The evolution of life expectancy in the capital city of Warsaw in 1931-1980

The author presents estimates of life expectancy in Warsaw, Poland, by age and sex for the period 1931-1980. The estimates involve modifications of previously calculated life tables for 1931 to ensure greater compatibility with more recent estimates.     

Statistical materials

Official population data for the USSR are presented for 1985 and 1986. Part 1 (pp. 65-72) contains data on capitals of union republics and cities with over one million inhabitants, including population estimates for 1986 and vital statistics for 1985. Part 2 (p. 72) presents population estimates by sex and union republic, 1986. Part 3 (pp. 73-6) presents data on population growth, including birth, death, and natural increase rates, 1984-1985; seasonal distribution of births and deaths; birth order; age-specific birth rates in urban and rural areas and by union republic; marriages; age at marriage; and divorces.     

Statistical materials. Part 2: natural population increase in the USSR

Selected vital statistics for the USSR for 1984 are presented. Data are included on birth, death, and natural increase rates, 1983-1984; the distribution of births, deaths, and marriages by month; birth order; age-specific birth rates by rural and urban areas; age-specific birth rates by union republics; distribution of marriages by age and sex; distribution of married couples by age of husband and wife; and divorces by length of marriage and age of husband and wife.     

Statistical materials: natural increase of population in the USSR

Data are included on the population of the USSR by sex and Union Republic as of January 1, 1981; birth, death, and natural growth rates for 1979 and 1980; distribution of births, deaths, and marriages by month, 1980; distribution of births by birth order; age distribution of birth rates in urban and rural areas and by Union Republic; death rates from cardiovascular disease and cancer, 1979 and 1980; age at first marriage and marriages by age of bride and groom, 1980; and divorces by duration of marriage and age of spouses, 1980.     

Births in remarriages (using data from sample surveys)

Data from sample surveys conducted between 1978 and 1981 are used to examine the fertility of women in second and subsequent marriages in the USSR. The results indicate that women up to age 25 who have been married more than once have higher fertility than women in a first marriage. However, total fertility is higher for women in uninterrupted marriages. The analysis is presented separately for various cohorts and for socioeconomic characteristics such as educational status and rural or urban residence.     

Tests of independence in incomplete multi-way tables using likelihood functions

Kang (2006) and Kang and Larsen (in press) used the log likelihood function with Lagrangian multipliers for estimation of cell probabilities in two-way incomplete contingency tables. This paper extends results and simulations to three-way and multi-way tables. Numerous studies cross-classify subjects by three or more categorical factors. Constraints on cell probabilities are incorporated through Lagrangian multipliers. Variances of the MLEs are derived from the matrix of second derivatives of the log likelihood with respect to cell probabilities and the Lagrange multiplier. Wald and likelihood ratio tests of independence are derived using the estimates and estimated variances. In simulation results in Kang and Larsen (in press), for data missing at random, maximum likelihood estimation (MLE) produced more efficient estimates of population proportions than either multiple imputation (MI) based on data augmentation or complete case (CC) analysis. Neither MLE nor MI, however, lead to an improvement over CC analysis with respect to power of tests for independence in two-way tables. Results are extended to multidimensional tables with arbitrary patterns of missing data when the variables are recorded on individual subjects. In three-way and higher-way tables, however, there is information relevant for judging independence in partially classified information, as long as two or more variables are jointly observed. Simulations study three-dimensional tables with three patterns of association and two levels of missing information.     

Statistical materials: natural increase of population in the USSR

Data on the population of the USSR by sex and Union republic as of January 1, 1982, are presented. Data are included on population by sex; birth, death, and natural growth rates, 1980 and 1981; distribution of births, deaths, and marriages by month, 1981; distribution of births by birth order, 1981; age-specific birth rates for rural and urban areas, 1980 and 1981; mortality from cardiovascular disease and cancer, 1980 and 1981; marriages by age of bride and groom, 1981; and divorces by duration of marriage and age of husband and wife, 1981.     

Statistical materials,Part 1: natural increase of population in the USSR

Data are presented on the population of the USSR by sex and Union Republic as of January 1, 1983. Data are included on birth rate, death rate, and natural growth rate, 1981 and 1982; distribution of births, deaths, and marriages by month, 1982; distribution of births by birth order, 1982; age-specific birth rates by rural or urban area and Union Republic, 1981 and 1982; mortality from cardiovascular disease and cancer, 1981 and 1982; marriages by age of bride and groom, 1982; and number of divorces by duration of marriage and age of husband and wife, 1982.     

Tests of symmetry with one-sided alternatives in three-way contingency tables

For a two-dimensional contingency table of probabilities, the concept of symmetry around the main diagonal is well defined. Statistical hypothesis test of symmetry versus positive bias have also been explored. For tables of higher (three or more) dimensions, however, different concepts of symmetry are available. In this study, we consider statistical inference procedures of symmetry in partial tables versus various biases in three-dimensional tables. We find the maximum likelihood estimates of the cell probabilities and the asymptotic distribution of the likelihood ratio test statistic in each case. Simulation studies are used to investigate the sizes and powers of the tests. The methodologies developed are applied on real data sets.     

Empirical bayes estimation of the log odds ratio in 2×2 contingency tables

We consider a sequence of contingency tables whose cell probabilities may vary randomly. The distribution of cell probabilities is modelled by a Dirichlet distribution. Bayes and empirical Bayes estimates of the log odds ratio are obtained. Emphasis is placed on estimating the risks associated with the Bayes, empirical Bayes and maximum lilkelihood estimates of the log odds ratio.     

Large sample bias of maximum likeihood estimates from a series of sparse ixj tables

For a large series of IxJ tables, each containing two observations, the bias of the maximum likelihood estimates of log linear partial association parameters is shown to be equal to the parameters, regardless of the size of I and J. The partial association considered is that between row and column variables; the three way interactions are assumed to be O. This is a generalization of Andersen's results (1973a, 1973b) for a series of 2x2 tables.     

The Box–Cox Transformation and Non‐Iterative Estimation Methods for Ordinal Log‐Linear Models

Recently Beh and Farver investigated and evaluated three non‐iterative procedures for estimating the linear‐by‐linear parameter of an ordinal log‐linear model. The study demonstrated that these non‐iterative techniques provide estimates that are, for most types of contingency tables, statistically indistinguishable from estimates from Newton's unidimensional algorithm. Here we show how two of these techniques are related using the Box–Cox transformation. We also show that by using this transformation, accurate non‐iterative estimates are achievable even when a contingency table contains sampling zeros.     

Bayesian inference for contingency tables with given marginals

Summary In this paper we introduce a class of prior distributions for contingency tables with given marginals. We are interested in the structrre of concordance/discordance of such tables. There is actually a minor limitation in that the marginals are required to assume only rational values. We do argue, though, that this is not a serious drawback for all applicatory purposes. The posterior and predictive distributions given anM-sample are computed. Examples of Bayesian estimates of some classical indices of concordance are also given. Moreover, we show how to use simulation in order to overcome some difficulties which arise in the computation of the posterior distribution.     

Statistical materials. Part 4: natural increase of population in the USSR

Data are presented on the natural increase of the population in the USSR. Data for 1982-1983 are included on birth, death, and natural increase rates; births, deaths, and marriages by month; age-specific birth rates by urban or rural area and by Union Republic; deaths due to circulatory disease or cancer; marriage by age; and divorces by marriage duration and age of husband and wife.     

Bayesian estimation methods for contingency tables

Summary A method of inputting prior opinion in contingency tables is described. The method can be used to incorporate beliefs of independence or symmetry but extensions are straightforward. Logistic normal distributions that express such beliefs are used as priors of the cell probabilities and posterior estimates are derived. Empirical Bayes methods are also discussed and approximate posterior variances are provided. The methods are illustrated by a numerical example.     

The demographic situation in European countries

Demographic trends in European countries are summarized for the period 1960 to 1980 using data taken primarily from published sources, including those of the Council of Europe and the United Nations. Information is included on age composition, natural increase, births, infant mortality, marriages and divorces, and population projections to the year 2000. The data are presented separately for Socialist and capitalist countries.     

Detection of the numbers of outliers present in a data set using an information theoretic criterion

We use an information theoretic criterion proposed by Zhao, Krishnaiah and Bai (1986) to detect the number of outliers in a data set. We consider univariable mean-slippage and dispersion-slippage outlier structure of the observations. Multivariate generalizations and the consistency of the estimates are also considered. Numerical examples are presented in tables.     

Regional types of mortality order in the light of statistical analysis of main components

This is an analysis of abbreviated life tables for Polish regions for 1973 to 1975. Life tables are given for 49 voivodships by age groups, and data on average life expectancies are provided.     

Exact inference in contingency tables via stochastic approximation Monte Carlo

Monte Carlo methods for the exact inference have received much attention recently in complete or incomplete contingency table analysis. However, conventional Markov chain Monte Carlo, such as the Metropolis–Hastings algorithm, and importance sampling methods sometimes generate the poor performance by failing to produce valid tables. In this paper, we apply an adaptive Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm (SAMC; Liang, Liu, & Carroll, 2007), to the exact test of the goodness-of-fit of the model in complete or incomplete contingency tables containing some structural zero cells. The numerical results are in favor of our method in terms of quality of estimates.     

Multiplicative-interaction logit models for i×j×2 three-way tables

Multiplicative-interaction (M-I) logit models are proposed for three-way IxJx2 contingency tables where the third variable constitutes a binary response. Models are derived by assigning unknown scores to the categories and forming product interactions from them. Asymptotic results under special sampling constraints are derived for maximum likelihood estimates and the goodness-of-fit statistics. The class of models proposed in this paper are found to be useful when no obvious scores are available. An example is included.