A reducible four-parameter system of model life tables

Abstract In this paper a four-parameter extension of Brass's relational system of model life tables is suggested that (1) matches a wide range of empirical age patterns of mortality, (2) is easy to apply, especially to partial life tables, and (3) contains demographically meaningful parameters. A test of the model on a set of 62 empirical life tables indicates that four parameters are necessary and sufficient for fitting a wide range of mortality patterns. A further test on an historical series of Swedish life tables reveals a consistent pattern of mortality change. Examination of the parameters for a set of geographicallyrelated life tables suggests a way to define families of life tables. Identification of such temporal and spatial relationships allows the model to be reduced to a form with twoor three-parameters for application to incomplete or inaccurate data.     

A design for a census information retrieval system

This article explores the methodology of designing a storage and retrieval system for information on the nature and subjects of censuses published internationally over the past two decades. The essential key is neither data storage nor bibliography but an index which will tell a researcher what censuses provide information on particular population characteristics and how those characteristics are defined, mapped, cross-indexed, compared, and discussed.The index should be based on specific, inclusive, and flexible classifying terms. The authors arrive at 24 variables which are grouped on two levels-category and specific item-by the use of either main tables or indexes. The use of indexes is preferred for its reduction of clerical and computer time.In addition to the index (which should be made available in machine-readable form), the authors suggest the concomitant publication (on the basis of unified classifications) of an analysis of the relative value of different definitions of population characteristics, a merged-item vocabulary, and indexes to various censuses. Once the study has developed beyond an experimental phase limited in geographic extent and in time, the authors envision a continuing service which will provide indexes to all new censuses.     

A log-logistic regression model for a transition rate with a starting threshold

The paper presents a new type of parametric transition rate model that is particularly suitable for studying household and union formation. In such studies, it is often not easy to determine the moment at which individuals actually enter the population at risk - or at least when the risk begins to become socially important. Even in the presence of regulations stipulated by law, one might be interested in studying ‘social’ timetables. We assume that there is a constant rate for any duration and that after a certain threshold point a log-logistic rate is added, with this threshold as its time origin. This can be justified in a behavioural sense by assuming that random and social transitions arise from separate processes. We then apply the model to union formation in Italy and show how threshold and intensity effects generated by theoretical hypotheses can be revealed.     

A modification of a continuous time model for first conception

The interval between marriage and the first conception leading to a live birth plays an important role in the determination of fertility components. Several probability models (Potter and Parker, 1964; Singh, 1961, 1964, 1967) based on varying sets of assumptions relating to this interval have been propounded in the recent past. All of them are based on the assumption that the females under study are susceptible to conception at the time of marriage. However, in certain situations, where some of the females already pregnant at the time of marriage report to have conceived within a short interval following marriage, this condition is not satisfied and these models become unsuitable. A probability distribution which is an inflated form of the continuous model proposed by Singh, for the time of the first conception leading to a live birth, is presented in this paper. It describes reasonably well the data on first conception times in the context of premarital conceptions. Simple expressions for the maximum likelihood estimators of the parameters involved in the model are obtained and a method for finding the asymptotic covariance matrix of the estimators is outlined. The model is applied to four sets of data.     

Programmed learning: a training alternative for population workers

Self-instruction (SI), also termed programmed learning, is a fairly new family planning training tool adopted in 1975 by the National Population Program in the Philippines. According to Antonia Coronel, project officer of the Population Center Foundation (PCF), SI uses carefully designed materials in order to meet specific objectives. The information is presented in logically sequenced small frames or sets and is followed by a series of practice exercises requiring immediate feedback from the learner. The learner's reward takes the form of correct answers at the frames' end. There are many forerunners to SI, including the Greek philosopher Socrates, the Roman orator Quintilian, and the American social scientist Sidney Pressey who thought of a programmed instructional review and multiple-choice testing materials as devices which required the learner's active participation and provided immediate knowledge of his/her accuracy. SI has 6 characteristics: emphasis on the needs of the learner shown by allowing self pacing, meaning, the learner proceeds at his/her own learning rate, and stressing feedback from the trainer who holds individual meetings with the learners; a clear statement of objectives; a breakdown of learning tasks into smaller and easy to absorb units; a self administered posttest which enables the learner and others to see whether or not the objectives have been realized; inclusion of frequent practice exercises relevant to the objectives and the posttest; and provision of immediate feedback, which reinforces and lets the learner improve his/her comprehension and retention. Operationally, the method takes 4 steps: the objectives of instruction are specified in terms of learner behavior; the learner is rated as to his/her level of knowledge with respect to the objectives; instructional activities built into SI modules are designed to bring about the intended objectives; and the learner's attainment of the objectives is evaluated. The modules referred to are the 12 SI modules on various aspects of family planning developed by the PCF. In the Philippines the need for programmed learning became apparent with the signing of Presidential Decree No. 79. Among the provisions of this decree are the following: nurses and midwives can dispense oral contraceptives (OCs) and insert IUDs; large business firms and factories must provide family planning services to their employees; and family planning services like sterilizations costs can be charged to Medicare. The SI method met the criteria of giving uniform training, cutting down training costs, and ability to upgrade knowledge, attitudes, and skills. Thus far there are 21 completed program learning materials and these are identified and described.     

A mathematical model of the food-consumer system I. A case without food replenishment

Summary A simple mathematical model was proposed to describe the dynamics of a food-consumer system. The model was based on the Logistic Theory and consisted of Eqs. (4), (5) and (6). The model was divided into the following three cases for further analyss; i) without food supply except at the initial time, ii) with continuous food supply at a constant rate, and iii) with food supply at varying rates. Only the first model was dealth with in this paper. The assumptions of the model 1 are that a definite amount of food is given only once at the initial time and only the feeding by animals is responsible for the decrease of food, and that the rate of decrease is proportional to the amount of animals. It is also assumed that the growth of animal population is represented by the logistic curve, and that the upper limit of the population is proportional to the amount of food at that time. For simplicity the parameters of basic differential equations are assumed to be constant throughout the time course. Analytical solutions of this non-linear model were given by Eqs. (8), (9), (10) and (11). The properties of time course of the food amount and consumer population were discussed from the mathematical and biological points of view. The method of the estimation of the three constants λ,b, andc from the experimental data was also suggested. Since we had no available data for animal populations, we applied the model, regarding reserve substance asx and new plant body asy, to the data of the initial growth of Azuki bean plant in the dark. This model is very simple, but it may be useful for analyzing the behavior of food-consumer system. And it may give some clue to the analysis of the more complex systems.     

The species-area relation III. A third model for a delimited community

A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed.     

A probability model for census adjustment

The census can be adjusted using capture‐recapture techniques: capture in the census, recapture in a special Post Enumeration Survey (PES) done after the census. The population is estimated using the Dual System Estimator (DSE). Estimates are made separately for demographic groups called post strata; adjustment factors are then applied to these demographic groups within small geographic areas. We offer a probability model for this process, in which several sources of error can be distinguished. In this model, correlation bias arises from behavioral differences between persons counted in the census and persons missed by the census. The first group may on the whole be more likely to respond to the PES: if so, the DSE will be systematically too low, and that is an example of correlation bias. Correlation bias is distinguished from heterogeneity, which occurs if the census has a higher capture rate in some geographic areas than others. Finally, ratio estimator bias and variance are considered. The objective is to clarify the probabilistic foundations of the DSE, and the definitions of certain terms widely used in discussing that estimator.     

A three parameter model for birth projections

The approach underlying the model proposed in this article constitutes a considerable departure from the conventional methods used for the projection of birth series. Instead of following the customary procedure of directly projecting the age-specific fertility rates, they can be derived with this model from only three relatively simple fertility measures, namely, total fertility rate, mean age of fertility, and modal age of fertility. The reduction of the number of fertility parameters offers appreciable operational and analytical advantages. Among these, the most significant is the fact that statistical manipulation is confined to only three fertility measures, all of which are particularly appropriate for the in-depth analysis which is required to provide a rationale for assumptions of future fertility.     

A modified hurdle model for completed fertility

In this paper it is argued that models for completed fertility have to take into consideration that childless couples and couples with an only child are qualitatively different from couples with two or more children. Indeed, these differences may be the cause of the underdispersion that characterizes completed fertility data. An empirical illustration using Portuguese data suggests that accounting for the qualitative difference between having zero, one, or more children leads to considerable improvements over a model of the type generally used to describe this sort of data.     

A Gompertz model for birth interval analysis

During recent years birth intervals have been analysed on a life table basis. This method retains both closed and open intervals, and so reflects behaviour that deliberately avoids the next birth entirely. When life tables are prepared separately for each birth order, markedly different patterns of movement toward the next birth can appear from one parity to the next. This is illustrated for Korean survey data, with historical trends given across marriage cohorts.

A Gompertz model is found to fit the family of curves that show the cumulative proportion giving birth within each interval closely. Its three parameters have direct intuitive interpretations, one being equal to the parity progression ratio and the other two controlling the pace of childbearing before and after the point of peak activity within the interval. The model is useful for interpolation and projection, and provides an efficient summary of the otherwise cumbersome detail given in a life table. Testing against additional data sets is suggested.     

A mathematical model for the survivorship curve

Summary A mathematical function describing the various kinds of survivorship curve is formulated with the useful parameter, environmental capacity. Three types of the survivorship curve illlustrated byDeevey can be obtained from changing the value of this function. When a cohort is large and the competition occurs in the scramble type, this function shows the third type ofDeevy's and this to the first type in the case of low density and the contest type of competition. But the second type would rather be obtained by the action of density independent agencies. Contribution from the Entomological Laboratory, Kyoto Univeristy. No. 400.     

A three parameter model for birth projections

Abstract The approach underlying the model proposed in this article constitutes a considerable departure from the conventional methods used for the projection of birth series. Instead of following the customary procedure of directly projecting the age-specific fertility rates, they can be derived with this model from only three relatively simple fertility measures, namely, total fertility rate, mean age of fertility, and modal age of fertility. The reduction of the number of fertility parameters offers appreciable operational and analytical advantages. Among these, the most significant is the fact that statistical manipulation is confined to only three fertility measures, all of which are particularly appropriate for the in-depth analysis which is required to provide a rationale for assumptions of future fertility.     

A temporary equilibrium model for international migration

This paper is concerned with the existence of temporary equilibria of migration with an overlapping generation structure and analyzes some of its properties. In the first part of the paper sufficient conditions for the existence of a temporary equilibrium of migration (in a given period) are given. In the second part some interesting properties of migration equilibria are analyzed. In particular the effects of differing degrees of information of the individuals on migration equilibria are investigated. Furthermore, it is shown that incomplete information alone suffices to induce migration flows even between countries that can be regarded as identical from an economic point of view.The paper was partly written during a research stay at the Sonderforschungsbereich 178 (University of Konstanz). Financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We wish to thank an anonymous referee for helpful comments.     

A model of the species rank-abundance relation for a community in an open habitat

Summary A mathematical model is proposed to describe the relationship between the abundance and the rank of species in order from the most abundant to the least in a community in an open habitat. This model is derived as a corollary of a species-area equation (Kobayashi, 1975) which could be expected in the case where the individuals of each species are uniformly distributed over a habitat area. Numerical simulation reveals that a rank-abundance curve for a universe results in different species-area or species-individual curves according to the spatial distribution of individuals, and that the relative abundance of each species in a sample varies with sample size unless the spatial distribution of individuals is uniform. A species-individual curve obtained bySanders’s (1968) rarefaction method agrees with that observed actually only for the spatially uniform distribution. Change in the pattern of rank-abundance curve with species diversity and with sample size is discussed in relation to the present model.     

Community perspectives on delivering trauma-aware and culturally safe perinatal care for Aboriginal and Torres Strait Islander parents

BackgroundSince colonisation, Aboriginal and Torres Strait Islander peoples have experienced violence, loss of land, ongoing discrimination and increased exposure to traumatic events. These include adverse childhood experiences which can lead to complex trauma, and are associated with increased incidence of high-risk pregnancies, birth complications and emergence of post-traumatic symptoms during the perinatal period, potentially impacting parenting and leading to intergenerational trauma. The perinatal period offers unique opportunities for processing experiences of trauma and healing yet can also be a time when parents experience complex trauma-related distress. Therefore, it is essential that trauma-aware culturally safe perinatal care is accessible to Aboriginal and Torres Strait Islander parents.AimThis study aimed to understand community perspectives of what ‘trauma-aware culturally safe perinatal care’ would look like for Aboriginal and Torres Strait Islander parents.MethodsData were collected during a workshop held with predominantly Aboriginal and Torres Strait Islander key stakeholders to co-design strategies to foster trauma-aware culturally safe perinatal care. Data were thematically analysed.FindingsFour overarching themes represent proposed goals for trauma-aware culturally safe care: Authentic partnerships that are nurtured and invested in to provide the foundations of care; a skilled workforce educated in trauma awareness; empowering and compassionate care for building trust; and safe and accessible environments to facilitate parent engagement.ConclusionsProvision of trauma-aware culturally safe care achieving these goals is likely to enable parents experiencing complex trauma to access appropriate support and care to foster healing in the critical perinatal period.     

Pareto improving transition from a pay-as-you-go to a fully funded pension system in a model of endogenous growth

In this paper we investigate the possibility of Pareto improving social security reforms within a framework of endogenous growth. Belan et al. (1998) propose a transition from a pay-as-you-go (PAYG) pension system to a system of savings–subsidization. We follow this approach and prove that a Pareto improving conversion from the PAYG system to a fully funded one is possible. Finally, we compare the subsidy system with the fully funded system and discuss the problem of implementing the transition to the fully funded system. Received: 07 March 1999/Accepted: 13 December 1999     

A modified Lee-Carter model for analysing short-base-period data

This paper introduces a new modified Lee-Carter model for analysing short-base-period mortality data, for which the original Lee-Carter model produces severely fluctuating predicted age-specific mortality. Approximating the unknown parameters in the modified model by linearized cubic splines and other additive functions, the model can be simplified into a logistic regression when fitted to binomial data. The expected death rate estimated from the modified model is smooth, not only over ages but also over years. The analysis of mortality data in China (2000-08) demonstrates the advantages of the new model over existing models.