individual. ResultsThe new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019a). As an application, we derive a model that includes age and parity. We obtain, for all types of kin, the joint agexparity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. We show how to use the agexparity distributions to calculate the distributions of sibship sizes of kin. As an example, we apply the model to Slovakia (1960-2014). The results include a dramatic shift in the parity distribution as the frequency of low-parity kin increased and that of high-parity kin decreased. ContributionThe new model extends the formal demographic analysis of kinship to agexstage-classified models. In addition to parity, other stage classifications, including marital status, maternal age effects, and sex are now open to analysis.