Assessing goodness-of-fit of categorical regression models based on case-control data

Demonstrated equivalence between a categorical regression model based on case‐control data and an I‐sample semiparametric selection bias model leads to a new goodness‐of‐fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov‐type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in the I‐sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets.     

谈音长在教学和修辞中的作用

语言是声音和意义的结合体。语音是语言的物质外壳。语音的音长决定着言语的速度 ,在交际中 ,对内容的表达起积极作用 ,在教学和修辞的语言实践中 ,应重视音长的作用。     

Bayesian analysis of elapsed times in continuous‐time Markov chains

The authors consider Bayesian analysis for continuous‐time Markov chain models based on a conditional reference prior. For such models, inference of the elapsed time between chain observations depends heavily on the rate of decay of the prior as the elapsed time increases. Moreover, improper priors on the elapsed time may lead to improper posterior distributions. In addition, an infinitesimal rate matrix also characterizes this class of models. Experts often have good prior knowledge about the parameters of this matrix. The authors show that the use of a proper prior for the rate matrix parameters together with the conditional reference prior for the elapsed time yields a proper posterior distribution. The authors also demonstrate that, when compared to analyses based on priors previously proposed in the literature, a Bayesian analysis on the elapsed time based on the conditional reference prior possesses better frequentist properties. The type of prior thus represents a better default prior choice for estimation software.     

On the shrinkage of local linear curve estimators

Local linear curve estimators are typically constructed using a compactly supported kernel, which minimizes edge effects and (in the case of the Epanechnikov kernel) optimizes asymptotic performance in a mean square sense. The use of compactly supported kernels can produce numerical problems, however. A common remedy is ridging, which may be viewed as shrinkage of the local linear estimator towards the origin. In this paper we propose a general form of shrinkage, and suggest that, in practice, shrinkage be towards a proper curve estimator. For the latter we propose a local linear estimator based on an infinitely supported kernel. This approach is resistant against selection of too large a shrinkage parameter, which can impair performance when shrinkage is towards the origin. It also removes problems of numerical instability resulting from using a compactly supported kernel, and enjoys very good mean squared error properties.     

Estimation of critical points in the mixture inverse Gaussian model

The maximum likelihood estimation for the critical points of the failure rate and the mean residual life function are presented in the case of mixture inverse Gaussian model. Several important data sets are analyzed from this point of view. For each of the data sets, Bootstrapping is used to construct confidence intervals of the critical points.     

An Assessment of Change in Risk Perception and Optimistic Bias for Hurricanes Among Gulf Coast Residents

This study focuses on levels of concern for hurricanes among individuals living along the Gulf Coast during the quiescent two‐year period following the exceptionally destructive 2005 hurricane season. A small study of risk perception and optimistic bias was conducted immediately following Hurricanes Katrina and Rita. Two years later, a follow‐up was done in which respondents were recontacted. This provided an opportunity to examine changes, and potential causal ordering, in risk perception and optimistic bias. The analysis uses 201 panel respondents who were matched across the two mail surveys. Measures included hurricane risk perception, optimistic bias for hurricane evacuation, past hurricane experience, and a small set of demographic variables (age, sex, income, and education). Paired t‐tests were used to compare scores across time. Hurricane risk perception declined and optimistic bias increased. Cross‐lagged correlations were used to test the potential causal ordering between risk perception and optimistic bias, with a weak effect suggesting the former affects the latter. Additional cross‐lagged analysis using structural equation modeling was used to look more closely at the components of optimistic bias (risk to self vs. risk to others). A significant and stronger potentially causal effect from risk perception to optimistic bias was found. Analysis of the experience and demographic variables’ effects on risk perception and optimistic bias, and their change, provided mixed results. The lessening of risk perception and increase in optimistic bias over the period of quiescence suggest that risk communicators and emergency managers should direct attention toward reversing these trends to increase disaster preparedness.     

Semi-doubly optimal concentric circles fitting with presence of heteroscedasticity

Previous studies focus on homogeneous and isotropic assumptions about the noisy data. Many methods have been developed recently for fitting concentric circles to data. In this paper, these statistical assumptions have been relaxed. To the best of our knowledge, only one iterative method has been recently developed. Due to its complexity, no such algorithm is available to compute the reliable maximum likelihood estimator (MLE). Accordingly, we have developed four new methods that outperform the existing methods including the orthogonal distance regression (ODR). We also discuss which of these methods is superior according to the four principles: statistical efficiency, accuracy, robustness, and computational efficiency. Numerical experiments on synthetic and real images have been conducted to validate our findings.     

Discovering hidden statistical issues through individual-level models in ecological studies

ABSTRACT

In ecological studies, individual inference is made based on results from ecological models. Interpretation of the results requires caution since ecological analysis on group level may not hold in the individual level within the groups, leading to ecological fallacy. Using an ecological regression example for analyzing voting behaviors, we highlight that the explicit use of individual-level models is crucial in understanding the results of ecological studies. In particular, we clarify three relevant statistical issues for each individual-level models: assessment of the uncertainty of parameter estimates obtained from a wrong model, the use of shrinkage estimation method for simultaneous estimation of many parameters, and the necessity of sensitivity analysis rather than adhering to one seemingly most compelling assumption.     

Why do participants in voluntary organizations leave? Exploring the relationship between value congruence and length of stay

Recognizing the importance of values and the specific characteristics of participants and situations in voluntary organizations, we examine how value congruence—the fit or compatibility of values between participants and the organization, or among participants—interacts with personal and situational factors to predict participants' length of stay in their organizations. Introducing the case of a voluntary organization that offers shared housing, we measure value congruence through textual similarity in the self‐introduction documents of 49 participants and the organization's mission statement. This approach differs from the self‐reported measures based on participants' perceptions or recalled interactions used in previous studies. In line with expectation‐disconfirmation theory, participants with the strongest beliefs in organizational values had shorter lengths of stay. The amount of intraorganizational communication also moderated the relationship between value congruence and length of stay. This study provides theoretical and methodological implications for nonprofit management by considering personal and situational factors and evaluating value congruence by textual similarity.     

Longitudinal relations between behavioral inhibition and social information processing: Moderating role of maternal supportive reactions to children's emotions

Utilizing multiple measures of interpretive biases, the current study examined the roles of toddlers’ behavioral inhibition (BI) and maternal supportive reactions to children's negative emotions in relation to children's interpretive biases across middle to late childhood. Toddlers’ BI was measured during several laboratory tasks (n = 248) at 2 and 3 years of age. Mothers reported on their reactions to children's negative emotional expressions when children were 7 years old (n = 203), and children's interpretations of social cues were assessed at 7 and 10 years of age (n s = 179 and 161, respectively). Toddlers with high levels of BI expressed less positivity toward social engagement with unfamiliar peers during discussion of ambiguous social situations. Further, children with high BI were less likely to attribute the cause of negative social situations to external factors, particularly when mothers were less accepting of children's negative emotional displays. Findings are discussed in terms of cognition related to the interpretation of ambiguous and threat‐related social situations among temperamentally at‐risk children.