Cohabitation in Great Britain: not for long, but here to stay

This paper uses a new source of data to study the dramatic increase in cohabiting unions in Great Britain. It analyses, in turn, entry into first partnership, the stability of cohabiting unions and repartnering after dissolution of cohabitation. In excess of 70% of first partnerships are now cohabitations, and these last a relatively short time before being either turned into marriage or dissolved. The shift to cohabitation as the dominant mode of first partnership plays an important role in the delay of first marriage and motherhood. The paper also investigates the factors that are associated with the outcome of cohabitations.     

Marriage or cohabitation: a competing risks analysis of first-partnership formation among the 1958 British birth cohort

A discrete time competing risks hazards model is used to analyse entry into first partnership among men and women born in Britain in 1958. Using a life-course approach we identify family background and current life experiences which affect the timing and type of first-partnership formation. Education is a key factor influencing the age of entry into first partnership and whether or not the respondent will experience pregnancy before forming the partnership. Religiosity, experience of parental separation and the geographical region of residence are more important in affecting the decision to cohabit rather than to marry directly. The analyses highlight the importance of transitions in other domains such as leaving the parental home in encouraging cohabitation.     

Employment, family union and childbearing decisions in Great Britain

Summary.  The paper investigates the life-cycle relationship of work and family life in Britain based on the British Household Panel Survey. Using hazard regression techniques we estimate a five-equation model, which includes birth events, union formation, union dissolution, employment and non-employment events. We find that transitions in and out of employment for men are relatively independent of other transitions. In contrast, there are strong links between employment of females, having children and union formation. By undertaking a detailed microsimulations analysis, we show that different levels of labour force participation by females do not necessarily lead to large changes in fertility events. Changes in union formation and fertility events, in contrast, have larger effects on employment.     

Another look into the effect of premarital cohabitation on duration of marriage: an approach based on matching

Summary.  The paper proposes an alternative approach to studying the effect of premarital cohabitation on subsequent duration of marriage on the basis of a strong ignorability assumption . The approach is called propensity score matching and consists of computing survival functions conditional on a function of observed variables (the propensity score), thus eliminating any selection that is derived from these variables. In this way, it is possible to identify a time varying effect of cohabitation without making any assumption either regarding its shape or the functional form of covariate effects. The output of the matching method is the difference between the survival functions of treated and untreated individuals at each time point. Results show that the cohabitation effect on duration of marriage is indeed time varying, being close to zero for the first 2–3 years and rising considerably in the following years.     

A segmented regression model for event history data: an application to the fertility patterns in Italy

We propose a segmented discrete-time model for the analysis of event history data in demographic research. Through a unified regression framework, the model provides estimates of the effects of explanatory variables and jointly accommodates flexibly non-proportional differences via segmented relationships. The main appeal relies on ready availability of parameters, changepoints, and slopes, which may provide meaningful and intuitive information on the topic. Furthermore, specific linear constraints on the slopes may also be set to investigate particular patterns. We investigate the intervals between cohabitation and first childbirth and from first to second childbirth using individual data for Italian women from the Second National Survey on Fertility. The model provides insights into dramatic decrease of fertility experienced in Italy, in that it detects a ‘common’ tendency in delaying the onset of childbearing for the more recent cohorts and a ‘specific’ postponement strictly depending on the educational level and age at cohabitation.     

A finite mixture approach to joint clustering of individuals and multivariate discrete outcomes

In this work, we modify finite mixtures of factor analysers to provide a method for simultaneous clustering of subjects and multivariate discrete outcomes. The joint clustering is performed through a suitable reparameterization of the outcome (column)-specific parameters. We develop an expectation–maximization-type algorithm for maximum likelihood parameter estimation where the maximization step is divided into orthogonal sub-blocks that refer to row and column-specific parameters, respectively. Model performance is evaluated via a simulation study with varying sample size, number of outcomes and row/column-specific clustering (partitions). We compare the performance of our model with the performance of standard model-based biclustering approaches. The proposed method is also demonstrated on a benchmark data set where a multivariate binary response is considered.     

A joint test for arch and bilinearity in the regression model

In this paper we argue that a simultaneous test for ARCH and bilinearity should be used to test for the possible nonlinearity of the error process in the regression model. We suggest such a joint test statistic. An empirical example shows that the individual tests of ARCH and bilinearity may not be conclusive while a joint test clearly rejects the linearity hypothesis. Our results are also applicable to pure time series models.     

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.     

Manipulating Statistical Hypotheses and Tests as Boolean Functions

Statistical hypotheses and test statistics are Boolean functions that can be manipulated using the tools of Boolean algebra. These tools are particularly useful for exploring multiple comparisons or simultaneous inference theory, in which multiparameter hypotheses or multiparameter test statistics may be decomposed into combinations of uniparameter hypotheses or uniparameter tests. These concepts are illustrated with both finite and infinite decompositions of familiar multiparameter hypotheses and tests. The corresponding decompositions of acceptance regions and rejection regions are also shown. Finally, the close relationship between hypothesis and test decompositions and Roy's union—intersection principle is demonstrated by a derivation of the union—intersection test of the univariate general linear hypothesis.     

Multilevel models for longitudinal data

Summary.  Repeated measures and repeated events data have a hierarchical structure which can be analysed by using multilevel models. A growth curve model is an example of a multilevel random-coefficients model, whereas a discrete time event history model for recurrent events can be fitted as a multilevel logistic regression model. The paper describes extensions to the basic growth curve model to handle auto-correlated residuals, multiple-indicator latent variables and correlated growth processes, and event history models for correlated event processes. The multilevel approach to the analysis of repeated measures data is contrasted with structural equation modelling. The methods are illustrated in analyses of children's growth, changes in social and political attitudes, and the interrelationship between partnership transitions and childbearing.     

Maximum likelihood estimation for incomplete multinomial data via the weaver algorithm

In a multinomial model, the sample space is partitioned into a disjoint union of cells. The partition is usually immutable during sampling of the cell counts. In this paper, we extend the multinomial model to the incomplete multinomial model by relaxing the constant partition assumption to allow the cells to be variable and the counts collected from non-disjoint cells to be modeled in an integrated manner for inference on the common underlying probability. The incomplete multinomial likelihood is parameterized by the complete-cell probabilities from the most refined partition. Its sufficient statistics include the variable-cell formation observed as an indicator matrix and all cell counts. With externally imposed structures on the cell formation process, it reduces to special models including the Bradley–Terry model, the Plackett–Luce model, etc. Since the conventional method, which solves for the zeros of the score functions, is unfruitful, we develop a new approach to establishing a simpler set of estimating equations to obtain the maximum likelihood estimate (MLE), which seeks the simultaneous maximization of all multiplicative components of the likelihood by fitting each component into an inequality. As a consequence, our estimation amounts to solving a system of the equality attainment conditions to the inequalities. The resultant MLE equations are simple and immediately invite a fixed-point iteration algorithm for solution, which is referred to as the weaver algorithm. The weaver algorithm is short and amenable to parallel implementation. We also derive the asymptotic covariance of the MLE, verify main results with simulations, and compare the weaver algorithm with an MM/EM algorithm based on fitting a Plackett–Luce model to a benchmark data set.     

A Potts‐mixture spatiotemporal joint model for combined magnetoencephalography and electroencephalography data

We develop a new methodology for determining the location and dynamics of brain activity from combined magnetoencephalography (MEG) and electroencephalography (EEG) data. The resulting inverse problem is ill‐posed and is one of the most difficult problems in neuroimaging data analysis. In our development we propose a solution that combines the data from three different modalities, magnetic resonance imaging (MRI), MEG and EEG, together. We propose a new Bayesian spatial finite mixture model that builds on the mesostate‐space model developed by Daunizeau & Friston [Daunizeau and Friston, NeuroImage 2007; 38, 67–81]. Our new model incorporates two major extensions: (i) We combine EEG and MEG data together and formulate a joint model for dealing with the two modalities simultaneously; (ii) we incorporate the Potts model to represent the spatial dependence in an allocation process that partitions the cortical surface into a small number of latent states termed mesostates. The cortical surface is obtained from MRI. We formulate the new spatiotemporal model and derive an efficient procedure for simultaneous point estimation and model selection based on the iterated conditional modes algorithm combined with local polynomial smoothing. The proposed method results in a novel estimator for the number of mixture components and is able to select active brain regions, which correspond to active variables in a high‐dimensional dynamic linear model. The methodology is investigated using synthetic data and simulation studies and then demonstrated on an application examining the neural response to the perception of scrambled faces. R software implementing the methodology along with several sample datasets are available at the following GitHub repository https://github.com/v2south/PottsMix . The Canadian Journal of Statistics 47: 688–711; 2019 © 2019 Statistical Society of Canada     

A revised Brown and Payne model of voting behaviour applied to the 2009 elections in Italy

When elections are close in time, voters may stick to their preferred party or chose a different option for several reasons; reliable estimates of the amount of transitions across the available options can allow to answer a number of relevant questions about electoral behaviour. We describe a modified version of the model due to Brown and Payne (J Am Stat Assoc 81:453–460, 1986) and argue that it is based on simple, yet realistic, assumptions with a direct interpretation in terms of individual behaviour and compares well with other models proposed more recently. We apply the model to an Italian borough where, during June 2009, two elections were held simultaneously and a runoff took place two weeks later. Estimates of the joint distribution of voters between the European Parliament election and the other two elections provide evidence of substantially different kinds of voting behaviour which, given the specific context, we interpret in the light of the recent literature on the subject.     

Modeling American marriage patterns

"This article investigates the application of the three-parameter, Coale-McNeil marriage model and some related hyperparameterized specifications to data on the first marriage patterns of American women. Because the model is parametric, it can be used to estimate the parameters of the marriage process for cohorts that have yet to complete their first marriage experience. Empirical evidence from three surveys is reported on the ability of the model to replicate and project observed marriage behavior. The results indicate that the model can be a useful tool for analyzing cohort marriage data and that recent cohorts are showing relatively strong proclivities to both delay and forego marriage. Consistent with earlier work, the results also indicate that education is a powerful covariate of the timing of first marriage and that race is a powerful covariate of its incidence." Data are from the U.S. Current Population Survey for 1976 and 1985 and Cycle III of the National Survey of Family Growth for 1982.     

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.     

Regularization in dynamic random-intercepts models for analysis of longitudinal data

This paper addresses the problem of simultaneous variable selection and estimation in the random-intercepts model with the first-order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra-class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random-intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low- and high-dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online.     

An approximation method for bivariate and multvariate normal equiprobability contours

This paper presents a very simple approximation, having “graph” accuracy, for calculating bivariate normal probability contours. Such contours are useful in simultaneous inference and other applications. This method is then adapted to approximate roughly bivariate and multivariate normal union probabilities.     

婚配概率及婚配对数估计方法的探讨

 估算独生子女和非独生子女之间婚配概率及婚配对数是生育政策仿真的关键技术之一。本文首次提出同龄概率法及多龄概率法,并对全国层面独生子女之间、独生子女与非独生子女之间、非独生子女之间的婚配概率及婚配对数进行了估算,详细阐述了两种方法的原理及运算步骤,并对两种方法的运算结果进行分析比较。结果表明,这两种方法都可以计算独生子女和非独生子女之间多种婚配概率,并能估算出各类婚配夫妇对数。其中,同龄概率法较直观,数据易取得, 但与实际存在一定的偏差;多龄概率法更接近于现实,受婚配对象人数突变的影响更小。     

Multiply robust inference for statistical interactions

A primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest. Interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures. When the main interest lies in the interaction, this approach is not entirely satisfactory because it is prone to (possibly severe) bias when the main exposure effects or the association between outcome and extraneous factors are misspecified. In this article, we therefore consider conditional mean models with identity or log link which postulate the statistical interaction in terms of a finite-dimensional parameter, but which are otherwise unspecified. We show that estimation of the interaction parameter is often not feasible in this model because it would require nonparametric estimation of auxiliary conditional expectations given high-dimensional variables. We thus consider 'multiply robust estimation' under a union model that assumes at least one of several working submodels holds. Our approach is novel in that it makes use of information on the joint distribution of the exposures conditional on the extraneous factors in making inferences about the interaction parameter of interest. In the special case of a randomized trial or a family-based genetic study in which the joint exposure distribution is known by design or by Mendelian inheritance, the resulting multiply robust procedure leads to asymptotically distribution-free tests of the null hypothesis of no interaction on an additive scale. We illustrate the methods via simulation and the analysis of a randomized follow-up study.