Political equilibria with electoral uncertainty

After an election, when party positions and strengths are known, there may be a centrally located large party at the core position. Theory suggests that such a core party is able to form a minority government and control policy. In the absence of a core party, theory suggests that the outcome be a lottery associated with coalition risk. Stochastic models of elections typically indicate that all parties, in equilibrium, will adopt positions at the electoral center. This paper first presents an existence theorem for local Nash equilibrium (LNE) under vote maximization, and then constructs a more general model using the notion of coalition risk. The model allows for the balancing of office and policy motivations. Empirical analyses of elections in the Netherlands and Israel are used as illustrations of the model and of the concept of a structurally stable LNE. The figures and tables are reproduced from Schofield and Sened (2006) with permission from Cambridge University Press.     

Ambivalence and the paradoxes of grandparenting

This paper focuses on ‘normative talk’ about grandparenting. It is based on a secondary analysis of a study involving 46 interviews with grandparents. It identifies two main cultural norms of grandparenting that emerged from the data –‘being there’ and ‘not interfering’. There were very high levels of consensus in the study that these constituted what grandparents ‘should and should not’ do. However, these two norms can be contradictory, and are not easy to reconcile with the everyday realities of grandparenting. The study found that norms of parenting and also of self determination were also very important for the grandparents in the study. They had a keen sense of what being a ‘good parent’ (to their own adult children) should mean – especially in terms of allowing them to be independent – but this could sometimes conflict with their sense of responsibility to descendant generations of grandchildren. Using the concept of ambivalence and drawing on the accounts of grandparents in the study, the paper explores and offers an explanation for both the coexistence and conflict between different sets of norms, as well as for the remarkably high levels of consensus about ‘being there’ and ‘not interfering’. The paper concludes with a discussion of some of the limitations of the data and the analysis, and with suggestions for the development of further work in this area.     

On estimation of covariate-specific residual time quantiles under the proportional hazards model

Estimation and inference in time-to-event analysis typically focus on hazard functions and their ratios under the Cox proportional hazards model. These hazard functions, while popular in the statistical literature, are not always easily or intuitively communicated in clinical practice, such as in the settings of patient counseling or resource planning. Expressing and comparing quantiles of event times may allow for easier understanding. In this article we focus on residual time, i.e., the remaining time-to-event at an arbitrary time t given that the event has yet to occur by t. In particular, we develop estimation and inference procedures for covariate-specific quantiles of the residual time under the Cox model. Our methods and theory are assessed by simulations, and demonstrated in analysis of two real data sets.     

A Critical Evaluation of Acupuncture Research

As Chinese medicine is going global, it is simultaneously adapting swiftly to local patterns of perception and interpretation, thereby being shaped into hitherto unknown forms. The globalization of Chinese medicine produces multiple localized visions of a healing system whose trademark is an “innate heterodoxy”. Barnes described the “psychologizing” of Chinese medicine in the USA (Barnes Cult Med Psychiatry 22(4):413–443, 1998). In Germany, however, biomedical instead of “holistic” patterns of perception and interpretation and a tendency to “physiologize” prevail among patients and Chinese Medical therapists. Here the recent German Acupuncture trials, and Acupuncture Randomized Trials (ART) and Cochrane data base metaanalysis (Linde et al., 2009a) shall serve as a prominent example of how German research centers around physiological phenomena and how these studies have triggered an international debate concerning the point-specific nature of acupuncture interventions. In order to evaluate the specific effect of acupuncture in randomized controlled trials, verum acupuncture, defined as acupuncture at “classical” acupuncture points, and sham acupuncture, defined as acupuncture at “non-acupuncture points”, are frequently compared. The anatomically exact location and specificity of acupuncture points are basic assumptions underlying this concept. But how clearly divisible are verum and sham acupuncture points if acupuncture physiology itself is a historical construct? To more adequately evaluate acupuncture’s effectiveness future clinical studies will have to tailor their methodology to the reality of the acupuncture encounter.     

The effects of model mis-specifications in linear measurement error models

In the literature, there are many results on the consequences of mis-specified models for linear models with error in the response only, see, e.g., Seber(1977). There are also discussions of estimation for the model writh errors both in the response and in the predictor variables (called measurement error models; see, e.g., Fuller(1987)). In this paper, we consider the problem of model mis-specification for measurement error models. Only a few special cases have been tackled in the past (Edland, 1996; Carroll and Ruppert, 1996 and Lakshminarayanan Amp; Gunst, 1984); we deal with the situation here in some generality. Results have been obtained as follows: (a) When a model is under-fitted, the estimate of the variance of the measurement error will be asymptotically biased, as will the regression coefficients, and the asymptotic biases in the estimates of the regression coefficients will always exist for under-fitted models. Even orthogonality of the variables in the model will not make the biases vanish. (b)For over-fitting, the estimates of the variances of measurement errors and of the regression coefficients are asymptotically unbiased. However, the variance of the estimated regression coefficients will increase. Over-fitting will cause larger changes in the variances of the estimated parameters in measurement error models than in no measurement error models.     

Ridge regression from principal component point of view

Ridge regression is often discussed as an estimation procedure for producing estimators which are biased but with a smaller mean squared error than the usual least square estimators. In this paper we show that this procedure can also be used to reflect the nature of dependency among a set of highly collinear regressor variables. In particular, we prove that, when data are severely multicollinear, the ridge estimators can be made very close to the principal component estimators. Examples are given to illustrate the point.