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Linear Predictor (linear + predictor)
Selected AbstractsSpace varying coefficient models for small area dataENVIRONMETRICS, Issue 5 2003Renato M. Assunção Abstract Many spatial regression problems using area data require more flexible forms than the usual linear predictor for modelling the dependence of responses on covariates. One direction for doing this is to allow the coefficients to vary as smooth functions of the area's geographical location. After presenting examples from the scientific literature where these spatially varying coefficients are justified, we briefly review some of the available alternatives for this kind of modelling. We concentrate on a Bayesian approach for generalized linear models proposed by the author which uses a Markov random field to model the coefficients' spatial dependency. We show that, for normally distributed data, Gibbs sampling can be used to sample from the posterior and we prove a result showing the equivalence between our model and other usual spatial regression models. We illustrate our approach with a number of rather complex applied problems, showing that the method is computationally feasible and provides useful insights in substantive problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] Short-term MPEG-4 video traffic prediction using ANFISINTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 6 2005Adel Abdennour Multimedia traffic and particularly MPEG-coded video streams are growing to be a major traffic component in high-speed networks. Accurate prediction of such traffic enhances the reliable operation and the quality of service of these networks through a more effective bandwidth allocation and better control strategies. However, MPEG video traffic is characterized by a periodic correlation structure, a highly complex bit rate distribution and very noisy streams. Therefore, it is considered an intractable problem. This paper presents a neuro-fuzzy short-term predictor for MPEG-4-coded videos. The predictor is based on the Adaptive Network Fuzzy Inference System (ANFIS) to perform single-step predictions for the I, P and B frames. Short-term predictions are also examined using smoothed signals of the video sequences. The ANFIS prediction results are evaluated using long entertainment and broadcast video sequences and compared to those obtained using a linear predictor. ANFIS is capable of providing accurate prediction and has the added advantage of being simple to design and to implement. Copyright © 2005 John Wiley & Sons, Ltd. [source] Ten-Year Longitudinal Relationship Between Physical Activity and Lumbar Bone Mass in (Young) Adults,JOURNAL OF BONE AND MINERAL RESEARCH, Issue 2 2003Ingrid Bakker Abstract Little is known about the influence of long-term daily physical activity (PA) on lumbar bone mass after peak bone mass has been reached, that is, during [young] adulthood. The purpose of this study was to investigate the longitudinal relationship between PA and lumbar bone mineral density (LBMD) in healthy subjects over a 10-year period. The data reported here relate to 225 male and 241 female participants in the Amsterdam Growth and Health Longitudinal Study, who were measured at the mean ages of 27, 32, and/or 36. LBMD, habitual daily PA, total body weight, and calcium intake were assessed at each measurement point. The effects of two aspects of PA were analyzed: the mechanical (MECHPA; sum of all ground reaction forces) and metabolic (METPA; weighted metabolic score of intensity, frequency, and duration) components, each within a separate model. Multilevel analysis was used to investigate the relationship between PA and LBMD over the 10-year period. Gender, total body weight, and calcium intake were included in the analysis as covariates. The results indicated that MECHPA was a significant positive linear predictor of LBMD for males (r = 0.09; p < 0.001) but not for females. For the METPA, no linear longitudinal relationship with LBMD was found. The results suggest that there is a metabolic threshold at which extra PA becomes "deleterious" and METPA in its totality becomes ineffective for LBMD. It is concluded that during the (young) adult period, between 27 and 36 years of age, PA causing mechanical loading on the skeleton has a small positive influence on LBMD in males. [source] Generalized Linear Models in Family StudiesJOURNAL OF MARRIAGE AND FAMILY, Issue 4 2005Zheng WU Generalized linear models (GLMs), as defined by J. A. Nelder and R. W. M. Wedderburn (1972), unify a class of regression models for categorical, discrete, and continuous response variables. As an extension of classical linear models, GLMs provide a common body of theory and methodology for some seemingly unrelated models and procedures, such as the logistic, Poisson, and probit models, that are increasingly used in family studies. This article provides an overview of the principle and the key components of GLMs, such as the exponential family of distributions, the linear predictor, and the link function. To illustrate the application of GLMs, this article uses Canadian national survey data to build an example focusing on the number of close friends among older adults. The article concludes with a discussion of the strengths and weaknesses of GLMs. [source] Model choice in time series studies of air pollution and mortalityJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 2 2006Roger D. Peng Summary., Multicity time series studies of particulate matter and mortality and morbidity have provided evidence that daily variation in air pollution levels is associated with daily variation in mortality counts. These findings served as key epidemiological evidence for the recent review of the US national ambient air quality standards for particulate matter. As a result, methodological issues concerning time series analysis of the relationship between air pollution and health have attracted the attention of the scientific community and critics have raised concerns about the adequacy of current model formulations. Time series data on pollution and mortality are generally analysed by using log-linear, Poisson regression models for overdispersed counts with the daily number of deaths as outcome, the (possibly lagged) daily level of pollution as a linear predictor and smooth functions of weather variables and calendar time used to adjust for time-varying confounders. Investigators around the world have used different approaches to adjust for confounding, making it difficult to compare results across studies. To date, the statistical properties of these different approaches have not been comprehensively compared. To address these issues, we quantify and characterize model uncertainty and model choice in adjusting for seasonal and long-term trends in time series models of air pollution and mortality. First, we conduct a simulation study to compare and describe the properties of statistical methods that are commonly used for confounding adjustment. We generate data under several confounding scenarios and systematically compare the performance of the various methods with respect to the mean-squared error of the estimated air pollution coefficient. We find that the bias in the estimates generally decreases with more aggressive smoothing and that model selection methods which optimize prediction may not be suitable for obtaining an estimate with small bias. Second, we apply and compare the modelling approaches with the National Morbidity, Mortality, and Air Pollution Study database which comprises daily time series of several pollutants, weather variables and mortality counts covering the period 1987,2000 for the largest 100 cities in the USA. When applying these approaches to adjusting for seasonal and long-term trends we find that the Study's estimates for the national average effect of PM10 at lag 1 on mortality vary over approximately a twofold range, with 95% posterior intervals always excluding zero risk. [source] Comparison of linear predictors obtained by data transformation, generalized linear models (GLM) and response modeling methodology (RMM)QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 4 2008Haim Shore Abstract The data-transformation approach and generalized linear modeling both require specification of a transformation prior to deriving the linear predictor (LP). By contrast, response modeling methodology (RMM) requires no such specifications. Furthermore, RMM effectively decouples modeling of the LP from modeling its relationship to the response. It may therefore be of interest to compare LPs obtained by the three approaches. Based on numerical quality problems that have appeared in the literature, these approaches are compared in terms of both the derived structure of the LPs and goodness-of-fit statistics. The relative advantages of RMM are discussed. Copyright © 2007 John Wiley & Sons, Ltd. [source] Recursive Relations for Multistep Prediction of a Stationary Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2001Pascal Bondon Recursive relations are established between the coefficients of the finite past multistep linear predictors of a stationary time series. These relations generalize known results when the prediction is based on infinite past and permit simplification of the numerical calculation of the finite past predictors. [source] Comparison of linear predictors obtained by data transformation, generalized linear models (GLM) and response modeling methodology (RMM)QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 4 2008Haim Shore Abstract The data-transformation approach and generalized linear modeling both require specification of a transformation prior to deriving the linear predictor (LP). By contrast, response modeling methodology (RMM) requires no such specifications. Furthermore, RMM effectively decouples modeling of the LP from modeling its relationship to the response. It may therefore be of interest to compare LPs obtained by the three approaches. Based on numerical quality problems that have appeared in the literature, these approaches are compared in terms of both the derived structure of the LPs and goodness-of-fit statistics. The relative advantages of RMM are discussed. Copyright © 2007 John Wiley & Sons, Ltd. [source] Prediction-based estimating functionsTHE ECONOMETRICS JOURNAL, Issue 2 2000Michael Sørensen A generalization of martingale estimating functions is presented which is useful when there are no natural or easily calculated martingales that can be used to construct a class of martingale estimating functions. An estimating function of the new type, which is based on linear predictors, is called a prediction-based estimating functions. Special attention is given to classes of prediction-based estimating functions given by a finite-dimensional space of predictors. It is demonstrated that such a class of estimating functions has most of the attractive properties of martingale estimating functions. In particular, a simple expression is found for the optimal estimating function. This type of prediction-based estimating functions only involve unconditional moments, in contrast to the martingale estimating functions where conditional moments are required. Thus, for applications to discretely observed continuous time models, a considerably smaller amount of simulation is, in general, needed for these than for martingale estimating functions. This is also true of the optimal prediction-based estimating functions. Conditions are given that ensure the existence, consistency and asymptotic normality of the corresponding estimators. The new method is applied to inference for sums of Ornstein,Uhlenbeck-type processes and stochastic volatility models. Stochastic volatility models are studied in considerable detail. It is demonstrated that for inference about models by Hull and White and Chesney and Scott, an explicit optimal prediction-based estimating function can be found so that no simulations are needed. [source] Multilevel Mixture Cure Models with Random EffectsBIOMETRICAL JOURNAL, Issue 3 2009Xin Lai Abstract This paper extends the multilevel survival model by allowing the existence of cured fraction in the model. Random effects induced by the multilevel clustering structure are specified in the linear predictors in both hazard function and cured probability parts. Adopting the generalized linear mixed model (GLMM) approach to formulate the problem, parameter estimation is achieved by maximizing a best linear unbiased prediction (BLUP) type log-likelihood at the initial step of estimation, and is then extended to obtain residual maximum likelihood (REML) estimators of the variance component. The proposed multilevel mixture cure model is applied to analyze the (i) child survival study data with multilevel clustering and (ii) chronic granulomatous disease (CGD) data on recurrent infections as illustrations. A simulation study is carried out to evaluate the performance of the REML estimators and assess the accuracy of the standard error estimates. [source] | ||||||||||