Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials

To be useful to clinicians, prognostic and diagnostic indices must be derived from accurate models developed by using appropriate data sets. We show that fractional polynomials, which extend ordinary polynomials by including non-positive and fractional powers, may be used as the basis of such models. We describe how to fit fractional polynomials in several continuous covariates simultaneously, and we propose ways of ensuring that the resulting models are parsimonious and consistent with basic medical knowledge. The methods are applied to two breast cancer data sets, one from a prognostic factors study in patients with positive lymph nodes and the other from a study to diagnose malignant or benign tumours by using colour Doppler blood flow mapping. We investigate the problems of biased parameter estimates in the final model and overfitting using cross-validation calibration to estimate shrinkage factors. We adopt bootstrap resampling to assess model stability. We compare our new approach with conventional modelling methods which apply stepwise variables selection to categorized covariates. We conclude that fractional polynomial methodology can be very successful in generating simple and appropriate models.     

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi‐likelihood and generalized quasi‐likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components.     

论李安电影的“性”和谐

对李安导演的电影文本剖析,认为李安电影呈现了多元文化下的"性"和谐特征:在"性"与伦理的冲突与调和中,呈现了人与自然、人自身、人际关系的和谐,并借生命的逝去达到"性"与伦理的调和,以包容、妥协及理智达到"性"与伦理的和谐。     

Model Selection and Regression t-Statistics

It is shown that dropping quantitative variables from a linear regression, based on t-statistics, is mathematically equivalent to dropping variables based on commonly used information criteria.     

Risk Factor Selection in Rate Making: EM Adaptive LASSO for Zero‐Inflated Poisson Regression Models

Risk factor selection is very important in the insurance industry, which helps precise rate making and studying the features of high‐quality insureds. Zero‐inflated data are common in insurance, such as the claim frequency data, and zero‐inflation makes the selection of risk factors quite difficult. In this article, we propose a new risk factor selection approach, EM adaptive LASSO, for a zero‐inflated Poisson regression model, which combines the EM algorithm and adaptive LASSO penalty. Under some regularity conditions, we show that, with probability approaching 1, important factors are selected and the redundant factors are excluded. We investigate the finite sample performance of the proposed method through a simulation study and the analysis of car insurance data from SAS Enterprise Miner database.     

Bayesian meta-analysis using skewed elliptical distributions

Meta-analysis refers to a quantitative method for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution proposed originally by Chen, Dey, and Shao [M. H. Chen, D. K. Dey, Q. M. Shao, A new skewed link model for dichotomous quantal response data, J. Amer. Statist. Assoc. 94 (1983), pp. 1172–1186.] and Branco and Dey [D. Branco and D.K. Dey, A general class of multivariate skew-elliptical distributions, J. Multivariate Anal. 79, pp. 99–113.]. These rich classes of models combine the information of independent studies, allowing investigation of variability both between and within studies and incorporating weight functions. We constructed a detailed computational scheme under skewed normal and skewed Student's t distribution using the MCMC method. Bayesian model selection was conducted by Bayes factor under a different skewed error. Finally, we illustrated our methodology using a real data example taken from Johnson [M.F. Johnson, Comparative efficacy of Naf and SMFP dentifrices in caries prevention: a meta-analysis overview, J Eur. Organ. Caries Res. 27 (1993), pp. 328–336.].     

Queering the Cosmology of the Vikings: A Queer Analysis of the Cult of Odin and “Holy White Stones”

ABSTRACT

Ideas concerning Eros, honor and death were central to the Norse perception of the world. Odin is the greatest war god, and associated with manliness. However, Odin is also the most powerful master of seid (sorcery), an activity associated with women. Seid may be interpreted as a form of shamanism. If a man performed seid he could be accused of ergi, that is, unmanliness. Therefore it could be said that Odin exercised an activity considered unmanly. How could Odin perform seid without losing his position as the god of war and warriors? This paradox is discussed from a queer theoretical perspective. On this basis a new interpretation of the so-called “holy white” phallic stones in western Norway is suggested. Most of these stones are associated with burials from the later part of the Scandinavian Early Iron Age. The temporal distribution of the white phallic stones correlates well with the increasing importance of the cult of Odin. There may be a cultic association between the cult of Odin and the burial practices involving white holy phallic stones.     

A comparison of methods for the fitting of generalized additive models

There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.     

试论我国铁路客运运价规制改革的模式选择

从20世纪80年代起,我国铁路客运经历了一系列运价改革,长期以来严格的运价规制开始松动。但规制手段陈旧,规制机制不清依然是不可否认的事实。本文通过对我国铁路客运现行规制模式的判断,找出其中存在的主要问题,并以现行规制为基础,提出两套运价规制改革的方案,同时论证了两种方案的可行性、局限性及利弊。     

A MORE GENERAL CRITERION FOR SUBSET SELECTION IN MULTIPLE LINEAR REGRESSION

ABSTRACT

In this article, we propose a more general criterion called S_p -criterion, for subset selection in the multiple linear regression Model. Many subset selection methods are based on the Least Squares (LS) estimator of β, but whenever the data contain an influential observation or the distribution of the error variable deviates from normality, the LS estimator performs ‘poorly’ and hence a method based on this estimator (for example, Mallows’ C_p -criterion) tends to select a ‘wrong’ subset. The proposed method overcomes this drawback and its main feature is that it can be used with any type of estimator (either the LS estimator or any robust estimator) of β without any need for modification of the proposed criterion. Moreover, this technique is operationally simple to implement as compared to other existing criteria. The method is illustrated with examples.