A Stochastic Regression Model for General Trend Analysis of Longitudinal Continuous Data

A predictive continuous time model is developed for continuous panel data to assess the effect of time‐varying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an Ornstein–Uhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time first‐order autoregressive regression model with time‐varying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasi‐likelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasi‐likelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a follow‐up study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.     

Sequential Classification Based on Regression

Let us consider m general populations π₁, …,π_m. Each object belonging to these populations is represented by (p ± 1) characteristics x₁, x₂,…,x_p,y. A certain object, which is an element of one of the m general populations π₁,…,π_m has to be classified into the correct population. It will be assumed that knowledge of the value of the characteristic y would permit its correct classification, but that the observation of this characteristic is expensive, difficult or dangerous, as e.g. in medical applications. y is correlated with a set of p characteristics x₁,x₂,…,x_p, which are observed sequentially. The classification procedure is based on the division of the space of the observed value of characteristics x₁,x₂,…,x_p into nonintersecting areas determined so as to minimize the value of BAYES' risk given by equation (3).     

Spline and General Regression of Polytomous Data

The paper shows a formulation for a general linear regression as well as a spline regression of multinomial responses on a quantitative input variables. Application of least squares and asymptotic theory yields the F-test for significance of coefficients and a t-test for structural discontinuity.     

A Classification of Trivariate Regression Models

The present study begins with a discussion of a topic frequently mentioned in the relevant literature, namely the division of multiple regression models with two predictors into five mutually excluding categories. The theoretical basis for this classification is criticized and a system of three mutually excluding categories is suggested which is free of the criticized inconsistencies.     

Locally Weighted Score Estimation for Quantile Classification in Binary Regression Models

One common use of binary response regression methods is classification based on an arbitrary probability threshold dictated by the particular application. Since this is given to us a priori, it is sensible to incorporate the threshold into our estimation procedure. Specifically, for the linear logistic model, we solve a set of locally weighted score equations, using a kernel-like weight function centered at the threshold. The bandwidth for the weight function is selected by cross validation of a novel hybrid loss function that combines classification error and a continuous measure of divergence between observed and fitted values; other possible cross-validation functions based on more common binary classification metrics are also examined. This work has much in common with robust estimation, but differs from previous approaches in this area in its focus on prediction, specifically classification into high- and low-risk groups. Simulation results are given showing the reduction in error rates that can be obtained with this method when compared with maximum likelihood estimation, especially under certain forms of model misspecification. Analysis of a melanoma dataset is presented to illustrate the use of the method in practice.     

Mixed Model Discrete Regression

Models and estimention procedures are given for linear regression models in discrete distributions when the regression contains both fixed and random effects. The methods are developed for discrete variables with typically a small number of possible outcomes such as occurs in ordinal regression. The method is applied to a problem arising in the comparison of microbiological test methods.     

Generalized Binomial Regression Model

The generalized negative binomial distribution has been found useful in fitting over-dispersed as well as under-dispersed count data. We define and study the generalized binomial regression model which is used to predict a count response variable affected by one or more explanatory variables. The methods of maximum likelihood and moments are given for estimating the model parameters. Approximate tests for the adequacy of the model are considered. The generalized binomial regression model has been applied to two observed data sets to which binomial regression model was applied earlier.     

Newer Classification and Regression Tree Techniques: Bagging and Random Forests for Ecological Prediction

The task of modeling the distribution of a large number of tree species under future climate scenarios presents unique challenges. First, the model must be robust enough to handle climate data outside the current range without producing unacceptable instability in the output. In addition, the technique should have automatic search mechanisms built in to select the most appropriate values for input model parameters for each species so that minimal effort is required when these parameters are fine-tuned for individual tree species. We evaluated four statistical models—Regression Tree Analysis (RTA), Bagging Trees (BT), Random Forests (RF), and Multivariate Adaptive Regression Splines (MARS)—for predictive vegetation mapping under current and future climate scenarios according to the Canadian Climate Centre global circulation model. To test, we applied these techniques to four tree species common in the eastern United States: loblolly pine (Pinus taeda), sugar maple (Acer saccharum), American beech (Fagus grandifolia), and white oak (Quercus alba). When the four techniques were assessed with Kappa and fuzzy Kappa statistics, RF and BT were superior in reproducing current importance value (a measure of basal area in addition to abundance) distributions for the four tree species, as derived from approximately 100,000 USDA Forest Service’s Forest Inventory and Analysis plots. Future estimates of suitable habitat after climate change were visually more reasonable with BT and RF, with slightly better performance by RF as assessed by Kappa statistics, correlation estimates, and spatial distribution of importance values. Although RTA did not perform as well as BT and RF, it provided interpretive models for species whose distributions were captured well by our current set of predictors. MARS was adequate for predicting current distributions but unacceptable for future climate. We consider RTA, BT, and RF modeling approaches, especially when used together to take advantage of their individual strengths, to be robust for predictive mapping and recommend their inclusion in the ecological toolbox.     

Children at High Risk for Overweight: A Classification and Regression Trees Analysis Approach

Objective: Early identification of children at high risk for childhood overweight is a major challenge in fighting the obesity epidemic. We tried to identify the most powerful set of combined predictors for childhood overweight at school entry. Research Methods and Procedures: A classification and regression trees analysis on risk factors for childhood overweight in 4289 children 5 to 6 years of age participating in the obligatory school entry health examination 2001/2002 in Bavaria, Germany, was performed. Parental questionnaires asked for children's weight at birth and 2 years, breastfeeding history, maternal smoking in pregnancy, parental education, parental overweight/obesity, nationality, and number of older siblings. Overweight was defined according to sex‐ and age‐specific BMI cut‐points proposed by the International Obesity Task Force. Results: Prevalence of overweight was 11% among the entire study population. Although high early weight gain >10, 000 grams was found in about one‐half of the overweight children, its positive predictive value reached only 25%, indicating that one of four children with a high early weight gain is overweight at school entry. The best reliable set of predictors included high early weight gain and obese parents and accounted for a likelihood ratio of 3.6, with a corresponding positive predictive value of 40%, and was found in 4% of all children. Discussion: A combination of predictors available at 2 years of age could improve predictability of overweight at school entry. However, corresponding low positive predictive values indicate a precision of the prediction that might be insufficient for targeting intervention programs for identified high‐risk children.     

Learning a Weighted Meta-Sample Based Parameter Free Sparse Representation Classification for Microarray Data

Sparse representation classification (SRC) is one of the most promising classification methods for supervised learning. This method can effectively exploit discriminating information by introducing a regularization terms to the data. With the desirable property of sparisty, SRC is robust to both noise and outliers. In this study, we propose a weighted meta-sample based non-parametric sparse representation classification method for the accurate identification of tumor subtype. The proposed method includes three steps. First, we extract the weighted meta-samples for each sub class from raw data, and the rationality of the weighting strategy is proven mathematically. Second, sparse representation coefficients can be obtained by regularization of underdetermined linear equations. Thus, data dependent sparsity can be adaptively tuned. A simple characteristic function is eventually utilized to achieve classification. Asymptotic time complexity analysis is applied to our method. Compared with some state-of-the-art classifiers, the proposed method has lower time complexity and more flexibility. Experiments on eight samples of publicly available gene expression profile data show the effectiveness of the proposed method.     

Regression Model for Time to Flowering of Chickpea Landraces

Russian Journal of Genetics - Regression models for time to flowering had been developed for VIR chickpea landraces collected in Turkey and Ethiopia. Predicted flowering time coincides closely with...     

Procedure for Detecting Outliers in a Circular Regression Model

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.     

A General Business Model for Marine Reserves

Marine reserves are an effective tool for protecting biodiversity locally, with potential economic benefits including enhancement of local fisheries, increased tourism, and maintenance of ecosystem services. However, fishing communities often fear short-term income losses associated with closures, and thus may oppose marine reserves. Here we review empirical data and develop bioeconomic models to show that the value of marine reserves (enhanced adjacent fishing + tourism) may often exceed the pre-reserve value, and that economic benefits can offset the costs in as little as five years. These results suggest the need for a new business model for creating and managing reserves, which could pay for themselves and turn a profit for stakeholder groups. Our model could be expanded to include ecosystem services and other benefits, and it provides a general framework to estimate costs and benefits of reserves and to develop such business models.     

Goodness-of-Fit Tests for the Logistic Regression Model for Matched Case-Control Studies

A number of statistics have recently been proposed to asssess the fit of the multiple logistic regression model in both prospective and retrospective studies involving two independent samples as well as in cross sectional studies. These statistics are not appropriate for assessing fit with matched case-control studies. This paper presents methods for assessing fit for matched case-control studies. Both parametric and nonparametric approaches are suggested even though none are directly analogous to the statistics proposed in the unmatched situation. Several examples are included to illustrate the methods.     

General Principles of Classification and Nomenclature in Folk Biology

Since about 1954, modern field research has been carried out by a number of ethnographers and biologists in an effort to understand more fully the nature of folk biological classification. Much of this work has been devoted to studies dealing with the naming and classification of plants and animals in non-Western societies. It has now become apparent that several important and far reaching generalizations can be formulated which promise to throw considerable light on prescientific man's understanding of his biological universe.