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.     

On the Prediction of the Subpopulation Total Based on Spatially Correlated Longitudinal Data

In a special case of the general linear mixed model, one random component obeys a spatial autoregressive process and another a temporal autoregressive process. The population and any affiliations to subpopulations may change in time. The empirical best linear unbiased predictor is derived and may be used even if the sample size in the subpopulation is null in the period of interest. The mean squared error and its estimator are expressed. The accuracy of the predictor and the bias of the mean squared error estimator are addressed through simulations.     

Sliders,visual analogue scales,or buttons: Influence of formats and scales in mobile and desktop surveys

ABSTRACT

In an experiment dealing with the use of personal computer, tablet, or mobile, scale points (up to 5, 7, or 11) and response formats (bars or buttons) are varied to examine differences in mean scores and nonresponse. The total number of “not applicable” answers does not vary significantly. Personal computer has the lowest item nonresponse, followed by mobile and tablet, and a lower mean score than for mobile. Slider bars showed lower mean scores and more nonresponses than buttons, indicating that they are more prone to bias and difficult in use. Sider bars, which work with a drag-and-drop principle, perform worse than visual analogue scales working with a point-and-click principle and buttons. Five-point scales have more nonresponses than eleven-point scales. Respondents evaluate 11-point scales more positively than shorter scales.     

Mixed estimation of old‐age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old‐age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.     

Simulating bias in the estimator of labor market discrimination

In this study, the statistical bias in the most widely used estimator of labor market discrimination is investigated. An algebraic expression for the bias is derived and then simulated for a selected set of explanatory variables and model parameters. The results for a large national dataset seem to indicate that when the variables years of schooling and labor market experience are used in earnings functions, the estimator tends to underestimate the actual or true amount of labor market discrimination.     

Estimating Allele Frequencies and Inbreeding Coefficients in K-Allele Models

Some of the methods of estimation of allele frequencies and inbreeding coefficients in a K-allele model are examined. A result that has long been assumed to be true is proved. That is, in the presence of inbreeding, the maximum likelihood estimators of the allele frequencies and of the inbreeding coefficient f do not in general equal their observed (or sample) values (except when K = 2). A least-squares way of looking at the estimation problem is presented, and simulations are used to compare the three types of estimators (sample, maximum likelihood, and least-squares) in a 3-allele model. Probability generating functions are used to derive exact expressions for the bias of the sample estimator of f in a 2-allele model for any sample size, and those biases are calculated for a number of situations. Finally, an approximately unbiased estimator of the inbreeding coefficient when an allele is rare or common is proposed, and its bias is compared with that of the sample estimator and with that of an estimator proposed by Weir (1996 Weir , B.S. ( 1996 ). Genetic Data Analysis 2 . Sinauer Associates , Sunderland , MA . [Google Scholar]).     

Turbulent dynamics in a Xviith century population

A reconstruction of the population of the Pays de Caux (1589–1700) yields the time series of a fertility behavior indicator, the overall Coale index If. In spite of the noisy appearance of its evolution, the trajectory of If looks ordered, as if it were confined alternatively to two given zones, looping in each of them for a while, then suddenly jumping from the low one to the higher one, or slowly whirling down from the high to the low one.

An attempt is made to explain this general temporal structure by using a simulation model based on the autoregulation model (the so‐called European Marriage Pattern), putting into play a choice of the spouse function, a fertility function, modalities of marriage and remarriage, under the environmental forcing of the reconstructed mortality conditions.

The correspondence between reconstruction and simulation turns out to be quite good, not only for the population size or the Coale index, but also for the marriage series, quite independently of the reconstructioa

A second simulation with simulated mortality conditions shows a bifurcation point: as the mean frequency of crisis increases, the state of the system leaves the lower level and concentrates more and more in the higher level.

Thus, not only does the autoregulator model appear validated by empirical data, but its bi‐modal structure is revealed, depicting the dynamic response of a traditional community both to the environment and to the endogeneous demographic process.     

In search of the ideal measure of accuracy for subnational demographic forecasts

We examine nonlinear transformations of the forecasterror distribution in hopes of finding a summary errormeasure that is not prone to an upward bias and usesmost of the information about that error. MAPE, thecurrent standard for measuring error, often overstatesthe error represented by most of the values becausethe distribution underlying the MAPE is right skewedand truncated at zero. Using a modification to theBox-Cox family of nonlinear transformations, wetransform these skewed forecast error distributionsinto symmetrical distributions for a wide range ofsize and growth rate conditions. We verify thissymmetry using graphical devices and statisticaltests; examine the transformed errors to determine ifre-expression to the scale of the untransformed errorsis necessary; and develop and implement a procedurefor the re-expression. The MAPE-R developed by ourprocess is lower than the MAPE based on theuntransformed errors and is more consistent with arobust estimator of location.     

A comparison of species diversity estimators

Although having been much criticized, diversity indices are still widely used in animal and plant ecology to evaluate, survey, and conserve ecosystems. It is possible to quantify biodiversity by using estimators for which statistical characteristics and performance are, as yet, poorly defined. In the present study, four of the most frequently used diversity indices were compared: the Shannon index, the Simpson index, the Camargo eveness index, and the Pielou regularity index. Comparisons were performed by simulating the Zipf–Mandelbrot parametric model and estimating three statistics of these indices, i.e., the relative bias, the coefficient of variation, and the relative root-mean-squared error. Analysis of variance was used to determine which of the factors contributed most to the observed variation in the four diversity estimators: abundance distribution model or sample size. The results have revealed that the Camargo eveness index tends to demonstrate a high bias and a large relative root-mean-squared error whereas the Simpson index is least biased and the Shannon index shows a smaller relative root-mean-squared error, regardless of the abundance distribution model used and even when sample size is small. Shannon and Pielou estimators are sensitive to changes in species abundance pattern and present a nonnegligible bias for small sample sizes (<1000 individuals). Received: May 8, 1998 / Accepted: May 6, 1999     

Statistical modeling of selected aspects of the childbearing process with application to world fertility survey countries∗

The childbearing process should be monitored in developing countries experiencing high population growth rates and high levels of maternal and infant mortality. A mathematical model for estimation of certain aspects of the childbearing process, which requires only data on age‐specific fertility rates, is developed. Synthetic maternal childbearing indices, namely, mean ages at first and last birth, length of reproductive life span, inter‐birth spacing, and proportion of childless women, in addition to the well‐known mean age at childbearing, for the WFS countries are obtained using the proposed model. The indices are free from age truncation effects, and, under certain assumptions, provide information about a cohort's completed fertility before the women stop reproducing. The effects of women's residence and education on fertility are also examined.     

Migration bias in indirect estimates of regional childhood mortality levels

Demographers often use Brass‐style indirect methods to obtain childhood mortality estimates for regions within developing countries. Regional populations are not closed to migration, however, and mortality reports of women resident in a certain region on the survey date may contain information on events and exposure that occurred elsewhere as the mother migrated. Including this “imported”; mortality information may cause significant bias in regional estimates. In this paper the authors: (1) investigate the possible magnitude of migration bias using a multiregional simulation model, (2) propose a modification to standard methods which should reduce bias in many circumstances, and (3) apply the modified technique to data from Brazil's 1980 Census. We find that migration bias can indeed be significant, and that in the specific case of São Paulo state, imported mortality information may result in overestimates of local mortality levels of 10–15% when using Brass‐style methods.     

Population forecast accuracy: does the choice of summary measure of error matter?

Population projections are judged primarily by their accuracy. The most commonly used measure for the precision component of accuracy is the mean absolute percent error (MAPE). Recently, the MAPE has been criticized for overstating forecast error and other error measures have been proposed. This study compares the MAPE with two alternative measures of forecast error, the Median APE and an M-estimator. In addition, the paper also investigates forecast bias. The analysis extends previous studies of forecast error by examining a wide range of trend extrapolation techniques using a dataset that spans a century for a large sample of counties in the US. The main objective is to determine whether the choice of summary measure of error makes a difference from a practitioner’s standpoint. The paper finds that the MAPE indeed produces error values that exceed the robust measures. However, except for situations where extreme outliers rendered the MAPE meaningless, and which are rare in real world applications, there was not a single instance where using an alternative summary measure of error would have led to a fundamentally different evaluation of the projections. Moreover, where differences existed, it was not always clear that the values and patterns provided by the robust measures were necessarily more correct than those obtained with the MAPE. While research into refinements and alternatives to the MAPE and mean algebraic percent error are worthwhile, consideration of additional evaluation procedures that go beyond a single criterion might provide more benefits to producers and users of population forecasts.

Adjustment for nonresponse with variables from different sources: Bias correction and precision loss,with application to the Swiss European Social Survey 2012

ABSTRACT

Adjustment for nonresponse should reduce the nonresponse bias without decreasing the precision of the estimates. Adjustment for nonresponses are commonly based on socio-demographic variables, although these variables may be poorly correlated with response propensities and with variables of interest. Such variables nevertheless have the advantage of being available for all sample units, whether or not they are participating in the survey. Alternatively, adjustment for nonresponse can be obtained from a follow-up survey aimed at sample units which did not participate in the survey and from which the variables are designed to be correlated with response propensities. However, information collected through these follow-up surveys is not available for people in the sample who participated neither in the survey nor in its nonresponse follow-up. These two sets of variables when used in a nonresponse model for the Swiss European Social Survey 2012 differ only slightly with regard to their effect on bias correction and on the precision of estimates. The variables from the follow-up are performing slightly better. In both cases, the adjustment for nonresponse performs poorly.     

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.     

Women’s childbirth experience emphasizing own capacity and safety: A cross-sectional Rwandan study

Problem and aimWomen’s childbirth experience is central when assessing intrapartum care quality. This study accordingly measures women’s childbirth experience in Rwandan health facilities, focusing on own capacity and perceived safety.MethodsA cross-sectional health facility-based study was conducted December 2014 to January 2015 in Kigali City and the Northern Province. Childbirth experience was assessed before discharge using an overall assessment and two subscales, Own capacity and Perceived safety, of the Childbirth Experience Questionnaire, with high scores reflecting a good experience. The questionnaire was translated from English into Kinyarwanda. Reliability was tested using Cronbach’s alpha; and mean scores between groups were compared using Mann–Whitney U test.FindingsAll invited women (n = 817) agreed to participate after informed consent. Mean age was 27.8 years and 63.6% were multiparous. A majority of women (82.3%) reported an overall positive childbirth experience (≥8 out of 10). Cronbach’s alpha indicated good reliability for Own capacity (0.78) and Perceived safety (0.76). In both subscales multiparous women had higher mean scores than primiparous, married women scored higher than unmarried, older women (>35) scored higher than younger (<35), and women with higher level of education scored higher than those with lower level. Women with HIV scored lower on perceived safety.ConclusionA majority of the women reported a positive overall childbirth experience. Own capacity and perceived safety are important dimensions of childbirth experience and should be addressed in building high-quality intrapartum care. Further research is needed and should include exploration of specific groups.     

On the intrinsic force of convergence to stability∗

Observed populations differ greatly in the speed with which they approach the stable form, but what determines rates of convergence is not fully understood. The present paper shows that the force of convergence does not approach a fixed value, but oscillates indefinitely around an “intrinsic”; level. That level, h?, is determined by the square of the ratio of the 2 largest eigenvalues of the Leslie matrix. The value of h? can be closely approximated by a simple function that changes directly with the square of the coefficient of variation and inversely with the mean of the stable net maternity function. Population entropy, another measure of dispersion relative to the mean, is also highly correlated with h?.     

Women's birth expectations,are they fulfilled? Findings from a longitudinal Swedish cohort study

BackgroundThe importance of women's expectations on the experience of birth has shown contradictory results regarding fulfilment. The aim of this study was to describe pregnant women's expectations of birth and to investigate if these expectations were fulfilled. An additional aim was to determine if unfulfilled expectations were related to the mode of birth, use of epidural and the birth experience.MethodsThis research investigated a prospective regional cohort study of 1042 Swedish-speaking women who completed a questionnaire about birth expectations in late pregnancy and were followed up with two months after birth. Five areas were under study: support from partner, support from midwife, control, participation in decision making and the midwife's presence during labour and birth. An index combining expectations and experiences was created.ResultsCertain background characteristics were associated with expectations as well as experiences. Statistically significant differences were shown between expectations and experiences in support from midwife (mean 3.41 vs 3.32), support from partner (mean 3.70 vs 3.77), and midwife's presence (mean 3.00 vs 3.39). Experiences ‘worse than expected’ regarding decision making and control were associated with modes of birth other than vaginal and four out of five areas were associated with a less positive birth experience.ConclusionSome women had high birth expectations of which some were fulfilled. An expectation on support from the midwife was less likely to be achieved, while support from partner and the midwives’ presence were fulfilled. If the woman's expectations were not fulfilled, e.g. became ‘worse than expected’ this was associated with a less positive overall birth experience as well as with instrumental or surgical mode of birth.     

Evaluating the relative accuracy and significance of net migration estimates

This paper presents the elements of a theory for evaluating the quality of a set of net migration estimates. The total error in a net migration estimate is decomposed into total bias and total variation. The bias is further decomposed into three bias elements-selection bias, estimator bias, and measurement bias. Tables of bounds for measurement and estimator biases in the vital statistics and the forward survival ratio estimates of net intercensal migration are presented. Both net migration levels and net migration ratios are treated, and provision is made for both life table and census survival ratio estimates. Some of the statistical tables are applied illustratively to net migration data for Canadian counties or census divisions during the 1951-61 decade. Tests of significance and confidence intervals are indicated for net migration estimates, and the basic technical notes are presented in appendices.     

Mortality and fertility: How large is the direct child replacement effect in China?

Olsen (1980) proposed a method for quantifying the fertility response to child mortality. He showed how to correct for bias in the OLS estimator. He also proposed the use of mortality rates as an instrumental variable. This method is applied here to a new Chinese microdata set. It appears that the method works well. The bias-corrected direct replacement effect based on the Chinese data is about 0.6, which is three times as large as the effects found by Olsen (1980, 1988) using data for Colombia and Malaysia. Several explanations are provided for this result.I am grateful to Frank Denton, Martin Dooley, Ronald Lee, Lonnie Magee, Byron Spencer and three anonymous referees for many helpful comments and suggestions. I would also like to thank the International Statistical Institute Research Center for supplying the data used in this study.     

The Divergent Meanings of Life Satisfaction: Item Response Modeling of the Satisfaction with Life Scale in Greenland and Norway

Cultural differences in response to the Satisfaction With Life Scale (SWLS) items is investigated. Data were fit to a mixed Rasch model in order to identify latent classes of participants in a combined sample of Norwegians (N = 461) and Greenlanders (N = 180). Initial analyses showed no mean difference in life satisfaction between the two subsamples. After transforming the ordinal raw scores into interval scales while simultaneously controlling for response bias, different results appeared. First, approximately 80% of the participants in the Greenlandic subsample fit a latent class with a large degree of random responding to the SWLS. Second, relative to the Norwegians, more Greenlanders were using extreme categories in responding to the SWLS. After statistically controlling for this tendency, Norwegians were in general more satisfied with their lives than Greenlanders. Third, Greenlanders who belonged to one specific latent class were more satisfied than their Norwegian counterparts. A salient feature of this class was the relative unwillingness of respondents to change the circumstances of their lives if they were given such an opportunity. The above results are a reminder of the care that must be used in analyzing survey data across cultures. The analytical strategy applied in the article offers an improved approach to handling such data.