A Graphical Tool for Interpreting Regression Coefficients of Trinomial Logit Models

Multinomial logit (also termed multi-logit) models permit the analysis of the statistical relation between a categorical response variable and a set of explicative variables (called covariates or regressors). Although multinomial logit is widely used in both the social and economic sciences, the interpretation of regression coefficients may be tricky, as the effect of covariates on the probability distribution of the response variable is nonconstant and difficult to quantify. The ternary plots illustrated in this article aim at facilitating the interpretation of regression coefficients and permit the effect of covariates (either singularly or jointly considered) on the probability distribution of the dependent variable to be quantified. Ternary plots can be drawn both for ordered and for unordered categorical dependent variables, when the number of possible outcomes equals three (trinomial response variable); these plots allow not only to represent the covariate effects over the whole parameter space of the dependent variable but also to compare the covariate effects of any given individual profile. The method is illustrated and discussed through analysis of a dataset concerning the transition of master’s graduates of the University of Trento (Italy) from university to employment.     

Robust Designs in Generalized Linear Models: A Quantile Dispersion Graphs Approach

This article studies design selection for generalized linear models (GLMs) using the quantile dispersion graphs (QDGs) approach in the presence of misspecification in the link and/or linear predictor. The uncertainty in the linear predictor is represented by a unknown function and estimated using kriging. For addressing misspecified link functions, a generalized family of link functions is used. Numerical examples are shown to illustrate the proposed methodology.     

Still-births among the offspring of male radiation workers at the Sellafield nuclear reprocessing plant: detailed results and statistical aspects

Summary. This study investigates whether there was evidence of increasing risk of still-birth with increasing paternal exposure to ionizing radiation received during employment at the Sellafield nuclear installation before the child was conceived. A significant positive association is found between the total paternal preconceptional exposure to external ionizing radiation and the risk of still-birth (after adjustment for year of birth, social class, birth order and paternal age, odds ratio at 100 mSv 1.24 (95% confidence interval 1.04–1.45)). A summary of the principal scientific findings of this study has been published in the Lancet . This paper describes in detail the statistical methods that were used in the investigation and presents the results in full.     

GMM tests for the Katz family of distributions

Generalized method of moments (GMM) is used to develop tests for discriminating discrete distributions among the two-parameter family of Katz distributions. Relationships involving moments are exploited to obtain identifying and over-identifying restrictions. The asymptotic relative efficiencies of tests based on GMM are analyzed using the local power approach and the approximate Bahadur efficiency. The paper also gives results of Monte Carlo experiments designed to check the validity of the theoretical findings and to shed light on the small sample properties of the proposed tests. Extensions of the results to compound Poisson alternative hypotheses are discussed.     

Robust testing with generalized partial linear models for longitudinal data

By approximating the nonparametric component using a regression spline in generalized partial linear models (GPLM), robust generalized estimating equations (GEE), involving bounded score function and leverage-based weighting function, can be used to estimate the regression parameters in GPLM robustly for longitudinal data or clustered data. In this paper, score test statistics are proposed for testing the regression parameters with robustness, and their asymptotic distributions under the null hypothesis and a class of local alternative hypotheses are studied. The proposed score tests reply on the estimation of a smaller model without the testing parameters involved, and perform well in the simulation studies and real data analysis conducted in this paper.     

Quadratic estimators of covariance components in a multivariate mixed linear model

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.     

Local influence in multilevel models

The authors study the local influence of observations in multilevel regression models. To this end, they perturb simultaneously the variances, responses and design matrix. To measure the local change caused by these perturbations, they use generalized Cook statistics for the fixed and random parameter estimates. Closed form local influence measures also allow them to assess the joint influence of various observations. They suggest a simple computation method and illustrate their results using two examples.     

LENGTH-BIASING, CHARACTERIZATIONS OF LAWS AND THE MOMENT PROBLEM

A positive random variable X with a finite mean has an induced length-biased law represented by Y, and Y is stochastically larger than X. An independent uniform random contraction of Y, UY, has the same law as X if and only if the latter is exponential. This property is extended to non-uniform contractions and a more general notion of length-biasing. The distributional equality of X and W leads to a functional equation for the moment function of X, which has either Infinitely many solutions or none. When U is constant, X can have a log-normal law, but it can also have laws with the same moment sequence as this log-nod law. The case where U has a certain beta, or generalized beta, law give t3 characterizations of generalized gamma laws, or to products of independent copies of them. This occurs even when these laws are not determined by their moment sequences.     

具有反馈控制的Logistic扩散系统周期解的存在与稳定

利用上下解，Ｂｒｏｕｗｅｒ不动点原理及Ｌｙａｐｕｎｏｖ泛函方法，讨论了一类具有反馈控制的Ｌｏｇｉｓｔｉｃ扩散系统的周期解问题；获得了周期解存在且稳定的判别条件．