Nonlinear mixed-effects models with scale mixture of skew-normal distributions

Aiming to avoid the sensitivity in the parameters estimation due to atypical observations or skewness, we develop asymmetric nonlinear regression models with mixed-effects, which provide alternatives to the use of normal distribution and other symmetric distributions. Nonlinear models with mixed-effects are explored in several areas of knowledge, especially when data are correlated, such as longitudinal data, repeated measures and multilevel data, in particular, for their flexibility in dealing with measures of areas such as economics and pharmacokinetics. The random components of the present model are assumed to follow distributions that belong to scale mixtures of skew-normal (SMSN) distribution family, that encompasses distributions with light and heavy tails, such as skew-normal, skew-Student-t, skew-contaminated normal and skew-slash, as well as symmetrical versions of these distributions. For the parameters estimation we obtain a numerical solution via the EM algorithm and its extensions, and the Newton-Raphson algorithm. An application with pharmacokinetic data shows the superiority of the proposed models, for which the skew-contaminated normal distribution has shown to be the most adequate distribution. A brief simulation study points to good properties of the parameter vector estimators obtained by the maximum likelihood method.     

Identification of longitudinal biomarkers for survival by a score test derived from a joint model of longitudinal and competing risks data

In this paper, we consider joint modelling of repeated measurements and competing risks failure time data. For competing risks time data, a semiparametric mixture model in which proportional hazards model are specified for failure time models conditional on cause and a multinomial model for the marginal distribution of cause conditional on covariates. We also derive a score test based on joint modelling of repeated measurements and competing risks failure time data to identify longitudinal biomarkers or surrogates for a time to event outcome in competing risks data.     

Prediction Error of Small Area Predictors Shrinking Both Means and Variances

The article considers a new approach for small area estimation based on a joint modelling of mean and variances. Model parameters are estimated via expectation–maximization algorithm. The conditional mean squared error is used to evaluate the prediction error. Analytical expressions are obtained for the conditional mean squared error and its estimator. Our approximations are second‐order correct, an unwritten standardization in the small area literature. Simulation studies indicate that the proposed method outperforms the existing methods in terms of prediction errors and their estimated values.     

Linear Quantile Regression Based on EM Algorithm

This article aims to put forward a new method to solve the linear quantile regression problems based on EM algorithm using a location-scale mixture of the asymmetric Laplace error distribution. A closed form of the estimator of the unknown parameter vector β based on EM algorithm, is obtained. In addition, some simulations are conducted to illustrate the performance of the proposed method. Simulation results demonstrate that the proposed algorithm performs well. Finally, the classical Engel data is fitted and the Bootstrap confidence intervals for estimators are provided.     

Local influence for incomplete data models

This paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data. The idea is to utilize Cook's approach to the conditional expectation of the complete-data log-likelihood function in the EM algorithm. It is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods. An application to the generalized linear mixed model is investigated. Some illustrative artificial and real examples are presented.     

Forecasting time series with missing data using Holt's model

This paper deals with the prediction of time series with missing data using an alternative formulation for Holt's model with additive errors. This formulation simplifies both the calculus of maximum likelihood estimators of all the unknowns in the model and the calculus of point forecasts. In the presence of missing data, the EM algorithm is used to obtain maximum likelihood estimates and point forecasts. Based on this application we propose a leave-one-out algorithm for the data transformation selection problem which allows us to analyse Holt's model with multiplicative errors. Some numerical results show the performance of these procedures for obtaining robust forecasts.     

Influence analysis in skew-Birnbaum–Saunders regression models and applications

In this paper, we propose a method to assess influence in skew-Birnbaum–Saunders regression models, which are an extension based on the skew-normal distribution of the usual Birnbaum–Saunders (BS) regression model. An interesting characteristic that the new regression model has is the capacity of predicting extreme percentiles, which is not possible with the BS model. In addition, since the observed likelihood function associated with the new regression model is more complex than that from the usual model, we facilitate the parameter estimation using a type-EM algorithm. Moreover, we employ influence diagnostic tools that considers this algorithm. Finally, a numerical illustration includes a brief simulation study and an analysis of real data in order to show the proposed methodology.     

GETTING THE ‘CORRECT’ ANSWER FROM SURVEY RESPONSES: A SIMPLE APPLICATION OF THE EM ALGORITHM

This note addresses a problem that can arise in surveys, namely when some respondents misinterpret the rating method and so assign high ratings when they intended to assign low ratings, and vice versa. We present a method that allows these misinterpretations to be corrected with high probability, and more meaningful conclusions to be drawn. The method is illustrated with data from a Community Value survey.     

航线网络中需求无约束估计的非参数选择模型

传统的航空客运需求无约束估计方法仅针对平行直达航班中的顾客需求“溢出”和“再 现”问题,未能考虑航空网络中直达和中转联程航班之间的网络替代效应． 基于顾客偏好排序列表定义了航空网络顾客类型集合,建立了考虑顾客策略行为的网络型非参数离散选择模型．考虑到网络环境下历史预售数据的不完备性,站在线上和线下交易平台的角度,分别建立了非截尾和截尾需求情况下的完备数据对数似然函数． 采用 EM 算法对顾客到达率和概率质量函数进行联合估计,并提出了网络环境下的顾客“初始需求”、“再现需求”和“溢出需求”无约束估计计算方法．通过数值模拟验证了所提方法的可行性和有效性,相较于现有方法能准确反映产品间网络替代效应对顾客选择行为影响,从而更加有效地避免对历史顾客“初始需求”的高估问题．