A problem in household composition

Abstract

"Distinction made between household-persons and household-markers [the person who identifies the family or household as a unit] is formalized in the notion of nested populations. This leads to an extension of the Leslie model into a formulation of growth for both population and households. The extended model involves the matrix presentation of household composition where ratios of household-persons who are age 0, per household-marker, function as surrogate values for fertility rates. The extended model describes change over time in the distribution of population by age, and in the distribution of households by age of household-marker, or household-head. The model involves the inversion of a nonnegative matrix, and is feasible only if it yields, projected over time, nonnegative entries in vectors representing distribution of population by age, and distribution of household-heads by age. Conditions for the feasibility of the extended model are discussed, and a sufficient condition for feasibility over a single interval is identified." (SUMMARY IN FRE)

Parameters of Household Composition as Demographic Measures

“…Yet the composition of households by age of household-heads and by age of their other household members has some particularly useful attributes. A tabular representation of age distribution of members within households by age of heads has been shown to constitute a linear relationship with the overall agedistribution of the population at large (Akkerman, 1996(Akkerman, , 2000. The age-specific household size is shown here to track the gamma probability density function, and in the product with the age-specific headship ratio to yield a demographic measure of housing, the age-specific headship coefficient.…”

“…The diagonal entries of the table are (a jj + 1), showing the average number of persons per household in the same age group as the householder. For any age group j of householders, j > r, the sum of the entries a ij (along with the diagonal entry, a jj + 1) in each column j yields the average household size, s j , for householders in age groups j (Akkerman, 1996).…”

“…The household composition table, with additional r columns prefixed according to a specified convention, yields the household composition matrix. The convention calls for all entries in the prefixed columns to be set to zero, except for the diagonal entries in the prefixed columns, which are set each to 1 (Akkerman, 1980(Akkerman, , 1996. The household composition matrix is a descriptive device of household population structure that involves a linear relationship between household heads and householdpersons.…”

Age-Specific Household Size as a Demographic Aspect of Regional Disparity: Czech Republic, 1991

“…The census depiction of households from which the age-specific household size arises is the matrix notion of household composition. The household composition matrix is a crosstabulation of individuals and their corresponding householders, usually by categories of age (Akkerman, 1996). Through the crosstabulation each individual is assumed to be a member of a household, and demographic traits are expressed jointly for individuals and for households.…”

“…The relation between these two concepts will require further attention, particularly within the context of housing and the interaction between local communities and the government (cf. also Carmin, 2003) The recognized benefit of the household composition table, particularly in demographically "smaller" populations such as those of cities or sub-national regions, is the formal linkage between family and household structure, and the aging of the population (Akkerman, 1996). Within the context of the city or the region the need for such methodological linkage becomes crucial with regard to urban development and the planning of residential housing.…”