A decomposition method based on a model of continuous change

A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations. We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifies the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function. A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied flexibly to a wide variety of decomposition problems. This study also suggests that when data are available at multiple time points over a long interval, it is more accurate to compute an aggregated decomposition based on multiple subintervals than to compute a single decomposition for the entire study period.     

Two fish species competition model with nonlinear interactions and equilibrium catches

Summary Two species competition model is built up by assuming the hypothetical second order interactions in order to consider effects of exploitation on two competing fish species with non-linear interactions. Most important characteristic of this model, compared withLotka-Volterra type linear competition model, is that this model can possess multiple stable equilibrium points. Therefore there is a possibility that two species keeping the equilibrium state at one stable equilibrium point will be attracted to the other stable equilibrium point after a heavy perturbation. In this model reversible change of the fishing pressure does not always results in that of the equilibrium catch. In this sence MSY concept for single species can not be extended to this model. If there are multiple stable equilibrium points, the change of the dominant fish species, catastrophic and irreversible change of each equilibrium catch may be observed when the perturbation by the exploitation is added. This phenomenon immediately reminds us of the change of the dominant fish species between Japanese common mackerel and Pacific saury in the northwest Pacific Ocean. In case of the management of two competing fish species with nonlinear interactions, the consideration on the balance between the fishing pressure for each species may be as important as the decision on the catch limit for each species. MSY level for each species based on the single-species theory could be quite erroneous.     

Measuring Human Development: A Multi-criteria Approach

In 2010 the Human Development Index (HDI) was revised with several major changes. Many of its problems were tackled, although some drawbacks still persist. This paper proposes a multi-criteria approach to measure human development, propounding two innovations for the computation of the HDI: (1) the introduction of a double reference point scheme in the normalization; (2) an aggregation function which deals with the problem of substitutability between components. In particular, for each component of the HDI the value of each country is normalized by means of two reference values (aspiration and reservation values) by using an achievement scalarizing function that is piecewise linear. Aggregating the new normalized values, we calculate a range of indices with different degrees of substitutability: (1) a weak index that allows total substitutability; (2) a strong index that measures the state of the worst component and allows no substitutability; and (3) a mixed index that is a combination of the first two.     

A behavioral two‐sex marriage model

In this paper we propose a particular marriage model, i.e., a model for the number of marriages for each age combination as a function of the vectors of the number of single men and women in each age group. The model is based on Dagsvik (2000) where it is demonstrated that a general type of matching behavior imply, under specific assumptions about the distribution of the preferences of the women and men, a convenient expression for the corresponding marriage model.

Data from the Norwegian Population Register for nine years are applied to estimate the model. We subsequently test the hypothesis that, apart from a random “noise”; component, the age‐specific parameters of the model change over time according to a common trend. We find that the hypothesis is not rejected by our data.     

The analysis of linkages in demographic theory

Many seemingly different questions that arise in the analysis of population change can be phrased as the same technical question: How, within a given demographic model, would variable y change if the age- or time-specific function f were to change arbitrarily in shape and intensity? At present demography lacks the machinery to answer this question in analytical and general form. This paper suggests a method based on modern functional calculus for deriving closed-form expressions for the sensitivity of demographic variables to changes in input functions or schedules. It uses this “linkage method” to obtain closed-form expressions for the response of the intrinsic growth rate, birth rate, and age composition of a stable population to arbitrary marginal changes in its age patterns of fertility and mortality. It uses it also to obtain expressions for the transient response of the age composition of a nonstable population to time-varying changes in the birth sequence, and to age-specific fertility and mortality patterns that change over time. The problem of “bias” in period vital rates is also looked at.     

Rapid evolution of larval development time during mass-rearing in the melon fly, Bactrocera cucurbitae

A quantitative genetic analysis of rapid evolution of a life history trait has been conducted on the first 24 generations of mass-rearing in the melon fly Bactrocera cucurbitae (Coquillett) (Diptera: Tephritidae). The phenotypic variance of larval development time in each generation was divided into genetic and residual components. Mean and phenotypic coefficients of variation of larval development time decreased gradually as generations proceeded as a result of artificial selection for shorter larval period in the mass-rearing procedure. There was a trend that additive genetic coefficients of variation in larval development time decreased with generations. These changes are entirely attributed to genetic responses to laboratory selection under the mass-rearing environment because the population was maintained at a very large size so as to exclude random genetic drift and inbreeding depression, which would be other factors responsible for the observed genetic changes. The residual coefficients of variation in larval development time did not change with generations. Realized heritability of larval development time was low. The heritabilities for larval development time estimated from parent–offspring regression at generations 60 and 70, when the evolutionary plateau was asymptotically reached, were not significantly larger than 0. Received: April 22, 1999 / Accepted: September 20, 1999     

The solution of time‐dependent population models

We analyze the dynamics of age‐structured population renewal when vital rates make a transition in a finite time interval from arbitrary initial values to any specified final values. The general solution to the renewal equation in such cases is obtained. This solution describes the birth sequence explicitly, and also leads to a general formula for population momentum. We show that the duration of the transition determines the complexity of the solution for the birth sequence. For transitions that are completed in a time smaller than the maximum age of reproduction, we show that the classical Lotka solution found in every textbook also applies, with a small modification, to the time‐dependent case. Our results substantially extend previous work that has often focused on instantaneous transitions or on slow and infinitely persistent change in vital rates.     

An overview of demographic analysis as a method for evaluating census coverage in the United States

"Since the 1950 U.S. census, demographic methods based on the fundamental balancing equation of demography have played an important role in the evaluation of the census net undercount. Application of this set of methods, called demographic analysis, results in national estimates of the net undercount for age-race-sex groups. Although results of demographic analysis are readily available in Bureau of the Census publications, the procedures used to estimate each of the components of population change are less well-known. In this paper we review the historical foundation of demographic analysis, beginning with Coale's 1950 census evaluation project and concluding with the recent evaluation of the 1990 census. We examine each of the components of the method, how their estimation has changed over time, and how they were estimated for the 1990 census."     

Determinants of Self-Rated Health Among Canadian Seniors Over Time: A Longitudinal Population-Based Study

Self-rated health has been found to be an effective and inexpensive measure of people’s overall health. Although cross-sectional studies have identified determinants of self-rated health (SRH), there is a limited insight into the determinants of SHR overtime and their impact on the change of SRH overtime. This present study compares determinants of SRH among a large community-dwelling cohort of Canadian seniors (N = 3255) at three points in time (1991, 1996, and 2001), and examines the effects of determinants on change in SRH over a 10-year period. Data analyzed were from the Canadian Study of Health and Aging—a large-scale longitudinal population-based study conducted between 1991 and 2001. The results showed that most seniors (over 80 %) rated their health as good, and their SRH remained surprisingly constant over time. Only a person’s physical and instrumental functioning and the number of chronic diseases were consistently associated with SRH at each point in time (1991, 1996, and 2001). Factors including cognition, daily functioning, chronic disease, and availability of help were significantly linked to self-rated health over time. These determinants should be considered important stimuli for improving health among seniors.     

Cost versus effectiveness of different birth control methods

Abstract This paper is an empirical investigation of the mix of birth control methods that would be, allocationally efficient in a real population. Current British resource cost and effectiveness data for each method are presented in order to test the prevalent opinion that expenditure on abortion is allocationally inefficient. Even when abortion resources are valued to give a conservatively high cost, however, this opinion is not upheld. When both quantifiable resource costs and effectiveness are plotted for each method, some linear combination of coitus interruptus, and coitus interruptus with all failures terminated by abortion is shown to be the allocationally efficient frontier.     

Components of change in adolescent fertility, 1971–1979

This article disaggregates change in adolescent fertility between 1971 and 1979 into four components: change in marriage patterns, in nonmarital sex, in pregnancy, and in birth. It also assesses quantitatively the relative contribution of each component to the change over time in two fertility outcomes: the probability of a nonmarital live birth and, given a live birth, the odds of its being nonmarital. The changes in the probability of sexual debut prior to marriage and in marriage patterns themselves are the two most important contributors to these changes. The influence on the change in adolescent fertility outcomes of the decreased likelihood of marriage following a nonmarital pregnancy was compensated for by the increased use of abortion to terminate the pregnancy.     

Modeling interregional migration flows: Continuity and change

This paper addresses the question of how to formally represent the spatial structure of an observed origin‐destination‐specific pattern of interregional migration flows. Such a representation allows an analyst to compare the spatial structures of different migration regimes and contrast their changes over time. It also facilitates the indirect estimation of migration flows, in the absence of such data, by allowing the analyst to impose a particular age or spatial structure when observed flow data are inadequate, partial, or completely nonexistent. In this paper, we focus on the level and allocation aspects (or the generation and distribution components) of age‐specific interregional migration flows. We find that over time these flows exhibit strong regularities that can be captured by generalized linear models, which can then be used in situations where data are inadequate or missing to indirectly estimate interregional migration patterns.     

泛珠江三角洲经济圈城市职能结构特征与分类研究

以城市的基本活动为出发点，运用因子分析法对泛珠江三角洲经济圈城市职能结构特征进行测度，并基于纳尔逊分类法对经济圈整体的城市职能进行分类。得出以下结论：经济圈以生产性和政策性职能为主，以其作为专业职能的城市数量占总数的比重超过80%，随时间演进，经济圈的生产性、服务性和基础性职能不断强化而政策性职能逐渐减弱；经济圈各产业部门整体的职能强度较低，侧重于多行业共同发展，拥有多种专业职能的城市为经济圈的主体；经济圈城市职能的专业化程度存在明显的空间分异，未来城市职能定位应基于现实职能特征进行调控。     

Capital accumulation,inertia of consumption and norms of reproduction

A model of capital accumulation is built in relation with fertility and consumption. Avoiding to impose a direct analytical relationship between these three variables, the author studies the set of possible evolutions under the constraints imposed by the inertia of habit change.The conflict between the necessity to avoid impoverishment, the desire to increase consumption when possible and the reproduction intensity delineate the set of viable solutions and the set of attitudes leading to capital extinction. This qualitative view of change of behaviors provides an alternative explanation to historical fertility fluctuations outside the usual Easterlin framework.I am grateful to the three anonymous referees, who helped to improve this article.     

The multiregional matrix growth operator and the stable interregional age structure

Current population-forecasting efforts generally adopt minor variants of the cohort-survival projection method. This technique focuses on a population disaggregated into cohorts, a group of people having one or more common characteristics at a point in time and, by subjecting each cohort to class-specific rates of fertility, mortality, and net migration, generates a distribution of survivors and descendants of the original population, at successive intervals of time.Although cohort-survival methods take on a large number of variations, they all are essentially trend-based, dynamic, aspatial models of growth. The temporal element is introduced by a recursive structure which operates over a sequence of unit time intervals. The spatial dimension, when it is included at all, typically is accommodated by replicating the analysis over as many areal units as comprise the study area. Realistically, however, time and space need to be considered jointly in population-forecasting models. The need for interregional models which systematically introduce place-to-place movements and simultaneously consider the spatial as well as the temporal character of interrelated population processes is becoming increasingly apparent.Recently several demographers have taken advantage of the conceptual elegance and computational simplicity of matrix methods of population analysis. Their models, however, assume a "closed" population which is subject only to the processes of fertility and mortality. These, therefore, are not directly applicable to interregional "open" systems in which migration is frequently a much more variable and important contributor to population change than births or deaths. However, a natural extension of the demographer's matrix model allows one to incorporate place-to-place migration and provides an integrated interregional population-forecasting model which easily may be programmed for any of the current generation of digital computers. Such a model is outlined in this paper.     

An automatic-democratic approach to weight setting for the new human development index

Perhaps the most difficult aspect of constructing a multi-dimensional index is that of choosing weights for the components. This problem is often bypassed by adopting the ‘agnostic’ option of equal weights, as in the human development index. This is an annual ranking of countries produced by the United Nations Development Programme based on life expectancy, education, and per capita gross national income. These three dimensions are now aggregated multiplicatively. Whatever weights (exponents) are chosen for these dimensions, some nations will feel disadvantaged. To avoid the use of arbitrary weights, we propose for consideration a two-step approach: (1) find the most advantageous set of weights for each nation in turn, and (2) regress the associated optimal scores on the underlying indicators to find a single weight set. This approach has the properties of non-subjectivity, fairness, and convenience. The result is that the highest weight is placed on the life expectancy dimension.     

Test of a field theory of consciousness and social change: Time series analysis of participation in the TM-Sidhi program and reduction of violent death in the U.S.

This study is part of a research program to test the hypothesis that consciousness has a fundamental field property that is relevant to social change in the direction of improved quality of life. The exogenous variable was the number of participants in the group practice of the Transcendental Meditation (TM) and TM-Sidhi program, a technology of consciousness predicted to reduce stress in society through a field of pure consciousness. The period of the study was 1982–1985, during which the size of a group of participants in Iowa was sufficient to have a measurable influence on the U.S. much of the time, according to theory; a secondary analysis also considered the period 1979–1985, including the time when the group of participants was smaller. The endogenous variable was a violence index comprising the number of weekly fatalities in the U.S. due to three major causes of violent death: motor vehicle fatalities, suicide, and homicide. Time series analysis using both the intervention analysis approach and the transfer function approach indicated a significant reduction in the violence index associated with the exogenous variable. Alternative hypotheses are discussed, as are the theoretical and practical implications of these findings for understanding social change and improving the quality of life.     

Measuring change and continuity in parity distributions

Procedures are developed to allocate the change in mean fertility to the change in specific parities or groups of parities. One procedure uses the proportion at each parity and another uses parity progression ratios. Both are based on the delta method for approximating change in a function of several variables. Drawing on an analogy to survival in a life table, the relational logit model is applied to parity progression. This method allows several parity distributions to be synthesized and to have differences summarized with two parameters. The three procedures are applied to successive cohorts of white U.S. women who completed their childbearing between 1920 and 1980.     

Dynamics of distribution in animal communities: Theory and analysis

Summary Theoretical and analytical problems of the dynamics of distribution and abundance in animal communities were examined. In many communities, species with low abundance and of limited spatial occurrence (i.e., rare species) typically form a conspicuous peak when a frequency distribution of the number of species is constructed with respect to the proportion of sites occupied within an area of distribution. Models of distribution dynamics, including a new model proposed here, were compared with a range of animal community data using a new procedure to assess single- and bi-modal patterns in frequency distributions of spatial occurrence. Data reveal that single-modality with an excess of rare species occurs more frequently than bimodality. Even when bimodality is detected, the mode representing wide-spread species is in the majority of cases smaller than that for rare species. Thus, a new model in which the rate of local extinctions is assumed to be negatively related to patch occupancy (or population abundance) is in better agreement with observed data than earlier models. Some problems of analysis, in particular model assumptions and testing, are discussed.