On Measuring Segregation in Samples With Small Units

Standard indexes of segregation measure a sample's distance from evenness, which occurs when each sample unit (e.g., an occupation) has the population share of both the minority and majority groups. We show that random allocation of individuals to units generates substantial unevenness among small units and hence that standard segregation indexes reflect random allocation as well as systematic group segregation. We then modify two popular indexes so that they measure deviations from random allocation rather than deviations from evenness. An empirical example suggests that these modified indexes provide improved measures of the systematic component of group segregation.     

Regression models for Boolean random sets

In this paper we consider the regression problem for random sets of the Boolean-model type. Regression modeling of the Boolean random sets using some explanatory variables are classified according to the type of these variables as propagation, growth or propagation-growth models. The maximum likelihood estimation of the parameters for the propagation model is explained in detail for some specific link functions using three methods. These three methods of estimation are also compared in a simulation study.     

Multilevel modelling of the geographical distributions of diseases

Multilevel modelling is used on problems arising from the analysis of spatially distributed health data. We use three applications to demonstrate the use of multilevel modelling in this area. The first concerns small area all-cause mortality rates from Glasgow where spatial autocorrelation between residuals is examined. The second analysis is of prostate cancer cases in Scottish counties where we use a range of models to examine whether the incidence is higher in more rural areas. The third develops a multiple-cause model in which deaths from cancer and cardiovascular disease in Glasgow are examined simultaneously in a spatial model. We discuss some of the issues surrounding the use of complex spatial models and the potential for future developments.     

A Note on the Computation of the Mean Random Consistency Index of the Analytic Hierarchy Process (Ahp)

In this paper, we use Saaty's Eigenvector Method and the Power Method as well as =1, 2, , 9, 1/2, 1/3, , 1/9} and -={1,2, ,9,1, 1/2, ,1/9} as the sets from which the pairwise comparison judgments are assigned at random to examine the variation in the values determined for the mean random consistency index. By extensive simulation analysis, we found that both methods produce the same values for the mean random consistency random index. Also, we found that the reason for producing two different sets of values is the use of vs. - and not the selection of the Power Method vs. Saaty's Eigenvector Method.     

A biomedical application of latent class models with random effects

Traditional latent class modelling has been used in many biomedical settings. Unfortunately, many of these applications assume that the diagnostic tests are independent given the true disease status, an assumption that is often violated in practice. Qu, Tan and Kutner developed general latent class models with random effects to model the conditional dependence among multiple diagnostic tests. In this paper latent class modelling with random effects is used to estimate the sensitivity and specificity of six screening tests for detecting Chlamydia trachomatis in endocervical specimens from women attending family planning clinics.     

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为了分流海南旺季客流，实现旅游业合理布局，构筑环岛旅游格局，海南应加大投入，开发尖峰岭旅游中心系统中的大广坝———猕猴岭大型景区     

State space mixed models for longitudinal observations with binary and binomial responses

We propose a new class of state space models for longitudinal discrete response data where the observation equation is specified in an additive form involving both deterministic and random linear predictors. These models allow us to explicitly address the effects of trend, seasonal or other time-varying covariates while preserving the power of state space models in modeling serial dependence in the data. We develop a Markov chain Monte Carlo algorithm to carry out statistical inference for models with binary and binomial responses, in which we invoke de Jong and Shephard’s (Biometrika 82(2):339–350, 1995) simulation smoother to establish an efficient sampling procedure for the state variables. To quantify and control the sensitivity of posteriors on the priors of variance parameters, we add a signal-to-noise ratio type parameter in the specification of these priors. Finally, we illustrate the applicability of the proposed state space mixed models for longitudinal binomial response data in both simulation studies and data examples.     

The Surrogate Henderson Filters in X-11

This paper explains the surrogate Henderson filters that are used in the X-11 variant of the Census Method II seasonal adjustment program to obtain trends at the ends of time series. It describes a prediction interpretation for these surrogate filters, justifies an approximation to the filters, proposed by Kenny & Durbin (1982), and proposes a further interpretation of the results. The starting point for the paper is unpublished work by Musgrave (1964a, 1964b). His work has continuing relevance to current seasonal adjustment practice. This paper makes that work generally available for the first time, and reviews and extends it.     

Manipulating and summarizing posterior simulations using random variable objects

Practical Bayesian data analysis involves manipulating and summarizing simulations from the posterior distribution of the unknown parameters. By manipulation we mean computing posterior distributions of functions of the unknowns, and generating posterior predictive distributions. The results need to be summarized both numerically and graphically. We introduce, and implement in R, an object-oriented programming paradigm based on a random variable object type that is implicitly represented by simulations. This makes it possible to define vector and array objects that may contain both random and deterministic quantities, and syntax rules that allow to treat these objects like any numeric vectors or arrays, providing a solution to various problems encountered in Bayesian computing involving posterior simulations. We illustrate the use of this new programming environment with examples of Bayesian computing, demonstrating missing-value imputation, nonlinear summary of regression predictions, and posterior predictive checking.     

An investigation of the spatial correlations for relative purchasing power in Baden–Württemberg

The relative purchasing power—i.e., the purchasing power per inhabitant—is one of the key characteristics for businesses deciding on site selection. Apart from that it also plays a major role in regional planning, pricing policy and market research. In this study we investigate the spatial correlations for relative purchasing power of the townships in Baden–Württemberg. In particular, changes in relative purchasing power are analysed for three different time intervals, 1987–1993, 1993–1998 and 1998–2004, by means of distance-dependent characteristics like the mark–correlation function, the Simpson indices α(r) and β(r) and by tests on random labelling. It is shown that there are positive correlations for small distances between different townships but that these positive correlations become weaker over the years until they are almost nonexistent (in the sense that hypotheses of random labelling are no longer rejected). A conclusion from this loss of spatial correlations with time is that the relative purchasing power might become more and more purely random. This means that the relative purchasing power in a township is less and less influenced by the relative purchasing power of townships nearby. We further analysed these changes in the Bodensee–Oberschwaben and Stuttgart regions to compare the development of the relative purchasing power in both urban and rural environments. This analysis was done in close cooperation with W. Brachat–Schwarz and W. Walla of the Statistical Office of Baden–Württemberg. S.E. is supported by a grant of the graduate college 1100 at Ulm University.