ASYMPTOTIC NORMALITY OF GOODNESS-OF-FIT STATISTICS FOR SPARSE POISSON DATA

Goodness-of-fit tests for discrete data and models with parameters to be estimated are usually based on Pearson's χ2 or the Likelihood Ratio Statistic. Both are included in the family of Power-Divergence Statistics SDλ which are asymptotically χ2 distributed for the usual sampling schemes. We derive a limiting standard normal distribution for a standardization Tλ of SDλ under Poisson sampling by considering an approach with an increasing number of cells. In contrast to the χ2 asymptotics we do not require an increase of all expected values and thus meet the situation when data are sparse. Our limit result is useful even if a bootstrap test is used, because it implies that the statistic Tλ should be bootstrapped and not the sum SDλ. The peculiarity of our approach is that the models under test only specify associations. Hence we have to deal with an infinite number of nuisance parameters. We illustrate our approach with an application.     

How the Reflection of Linear Correlation in Odds Ratios Depends on the Cut-Off Points

When an OR is calculated based on data measured on continuous scales, the magnitude of the OR is dependent on the cut-offs chosen for dichotomizing both dependent and independent variables even when the relationship is strictly linear. Cuts away from the median on either or both dependent and independent variables increase the expected OR. This increase is quite substantial when the cut-off is made at the extremes. Illustrations of the consequences of cut-off on OR for populations with varying values of linear correlation are provided in simulated and real data. Potential circumstances and motivations for such dichotomizations are discussed.     

Reducing Bias and Mean Squared Error Associated With Regression-Based Odds Ratio Estimators

Ratio estimators of effect are ordinarily obtained by exponentiating maximum-likelihood estimators (MLEs) of log-linear or logistic regression coefficients. These estimators can display marked positive finite-sample bias, however. We propose a simple correction that removes a substantial portion of the bias due to exponentiation. By combining this correction with bias correction on the log scale, we demonstrate that one achieves complete removal of second-order bias in odds ratio estimators in important special cases. We show how this approach extends to address bias in odds or risk ratio estimators in many common regression settings. We also propose a class of estimators that provide reduced mean bias and squared error, while allowing the investigator to control the risk of underestimating the true ratio parameter. We present simulation studies in which the proposed estimators are shown to exhibit considerable reduction in bias, variance, and mean squared error compared to MLEs. Bootstrapping provides further improvement, including narrower confidence intervals without sacrificing coverage.     

农村居民生活满意度的影响因素分析

 本文将Logistic回归方法运用于生活满意度影响因素的分析,首先根据国内外研究成果选取五个影响因素并提出研究假设,其次运用无序多分类Logistic回归模型拟合调查数据,科学确定各因素的影响程度。研究发现家庭年收入、居住区域和对社会公平的看法这三个因素对江苏农村居民生活满意度有显著影响。因此,以经济持续稳定增长促进农村居民持续增收,以社会公平为目标推进政治经济建设将成为提高江苏农村居民生活满意度的有效措施。     

Optimal predictive sample size for case–control studies

Summary.  The identification of factors that increase the chances of a certain disease is one of the classical and central issues in epidemiology. In this context, a typical measure of the association between a disease and risk factor is the odds ratio. We deal with design problems that arise for Bayesian inference on the odds ratio in the analysis of case–control studies. We consider sample size determination and allocation criteria for both interval estimation and hypothesis testing. These criteria are then employed to determine the sample size and proportions of units to be assigned to cases and controls for planning a study on the association between the incidence of a non-Hodgkin's lymphoma and exposition to pesticides by eliciting prior information from a previous study.     

Estimating and contextualizing the attenuation of odds ratios due to non collapsibility

The odds ratio is a measure commonly used for expressing the association between an exposure and a binary outcome. A feature of the odds ratio is that its value depends on the choice of the distribution over which the probabilities in the odds ratio are evaluated. In particular, this means that an odds ratio conditional on a covariate may have a different value from an odds ratio marginal on the covariate, even if the covariate is not associated with the exposure (not a confounder). We define the individual odds ratio (IORs) and population odds ratios (PORs) as the ratio of the odds of the outcome for a unit increase in the exposure, respectively, for an individual in the population and for the whole population, in which case the odds are averaged across the population. The attenuation of conditional odds ratio, marginal odds ratio, and PORs from the IOR is demonstrated in a realistic simulation exercise. The degree of attenuation differs in the whole population and in a case–control sample, and the property of invariance to outcome-dependent sampling is only true for the IOR. The relevance of the non collapsibility of odds ratios in a range of methodological areas is discussed.     

What keeps young adults in permanent poverty? A comparative analysis using ECHP

Previous studies suggest that there are strong differences in the rates of youth poverty across European countries. Rather surprisingly, it is found to be high in Scandinavian countries, and relatively speaking, lower in Mediterranean and Anglo-Saxon countries. This somewhat unexpected finding prompts the question whether the incidence of poverty is an appropriate measure of youth disadvantage. Instead of considering poverty rates we consider the length of recorded poverty spells, taking into account explicitly the temporal sequencing of the episodes of poverty. Using the European Community Household Panel, individuals are classified into different groups of poverty permanence, each reflecting severity of social disadvantage. Based on these categories we implement a generalized ordinal logit model to assess the various factors associated with social disadvantage among youth. We find that cross-national patterns differ from those found in previous studies. In particular from our findings it does not result that poverty is highest among young people in Social Democratic countries. Our analysis shows important gender differences, though they are not the same across the countries included in the study. For some countries it turns out that being a woman is a protective factor against long-term poverty. As previous studies suggests, young individuals’ living arrangements matter.     

The Robustness of Common Measures of 2×2 Association to Bias Due to Misclassifications

The strength of association between two dichotomous characteristics A and B can be measured in many ways. All of these statistics are biased when there is misclassification, and all are prevalence dependent whether or not their population values are. Measures lacking fixed endpoints for random and perfect association, such as sensitivity, specificity, risk ratios, and odds ratio, have a bias either so unpredictable or so large that the observable and true measures of association may bear little resemblance to each other. Reexpressions of these measures that fix the endpoints and other measures with fixed endpoints, such as kappa, phi, gamma, risk difference, and attributable risk, produce attenuated estimates of their true values. Disattenuating such estimators is possible using test—retest data.     

Comparisons of Three Approaches for Discrete Conditional Models

This article describes three methods for computing a discrete joint density from full conditional densities. They are the Gibbs sampler, a hybrid method, and an interaction-based method. The hybrid method uses the iterative proportional fitting algorithm, and it is derived from the mixed parameterization of a contingency table. The interaction-based approach is derived from the canonical parameters, while the Gibbs sampler can be regarded as based on the mean parameters. In short, different approaches are motivated by different parameterizations. The setting of a bivariate conditionally specified distribution is used as the premise for comparing the numerical accuracy of the three methods. Detailed comparisons of marginal distributions, odds ratios and expected values are reported. We give theoretical justifications as to why the hybrid method produces better approximation than the Gibbs sampler. Generalizations to more than two variables are discussed. In practice, Gibbs sampler has certain advantages: it is conceptually easy to understand and there are many software tools available. Nevertheless, the hybrid method and the interaction-based method are accurate and simple alternatives when the Gibbs sampler results in a slowly mixing chain and requires substantial simulation efforts.