An efficient two-stage randomized response model under stratified random sampling

A two-stage randomized response model is extended to stratified random sampling in order to find out more efficient estimators of proportions built from sensitive questions, which respondents may not answer truthfully, in a population divided into homogeneous subgroups. In each subgroup, the respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating “yes” or “no”. In the latter case, they are required to report the outcome. Such extension provides a more efficient estimator of the proportion of the population having a given sensitive attribute than its counterpart in simple random sampling. The extended two-stage randomized response model is more efficient than the stratified randomized response model, where respondents must answer the sensitive question either in the first or in the second stage. Moreover, it increases the respondents’ cooperation. When strata weights are unknown, they are estimated by the double sampling method.     

Computing a population budget from sequentially sacrificed, replicated cultures

Summary When a population budget must be obtained from censuses based on replicated, sacrificed cultures, it is difficult to obtain estimates of transition probabilities and of the errors of such estimates, because there is no logical basis for pairing successive census counts. In a study of this nature estimating a population budget of immature stages of the housefly, the problem was solved by a randomization treatment of the original census results obtained at two densities. One hundred randomly generated census matrices over all census times for each density were smoothed to remove the effects of sampling error and a population budget constructed according to defined rules. Transition probabilities computed from the population budget were plotted on triangular coordinate paper and mean probabilities, 95% confidence regions for these means, and 95% equal frequency ellipses computed. All computations and the graphing of the results were carried out on a digital computer. The computer program, available from the authors, is written in FORTRAN IV and could be easily modified for similar studies. Contribution No. 1364 from the Department of Entomology, The University of Kansas. This study has been supported by the Medical Research and Development Command of the Office of the Surgeon General of the Army under contract No. DA-49-007-MD-738, U.S.A. and by a Public Health research career program award (No. 3-K3-GM-22, 021-01S1) from the National Institute of General Medical Sciences, U.S.A. to RobertR. Sokal. It was carried out during the tenure of a National Science Foundation predoctoral fellowship by EdwinH. Bryant. The authors appreciate the help of Dr.F.J. Rohlf with computational aspects.     

On the ranking uncertainty of labor market wage gaps

Using a log-wage model, Horrace and Oaxaca (2001) propose estimators of the gender wage gap across industry classifications. One estimator involves the maximum over sample estimates of population parameters, and inference on this estimator follows with the implicit assumption that the sample maximum equals the population maximum. This paper proposes inference procedures for this estimator that relax this assumption. Specifically, multiple comparisons with the best methods are used to construct simultaneous confidence intervals for industry wage gaps. Using data on fourteen industry classifications, inference experiments indicate that differences in gender wage gaps across industries are insignificant at the 95% level.I would like to thank Dan Hamermesh, Dan Houser, Jason Hsu, Tom Kniesner, Ron Oaxaca, and Peter Schmidt for comments. All errors are mine. The generous support of the Office of the Vice Chancellor of Syracuse University is gratefully acknowledged. Responsible editor: Daniel S. Hamermesh.     

Using the Pao as the primary sampling unit. Some notes and reflections on the possibilities of a census of China by sampling

Recently sample surveys of the population have been taken in Greece and the United States. In this paper the author considers how far the methods adopted in these two sample surveys may be applied to a study of the Chinese population. In particular, the pao-chia system of administration would make it possible to have a sampling scheme in which the pao (or district) would be the primary sampling unit. A sampling scheme of this kind has been worked out and is presented at the end of the paper.     

A New Malaysian Quality of Life Index Based on Fuzzy Sets and Hierarchical Needs

The Malaysian Quality of Life Index (MQLI) released by the Economic Planning Unit (EPU), has led authors to search for alternative method of expressing this index. One of the limitations in MQLI computations is the failure to recognise unequal weights for each accounted component. This paper offers a new way of expressing the quality of life index using a mathematical modelling based on fuzzy sets theory and the proposed weights based on Maslow’s theory of hierarchical human needs. The indices of 11 components that were used to compute MQLI, again be gathered as a basis in expressing a new Malaysian Fuzzy Quality of Life Index (MFQLI). The new indices for each component yielded through a normalisation process prior weighting and aggregation to compose a new MFQLI. It was found that a fuzzy sets approach with the inclusion of weights based on human needs yielded a better index of quality of life than the MQLI.     

The impact of incomplete geocoding on small area population estimates

Small-area population estimates are often made using geocoded address data in conjunction with the housing-unit method. Previous research, however, suggests that these data are subject to systematic incompleteness that biases estimates of race, ethnicity, and other important demographic characteristics. This incompleteness is driven largely by an inability to complete georeference address-based datasets. Given these challenges, small-area demographers need further, and to date largely unavailable, information on the amount of error typically introduced by using incompletely geocoded data to estimate population. More specifically, we argue that applied demographers should like to know if these errors are statistically significant, spatially patterned, or systematically related to specific population characteristics. This paper evaluates the impact of incomplete geocoding on accuracy in small-area population estimates, using a Vintage 2000 set of block-group estimates of the household population for the Albuquerque, NM metro area. Precise estimates of the impact of incomplete geocoding on the accuracy of estimates are made, associations with specific demographic characteristics are considered, and a simple potential remediation based on Horvitz-Thompson theory is presented. The implications of these results for the practice of applied demography are reviewed.     

Adjusting Life Expectancy to Account for Disability in a Population: A Comparison of Three Techniques

Sullivan (1971) first suggested weighting life expectancy (LE) to account for the health of a population using a single indicator. Known as disability free life expectancy (DFLEs), this measure was somewhat limited due to a overly simplistic weighting scheme. Its introduction, however, spurred the development of a whole new class of measures known as health expectancy indicators. One of the first, disability-adjusted life expectancy (DALEs) (Wilkins and Adams, 1983), identified the period of time in a particular level of disability and weighted each level accordingly. While the weighting allowed for a health related quality-of-life distinction to be introduced into the DALE measure, the weights, by level of disability, were arbitrarily chosen and fixed for all ages and gender. To overcome this limitation, a health-adjusted life expectancy (HALE) was developed based in large part on the DALE methodology but utilizes more refined weights. The McMaster Health Utility Index Mark III (HUI3)) scores health on a continuum from 0 to 1 and when included on a national health survey, provides estimates that reflect important age, gender, and socio-economic factors. All three measures were calculated for the years 1986, 1991, and 1994 (household and institutional populations). Analysis revealed that HALEs were more appropriate for policy purposes due to their ability to account for indirect morbidity in both a disabled and non-disabled population.     

A Church-Based Sampling Design for Research with Latina Immigrant Women

The U.S. is experiencing its highest immigration rate since the 1930s. The largest proportion of immigrants comes from Latin America, and women constitute a large and growing fraction of this group. Although our knowledge of the relationship between migration and women’s health is increasing, research in this area is still needed, particularly in areas experiencing rapid changes in their Latino populations. Yet research is impeded by the absence of an adequate sampling frame: Latina immigrants remain a largely hidden population. This study tests in four North Carolina counties a church-based sampling frame for Latina immigrant women in their reproductive years. In the study area, on an average week, 20% of the Spanish-speaking population attends church (two-thirds are Catholic). Compared against Census data for the study area, the study sample (n = 706) provided a comparable representation of different national origins. New entrants to the U.S. and married women were overrepresented in the church-based sample. The young (under age 30), and women at the lowest and highest extremes of educational attainment were underrepresented in churches. While a church-based sample is not entirely comparable to the Census, churches can provide timely and cost-effective access to a rapidly changing population of new immigrants. Church-based research should be complemented with research in other settings, adjusting sampling weights for overlap between sampling frames.     

对我国2010年人口普查事后调查工作的若干建议

人口普查不可能100％计数每一个人。世界上许多国家都在人口普查后组织事后调查,使用双系统估计量另行求得一个全国人口真实数的估计数,并以此为标准估计人口普查的净遗漏率。我国历次人口普查后都进行了事后调查,其主要缺陷是未对抽取的样本事后分层,未估计“全国真实的人口数”。建议我国2010年事后调查方案在克服这两个缺陷的基础上科学确定全国的样本总量。实行两步抽样等。     

A refined estimator of measures of location of the age at first marriage

Because of bias of unknown sign and extent introduced by age misreporting when calculating the singulate mean age of marriage in the usual manner, Van de Walle has suggested a fairly robust estimator based on stable population structure. Unfortunately not much is known about the properties of this estimator. Various demographers have argued informally that it indeed estimates the SMAM; others feel that it instead estimates the mean age of marriage in a cohort, the mean age of marriage in the stable population, or the singulate median age of marriage. In this paper the properties of this estimator are examined. Further, extensions of the Van de Walle estimator based on regression are shown to be significantly superior to the estimator alone.     

Estimating adult mortality levels from information on widowhood

Summary A range of indirect techniques has been developed for mortality estimation in societies lacking adequate vital registration records. Information on orphanhood has been widely used as an estimator of adult mortality, with generally plausible results. Doubts have remained, however, about potential biases, and the method is less satisfactory for the estimation of male mortality. Information on widowhood, or more strictly the survival of first spouse, has several possible advantages over information on orphanhood. Model first marriage functions and model life tables are used to calculate proportions widowed of first spouse, for both females and males, by marital duration and by age. These proportions widowed are then related to life table survivorship probabilities to provide weighting factors for the conversion of observed proportions widowed into estimates of survivorship probabilities. The application of the method is illustrated with data collected by the 1974 post-enumeration survey of Bangladesh, with apparently encouraging results.     

A long period multistate life table using micro data

"The multistate life table (MLT) has been widely used by demographers for the past twenty years. However, the pivotal Markov condition upon which the entire methodology rests is rarely satisfied in practice. We lessen reliance upon the assumption by computing transition probabilities for longer periods of time than was previously practical. An extended Kaplan-Meier estimator accomplishes this task, simultaneously addressing the issue of censoring.... We provide an illustrative example of a 10-year period MLT, with comparison to a 1-year period MLT." The data for California are used as an illustration. (EXCERPT)     

The Eventual Frequencies of Kin in a Stable Population

Associated with every real birth cohort of women is a set of probabilities {f _k} of eventually having _k daughters. With a variant of stable population theory, these probabilities are used to generate the entire probability distributions, as well as all moments, for all categories of kin who are female and female-related. With additional assumptions, a full two-sex model for all kin also is given. The two-sex model is applied to a cohort of U.S. women born in the mid-twentieth century, suggesting plausible frequencies of kin in a stationary population.     

中国女性初婚模式变动趋势研究

20世纪80年代以来我国女性的初婚模式发生了显著的变化。本文使用人口普查资料、全国1%人口抽样调查数据、人口变动情况抽样调查数据以及IPUMS数据,通过女性平均初婚年龄、曾婚比例、年龄别初婚概率、终身结婚期待率和预期单身寿命等指标探究我国女性自20世纪80年代以来的初婚模式变动情况。研究发现30多年来我国女性平均初婚年龄在波动中上升,到2017年女性平均初婚年龄已经达到25.60岁,而教育程度的提高会推迟女性进入婚姻的时间,接受过高等教育的女性平均初婚年龄明显高于未受过高等教育的女性;另外,通过对各教育程度平均初婚年龄标准化与分解看到随着时间的推移,教育对女性的平均初婚年龄影响作用增大;20-30岁年龄段女性婚姻推迟明显,曾婚比例不断降低,但女性终身未婚比例很低,其中受过高等教育的女性婚姻推迟现象最为明显,但其自身的结婚意愿并未降低,大部分女性只是推迟结婚时间,并不是不结婚。对净婚姻表各指标进行计算发现1982-2010年女性的年龄别初婚概率下降,尤其在20-30岁年龄段下降明显,初婚峰值年龄推迟,结婚年龄集中现象减弱。终身结婚期待率下降速度趋缓,随着女性初婚年龄的推迟,2010年27岁之后的终身结婚期待率要高于1990年与2000年,29-35岁女性的预期单身寿命也较前30年低,较大年龄未婚女性结婚等待时间缩短。     

Composite Indicator of Social Inclusion for European Countries

Social inclusion is one of the key challenges of the European Union (EU) Sustainable Development Strategy. We use four indicators from EU policies to measure social inclusion for the 27 member countries of Europe. In particular, we aggregate the four indicators in a multiplicative composite indicator via a DEA-BoD approach with weights determined endogenously with proportion constraints. We obtain a score of social inclusion that allows us to grade the 27 EU countries from 2006 to 2010. In this way, we highlight the specific role played by the four indicators in determining improvements and deteriorations of social inclusion during the European phase of the financial and economic crisis.     

The estimation of Unwanted Fertility

The estimation of unwanted fertility is a major objective of demographic surveys, including DHS surveys conducted in Asia, Africa, and Latin America. Levels and trends in unwanted fertility are important input to the formulation of population policy and the evaluation of family planning programs. Yet existing methods for estimating unwanted fertility are known to be defective, among other reasons because they rely on subjective data whose validity and reliability are questionable. In this article, we propose a new estimator of unwanted fertility-the "aggregate prospective estimator"--so named because it depends on the stated preference for another child at the time of the survey, the fertility-desires item consistently shown to possess the highest validity and reliability. Under reasonable assumptions, the aggregate prospective estimator produces less biased estimates of unwanted fertility than the most widely used existing methods. The new estimator has the limitation of generating only aggregate-level estimates, but such estimates are the primary data for policy formulation and program evaluation. The new estimator is presented in this article, along with an evaluation of its underlying assumptions and its sensitivity to several sources of error. In an illustrative application to recent DHS data from six countries, the new estimator yields substantially higher estimates of unwanted fertility than existing methods in all six countries.     

Application of the “Benefit-Of-the-Doubt” Approach for the Construction of a Digital Access Indicator: A Revaluation of the “Digital Access Index”

The use of composite indicators as a tool for ranking and making decisions is ever increasing in a world marked by the inequalities and competition in all domains. However, the dependence of countries ranking on the weighing scheme used to aggregate individual indices or sub-indicators, most of the time set by experts/stakeholders may weaken the credibility of composite indicators. One method which is able to overcome these limits is the “Data Envelopment Analysis” approach, particularly named “Benefit-Of-the-Doubt” in the context of composite indicators’ construction. We propose a revaluation of the Digital Access Index given that Information technology is the most important factor driving improvement in a wide array of areas critical for the quality of life for individuals as well as societies. We have shown that this method is more suitable for identifying trends and drawing attention to particular issues and also for setting policy priorities. In fact, the weights of the individual indices, used to compute the composite indicators are based on the data itself and are proper for the country under consideration. These weights contain adequate information in order to help policy-makers to better understand the nature of the new innovation economy and the types of public policies needed to drive innovation, productivity and broad-based prosperity for its citizens.     

Sampling Weights for Analyses of Couple Data: Example of the Demographic and Health Surveys

In some surveys, women and men are interviewed separately in selected households, allowing matching of partner information and analyses of couples. Although individual sampling weights exist for men and women, sampling weights specific for couples are rarely derived. We present a method of estimating appropriate weights for couples that extends methods currently used in the Demographic and Health Surveys (DHS) for individual weights. To see how results vary, we analyze 1912 estimates (means; proportions; linear regression; and simple and multinomial logistic regression coefficients, and their standard errors) with couple data in each of 11 DHS surveys in which the couple weight could be derived. We used two measures of bias: absolute percentage difference from the value estimated with the couple weight and ratio of the absolute difference to the standard error using the couple weight. The latter shows greater bias for means and proportions, whereas the former and a combination of both measures show greater bias for regression coefficients. Comparing results using couple weights with published results using women’s weights for a logistic regression of couple contraceptive use in Turkey, we found that 6 of 27 coefficients had a bias above 5 %. On the other hand, a simulation of varying response rates (27 simulations) showed that median percentage bias in a logistic regression was less than 3 % for 17 of 18 coefficients. Two proxy couple weights that can be calculated in all DHS surveys perform considerably better than either male or female weights. We recommend that a couple weight be calculated and made available with couple data from such surveys.     

Evaluating the products of alternative sampling methods

While theoretical work in survey sampling has offered the promise that selection procedures based on probabilities proportional to size would produce subgroups for surveys as efficiently as oversampling, there were fewer expectations that the two methods would produce comparable products. This research reports the results of an experiment conducted within the 1982 General Social Survey (GSS), which compares two subsamples of blacks (N=510). The multivariate normal distributions of the oversample and the black probability sample are demonstrated to be statistically similar. This similarity extends to subsets of demographic and substantive variables, and to most individual variables as well. For survey directors, these results imply that the choice between oversampling and pps methodologies used for locating population subgroups should depend more on the relative costs/efficiencies involved, than on concerns over product quality. More generally, these results mean that all of the blacks in the 1982 GSS may be combined and treated as a single, national probability sample of the American black population.     

A new look at the marriage market and nuptiality rates, 1915–1958

The system of nuptiality probabilities for never married males and females, the “marriage regime,” is viewed as a population transformation, which operates on a population thereby changing the composition. The marriage regime has many properties common to other population transformations, but embodies a constraint such that, in general, the marriage regime cannot be strictly stable over time. The approach is applied to study the “marriage squeeze,” the alteration in marriage patterns that results from an imbalance in the “marriage market” or numbers of never married males and females at the usual marriage ages. Using data on age at first marriage for the 1960 American white population, nuptiality probabilities by single year of age and sex are estimated for the years 1915–58. Annual estimates also are made of the relative number of eligible mates (never married of the usual marriage ages) for never married persons of a given age and sex. No close correspondence is found between annual fluctuations in the marriage market and in the nuptiality probability, possibly because of the crudeness of the estimates. Alternatively, response to the imbalance may take another form such as marriage postponement or a redefinition of eligibility.