Should a Second Demographic Transition Follow the First? Demographic Contrasts: Canada and South Korea

Social Indicators Research -     

On the distribution of linear combinations of the components of a Dirichlet random vector

On making use of a result of Imhof, an integral representation of the distribution function of linear combinations of the components of a Dirichlet random vector is obtained. In fact, the distributions of several statistics such as Moran and Geary's indices, the Cliff‐Ord statistic for spatial correlation, the sample coefficient of determination, F‐ratios and the sample autocorrelation coefficient can be similarly determined. Linear combinations of the components of Dirichlet random vectors also turn out to be a key component in a decomposition of quadratic forms in spherically symmetric random vectors. An application involving the sample spectrum associated with series generated by ARMA processes is discussed.     

A mixture model with Poisson and zero-truncated Poisson components to analyze road traffic accidents in Turkey

The analysis of traffic accident data is crucial to address numerous concerns, such as understanding contributing factors in an accident''s chain-of-events, identifying hotspots, and informing policy decisions about road safety management. The majority of statistical models employed for analyzing traffic accident data are logically count regression models (commonly Poisson regression) since a count – like the number of accidents – is used as the response. However, features of the observed data frequently do not make the Poisson distribution a tenable assumption. For example, observed data rarely demonstrate an equal mean and variance and often times possess excess zeros. Sometimes, data may have heterogeneous structure consisting of a mixture of populations, rather than a single population. In such data analyses, mixtures-of-Poisson-regression models can be used. In this study, the number of injuries resulting from casualties of traffic accidents registered by the General Directorate of Security (Turkey, 2005–2014) are modeled using a novel mixture distribution with two components: a Poisson and zero-truncated-Poisson distribution. Such a model differs from existing mixture models in literature where the components are either all Poisson distributions or all zero-truncated Poisson distributions. The proposed model is compared with the Poisson regression model via simulation and in the analysis of the traffic data.     

Recursive and en-bloc approaches to signal extraction

In the literature on unobservable component models , three main statistical instruments have been used for signal extraction: fixed interval smoothing (FIS), which derives from Kalman's seminal work on optimal state-space filter theory in the time domain; Wiener-Kolmogorov-Whittle optimal signal extraction (OSE) theory, which is normally set in the frequency domain and dominates the field of classical statistics; and regularization , which was developed mainly by numerical analysts but is referred to as 'smoothing' in the statistical literature (such as smoothing splines, kernel smoothers and local regression). Although some minor recognition of the interrelationship between these methods can be discerned from the literature, no clear discussion of their equivalence has appeared. This paper exposes clearly the interrelationships between the three methods; highlights important properties of the smoothing filters used in signal extraction; and stresses the advantages of the FIS algorithms as a practical solution to signal extraction and smoothing problems. It also emphasizes the importance of the classical OSE theory as an analytical tool for obtaining a better understanding of the problem of signal extraction.     

Why is the Divorce Rate Declining in Indonesia?

This article examines trends in marital dissolution in Indonesia. Analysis considers the impact of educational expansion, delayed marriage, urbanization, increasing employment before marriage, legislative change, and increased free choice in marriage on the decline in marital disruption. Trends such as delayed marriage and educational expansion account for about one third of the decline in marital dissolution. Moreover, factors associated with marital disruption are shifting in importance. In particular, age at marriage and marital duration are becoming less reliable predictors of marital stability, whereas education is becoming more important. We conclude that the shifting forces governing marital formation and dissolution in Indonesia have modified the linkages between the conjugal couple, broader kinship systems, and modes of economic support such that traditional patterns sustaining high levels of marital instability are no longer in effect.     

Assessing the structural heterogeneity of urban areas: an example from the Black Country (UK)

The increasing acknowledgement of the importance of urban habitats in the maintenance of biodiversity has brought with it a need to quantify this importance at a scale appropriate to the characteristic patch sizes encountered in urban areas. Taking a study area in the Black Country (UK) we used a spatially complete, rapid assessment method to evaluate habitat patches in terms of their internal structural heterogeneity. This method recognises the importance of both natural and anthropogenic processes in providing a diverse range of habitats and niches for both flora and fauna. It also recognises the key role of context in determining the ecological significance of each patch within the urban landscape.All habitats studied had a complex mix of both natural and artificial structural elements, where an element is a within-patch contributor to structural diversity, with each habitat type having a large range of element totals. Characteristic totals, reflecting the level of habitat structural diversity, were observed in some habitat types with residential areas having high values and industrial and commercial areas having low values. Certain structural elements were also associated with each habitat type allowing characteristic element assemblages to be derived. If structural diversity is linked with biodiversity, as seems to be the case in many (though not all) habitat types, then this unique method of viewing the urban landscape becomes a powerful tool for informing wildlife ecologists, nature conservationists, urban planners, environmental managers and landscape architects.     

Multiple Choice Knapsack Problem: Example of planning choice in transportation

Transportation programming, a process of selecting projects for funding given budget and other constraints, is becoming more complex as a result of new federal laws, local planning regulations, and increased public involvement. This article describes the use of an integer programming tool, Multiple Choice Knapsack Problem (MCKP), to provide optimal solutions to transportation programming problems in cases where alternative versions of projects are under consideration. In this paper, optimization methods for use in the transportation programming process are compared and then the process of building and solving the optimization problems is discussed. The concepts about the use of MCKP are presented and a real-world transportation programming example at various budget levels is provided. This article illustrates how the use of MCKP addresses the modern complexities and provides timely solutions in transportation programming practice. While the article uses transportation programming as a case study, MCKP can be useful in other fields where a similar decision among a subset of the alternatives is required.     

The Relationship Between the T2 Statistic and the Influence Function

Hotelling's T² statistic has many applications in multivariate analysis. In particular, it can be used to measure the influence that a particular observation vector has on parameter estimation. For example, in the bivariate case, there exists a direct relationship between the ellipse generated using a T² statistic for individual observations and the hyperbolae generated using Hampel's influence function for the corresponding correlation coefficient. In this paper, we jointly use the components of an orthogonal decomposition of the T² statistic and some influence functions to identify outliers or influential observations. Since the conditional components in the T² statistic are related to the possible changes in the correlation between a variable and a group of other variables, we consider the theoretical influence functions of the correlations and multiple correlation coefficients. Finite-sample versions of these influence functions are used to find the estimated influence function values.