Inferences on the Among-Group Variance Component in Unbalanced Heteroscedastic One-Fold Nested Design

This article studies the hypothesis testing and interval estimation for the among-group variance component in unbalanced heteroscedastic one-fold nested design. Based on the concepts of generalized p-value and generalized confidence interval, tests and confidence intervals for the among-group variance component are developed. Furthermore, some simulation results are presented to compare the performance of the proposed approach with those of existing approaches. It is found that the proposed approach and one of the existing approaches can maintain the nominal confidence level across a wide array of scenarios, and therefore are recommended to use in practical problems. Finally, a real example is illustrated.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Splines for financial volatility

Summary.  We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B -splines of lagged observations and volatilities. Estimation of such a B -spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B -spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.     

Statistical inference for olfactometer data

Summary.  Olfactometer experiments are used to determine the effect of odours on the behaviour of organisms such as insects or nematodes, and typically result in data comprising many groups of small overdispersed counts. We develop a non-homogeneous Markov chain model for data from olfactometer experiments with parasitoid wasps and discuss a relation with the Dirichlet–multinomial distribution. We consider the asymptotic relative efficiencies of three different observation schemes and give an analysis of data intended to shed light on the effect of previous experience of odours in the wasps.     

米氮平治疗广泛性焦虑症的临床观察

目的探讨米氮平治疗广泛性焦虑症(GAD)的临床疗效及安全性。方法共85例广泛性焦虑症患者入组,米氮平治疗46例,对照观察组39例,共观察8周,使用HAMA判断疗效,并记录不良反应。结果74例完成研究(米氮平41例,对照组33例)。研究终点,米氮平组HAMA减分平均为12.5±5.8,对照组减分平均为7.7±6.5,两组比较差异有统计学意义(t=3.35,P(0.01);米氮平治疗后14天及其后各随访点HAMA减分与观察组比较差异均有统计学意义;米氮平治疗GAD的有效率71%,显著优于观察组(39%)(2χ=7.32,P<0.01);米氮平的主要不良反应为体重增加、食欲增强、嗜睡及头晕。结论米氮平治疗GAD有效,依从性高,不良反应不多见,可作为临床治疗GAD的一种选择。     

EXPONENTIAL DISPERSION MODELS AND THE GAUSS-NEWTON ALGORITHM

It is known that the Fisher scoring iteration for generalized linear models has the same form as the Gauss-Newton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the analogy with normal regression is preserved. The multinomial distribution is used as an example.     

Generalized linear models with functional predictors

Summary. We present a technique for extending generalized linear models to the situation where some of the predictor variables are observations from a curve or function. The technique is particularly useful when only fragments of each curve have been observed. We demonstrate, on both simulated and real data sets, how this approach can be used to perform linear, logistic and censored regression with functional predictors. In addition, we show how functional principal components can be used to gain insight into the relationship between the response and functional predictors. Finally, we extend the methodology to apply generalized linear models and principal components to standard missing data problems.     

Analysing partial ranks by using smoothed paired comparison methods: an investigation of value orientation in Europe

Summary. This paper introduces the paired comparison model as a suitable approach for the analysis of partially ranked data. For example, the Inglehart index, collected in international social surveys to examine shifts in post-materialistic values, generates such data on a set of attitude items. However, current analysis methods have failed to account for the complex shifts in individual item values, or to incorporate subject covariates. The paired comparison model is thus developed to allow for covariate subject effects at the individual level, and a reparameterization allows the inclusion of smooth non-linear effects of continuous covariates. The Inglehart index collected in the 1993 International Social Science Programme survey is analysed, and complex non-linear changes of item values with age, level of education and religion are identified. The model proposed provides a powerful tool for social scientists.     

Smoothing spline Gaussian regression: more scalable computation via efficient approximation

Summary.  Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O ( n ³), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is presented and the Bayes model that is associated with the approximations is derived, with the latter guiding the porting of Bayesian confidence intervals. The practical choice of the dimension of the approximating space is determined through simulation studies, and empirical comparisons of the approximations with the exact solution are presented. Also evaluated is a simple modification of the generalized cross-validation method for smoothing parameter selection, which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross-validation.     

Inferences of variance function - a parametric robust way

Tsou (2003a) proposed a parametric procedure for making robust inference for mean regression parameters in the context of generalized linear models. This robust procedure is extended to model variance heterogeneity. The normal working model is adjusted to become asymptotically robust for inference about regression parameters of the variance function for practically all continuous response variables. The connection between the novel robust variance regression model and the estimating equations approach is also provided.