A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes

Mortality forecasts are critically important inputs to the consideration of a range of demographically-related policy challenges facing governments in more developed countries. While methods for jointly forecasting mortality for sub-populations offer the advantage of avoiding undesirable divergence in the forecasts of related populations, little is known about whether they improve forecast accuracy. Using mortality data from ten populations, we evaluate the data fitting and forecast performance of the Poisson common factor model (PCFM) for projecting both sexes’ mortality jointly against the Poisson Lee–Carter model applied separately to each sex. We find that overall the PCFM generates the more desirable results. Firstly, the PCFM ensures that the projected male-to-female ratio of death rates at each age converges to a constant in the long run. Secondly, using out-of-sample analysis, we find that the PCFM provides more accurate projection of the sex ratios of death rates, with the advantage being greater for longer-term forecasts. Thus the PCFM offers a viable and sensible means for coherently forecasting the mortality of both sexes. There are also significant financial implications in allowing for the co-movement of mortality of females and males properly.     

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 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.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.     

A model for analyzing insect stage-frequency data when mortality varies with time

Summary A model is developed for the analysis of insect stage-frequency data which may be applied to populations with age-dependent mortality. The analysis of stage-frequency data is divided into two steps. In the first step, the number of different mortality rates and their values are estimated. The second step provides estimates of developmental rates and variances for each developmental stage and in addition provides estimates of the number of recruits to each stage. The model may be used both in analysis and prediction of insect stage frequencies. Hence, in addition to estimating developmental and mortality rates from stage-frequency data, it may also be used as a simulation model for an insect population. The model is applied to two populations ofHemileuca oliviae Cockerell, a lepidopterous pest of New Mexico grasslands. The model identifies, in the two populations, different mortality rates that are related to plant productivity.     

A mortality model based on a mixture distribution function

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman–Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman–Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture ‘accident humps’).     

A framework for modelling fertility motivation in couples

We present a theoretical framework that organizes individual-level fertility motivations into a couple-level model. One feature of this framework is the Traits-Desires-Intentions-Behaviour (TDIB) sequence through which the fertility motivations of individuals produce instrumental behaviours that are designed to promote or prevent childbearing. A second feature of this framework is the cognitive capacity of individuals to perceive a partner's motivational structure. We combine these two features into a dyad-level model that addresses interactions between partners at each step of the motivational sequence. We elaborate this model first with respect to the perception of partner's motivational structure and second with respect to the combination of partner's and own motivational structure. In the process we consider how couple-level processes of communication, influence, and disagreement can be measured and studied through these interactions. We conclude with a summary discussion of the framework and a consideration of the implications it has for a theory of reproductive psychology, population surveys, and family planning services.     

A census-based method for estimating adult mortality

Abstract A simple method is presented for converting an age distribution in any closed population into the stationary population corresponding to its current mortality conditions. The conversion only requires a set of age-specific growth rates, which will normally be available from successive censuses. From the stationary population, any life table mortality measure of interest can be computed. The index most robust to normal data errors in developing countries is life expectancy, and the paper focuses on its calculation. The sensitivity of results to various forms of data error is considered, and procedures are proposed for removing errors resulting from differential census coverage completeness and from age misstatement at older ages. Applications of the procedures are made to data from Sweden, India and South Korea. Because of the absence of a radix, estimation of life expectancy usually will begin at the fifth birthday.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

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 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.     

The use of model life tables to estimate mortality for the United States in the late nineteenth century

This paper seeks to extend our knowledge about mortality in the late nineteenth century United States by using census mortality data for older children and teenagers to fit model tables. The same method can also be used with partially underregistered death data. The most commonly used model tables, the Coale and Demeny West Model, apparently do not adequately depict the changing shape of mortality over the period 1850--1910. An alternative model life table system is presented, based on the Brass two parameter logit system and available reliable life tables from the period 1850--1910. The two parameter system must be reduced to a one parameter system by means of estimated relationships between the parameters so that the fitting procedure can be used. The resulting model system is, however, heavily dependent on the experience of northern, industrial states, especially Massachusetts.     

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 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 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 stochastic computer model for simulating population growth

Summary A model is described for investigating the interactions of age-specific birth and death rates, age distribution and density-governing factors determining the growth form of single-species populations. It employs Monte Carlo techniques to simulate the births and deaths of individuals while density-governing factors are represented by simple algebraic equations relating survival and fecundity to population density. In all respects the model’s behavior agrees with the results of more conventional mathematical approaches, including the logistic model andLotka’s Law, which predicts a relationship betwen age-specific rates, rate of increase and age distribution. Situations involving exponential growth, three different age-independent density functions affecting survival, three affecting fecundity and their nine combinations were tested. The one function meeting the assumptions of the logistic model produced a logistic growth curve embodying the correct values orr _m andK. The others generated sigmoid curves to which arbitrary logistic curves could be fitted with varying success. Because of populational time lags, two of the functions affecting fecundity produced overshoots and damped oscillations during the initial approach to the steady state. The general behavior of age-dependent density functions is briefly explored and a complex example is described that produces population fluctuations by an egg cannibalism mechanism similar to that found in the flour beetleTribolium. The model is free of inherent time lags found in other discrete time models yet these may be easily introduced. Because it manipulates separate individuals, the model may be combined readily with the Monte Carlo simulation models of population genetics to study eco-genetic phenomena.     

A model for culturally adapting a learning system

The Cross-Cultural Adaption Model (XCAM) is designed to help identify cultural values contained in the text, narration, or visual components of a learning instrument and enables the adapter to evaluate his adapted model so that he can modify or revise it, and allows him to assess the modified version by actually measuring the amount of cultural conflict still present in it. Such a model would permit world-wide adaption of learning materials in population regulation. A random sample of the target group is selected. The adapter develops a measurin g instrument, the cross-cultural adaption scale (XCA), a number of statements about the cultural affinity of the object evaluated. The pretest portion of the sample tests the clarity and understandability of the rating scale to be used for evaluating the instructional materials; the pilot group analyzes the original version of the instructional mater ials, determines the criteria for change, and analyzes the adapted version in terms of these criteria; the control group is administered the original version of the learning materials; and the experimental group is administered the adapted version. Finally, the responses obtained from the XRA rating scale and discussions of both the experimental and control groups are studied and group differences are ev aluated according to cultural conflicts met with each version. With this data, the preferred combination of elements is constructed.