An employee assistance program for caregiver support

The Comprehensive Caregiver Choices Program provided support for employee caregivers of elderly people for employees at a hospital in Fort Worth, Texas. Key informant interviews and focus groups provided direction for program development and implementation. A full-time MSW and professionals with expertise in gerontology/geriatrics provided education and care coordination services to caregivers. Approximately 4% of the hospital's workforce participated in the program. Attendees evaluated educational sessions and follow-up interviews were conducted with program participants. Caregiver support programs must continue to seek innovative and creative marketing and service delivery methods to reach out and assist working caregivers in need of support.     

A geometrically motivated parametric model in manifold estimation

The general aim of manifold estimation is reconstructing, by statistical methods, an m-dimensional compact manifold S on ^d (with m≤d) or estimating some relevant quantities related to the geometric properties of S. Focussing on the cases d=2 and d=3, with m=d or m=d?1, we will assume that the data are given by the distances to S from points randomly chosen on a band surrounding S. The aim of this paper is to show that, if S belongs to a wide class of compact sets (which we call sets with polynomial volume), the proposed statistical model leads to a relatively simple parametric formulation. In this setup, standard methodologies (method of moments, maximum likelihood) can be used to estimate some interesting geometric parameters, including curvatures and Euler characteristic. We will particularly focus on the estimation of the (d?1)-dimensional boundary measure (in Minkowski's sense) of S. It turns out, however, that the estimation problem is not straightforward since the standard estimators show a remarkably pathological behaviour: while they are consistent and asymptotically normal, their expectations are infinite. The theoretical and practical consequences of this fact are discussed in some detail.     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

Chance-Corrected Measures of Reliability and Validity in 2 × 2 Tables

It is customary to use two groups of indices to evaluate a diagnostic method with a binary outcome: validity indices with a standard rater (sensitivity, specificity, and positive or negative predictive values) and reliability indices (positive, negative and overall agreements) without a standard rater. However neither of these classic indices is chance-corrected, and this may distort the analysis of the problem (especially in comparative studies). One way of chance-correcting these indices is by using the Delta model (an alternative to the Kappa model), but this means having to use a computer program to work out the calculations. This paper gives an asymptotic version of the Delta model, thus allowing simple expressions to be obtained for the estimator of each of the above-mentioned chance-corrected indices (as well as for its standard error).     

Distributions with Generalized Skewed Conditionals and Mixtures of Such Distributions

Mixtures of skewed distributions (univariate and bivariate) provide flexible models. An alternative modeling approach involves distributions with skewed conditional distributions and mixtures of such distributions. We consider the interrelationships between such models. Examples are provided to show that several skewed distributions already considered in the literature can be viewed as having been constructed via a combination of mixing and skewing.     

Varying-Coefficient Functional Linear Regression Models

This article considers a generalization of the functional linear regression in which an additional real variable influences smoothly the functional coefficient. We thus define a varying-coefficient regression model for functional data. We propose two estimators based, respectively, on conditional functional principal regression and on local penalized regression splines and prove their pointwise consistency. We check, with the prediction one day ahead of ozone concentration in the city of Toulouse, the ability of such nonlinear functional approaches to produce competitive estimations.     

The Characterization of the Symmetric Lorenz Curves by Doubly Truncated Mean Function

We characterize symmetric Lorenz curves by the relation m(x, μ²/x) = μ (where μ =E(X) and m(x, y) = E(X | x ≤ X ≤ y) is the doubly truncated mean function). We establish that the points of the r.v. which generate the symmetric points on the Lorenz curve are x and μ²/x, and that all the distribution functions defined on the same support which are generators of the symmetric Lorenz curves have the same mean. We obtain the conditions under which doubly truncated distributions generate symmetrical Lorenz curves.     

A Note on Unwanted Variance in Exploratory Factor Models

One strategy of exploratory factor analysis is to decide on the number of factors to extract by means of the eigenvalues of an initial principal component analysis. The present article proves that there is a non zero covariance of the factors with the components rejected when the number of factors to extract is determined by means of principal components analysis. Thus, some of the variance declared as irrelevant or unwanted in an initial principal component analysis is again part of the final factor model.     

Gamma-Generalized Inverse Gaussian Class of Distributions with Applications

In this article, a new family of probability distributions with domain in ?⁺ is introduced. This class can be considered as a natural extension of the exponential-inverse Gaussian distribution in Bhattacharya and Kumar (1986 Bhattacharya , S. K. , Kumar , S. ( 1986 ). E-IG model in life testing . Calcutta Statist. Assoc. Bull. 35 : 85 – 90 . [Google Scholar]) and Frangos and Karlis (2004 Frangos , N. , Karlis , D. ( 2004 ). Modelling losses using an exponential-inverse Gaussian distribution . Insur. Math. Econo. 35 : 53 – 67 .[Crossref], [Web of Science ®] , [Google Scholar]). This new family is obtained through the mixture of gamma distribution with generalized inverse Gaussian distribution. We also show some important features such as expressions of probability density function, moments, etc. Special attention is paid to the mixture with the inverse Gaussian distribution, as a particular case of the generalized inverse Gaussian distribution. From the exponential-inverse Gaussian distribution two one-parameter family of distributions are obtained to derive risk measures and credibility expressions. The versatility of this family has been proven in numerical examples.     

Independence in Contingency Tables Using Simplicial Geometry

Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example.