A Comparative Study of Approaches for Predicting Prostate Cancer from Longitudinal Data

Disease prediction based on longitudinal data can be done using various modeling approaches. Alternative approaches are compared using data from a longitudinal study to predict the onset of disease. The data are modeled using linear mixed-effects models. Posterior probabilities of group membership are computed starting with the first observation and sequentially adding observations until the subject is classified as developing the disease or until the last measurement is used. Individuals are classified by computing posterior probabilities using the marginal distributions of the mixed-effects models, the conditional distributions (conditional on the group-specific random effects), and the distributions of the random effects.     

New Prediction Interval and Band in the Nonlinear Regression Model: Application to Predictive Modeling in Foods

This article is concerned with the proposal of a new prediction interval and band for the nonlinear regression model. The construction principle of this interval and band is based on an exact (the meaning of the term “exact” will be given later) confidence region for parameters of the nonlinear regression model. This region, fully described in Vila and Gauchi (2007 Vila , J.-P. , Gauchi , J.-P. ( 2007 ). Optimal designs based on exact confidence regions for parameter estimation of a nonlinear regression model . Journal of Statistical Planning and Inference 137 ( 9 ): 2935 – 2953 .[Crossref], [Web of Science ®] , [Google Scholar]), provides a rigorous justification for the new prediction interval and band that we propose. This new band is then compared to the classical bands (which are asymptotic and thus approximate for small n), and also to the band based on the bootstrap resampling method. The comparison of these bands is undertaken with simulated and real data from predictive modeling in food science.     

Predicting weed invasion in a sugarcane cultivar using multispectral image

The cultivation of sugar cane has been gaining great focus in several countries due to its diversity of use. The modernization of agriculture has allowed high productivity, which is affected by the invasion of weeds. With sustainable agriculture, the use of herbicides has been increasingly avoided in society, requiring more effective weed control methods. In this paper, we propose a statistical model capable of identifying the invasion of weeds in the field, using four color spectra as regressor variables obtained by a multispectral camera mounted on an unmanned aerial vehicle. With the exact identification of the weed infestation, it is possible to carry out the management in the field with herbicide applications in the exact places, thus avoiding the increase of the cost of production or even dispensing with the use of herbicides, effecting the mechanical removal of them. Results show that in the experimental field, it was possible to reduce herbicide spraying by 57%.     

Tuning Parameter Selection and Various Good Fitting Characteristics for the Liu-Type Estimator in Linear Regression

Liu (2003 Liu , K. ( 2003 ). Using Liu-Type estimator to combat collinearity . Commun. Statist. Theor. Meth. 32 ( 5 ): 1009 – 1020 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed the Liu-Type estimator (LTE) to combat the well-known multicollinearity problem in linear regression. In this article, various better fitting characteristics of the LTE than those of the ordinary ridge regression estimator (Hoerl and Kennard, 1970 Hoerl , A. E. , Kennard , R. W. ( 1970 ). Ridge regression: Biased estimation for non-orthogonal problems . Technometrics 12 : 55 – 67 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) are considered. In particular, we derived two methods to determine the parameter d for the LTE and find that the ridge parameter k could serve for regularization of an ill-conditioned design matrix, while the other parameter d could be used for tuning the fit quality. In addition, the coefficients of regression, coefficient of multiple determination, residual error variance, and generalized cross validation (GCV) of the prediction quality are very stable, and as the ridge parameter increases they eventually reach asymptotic levels, which produces robust regression models. Furthermore, a Monte Carlo evaluation of these features is also given to illustrate some of the theoretical results.     

Save: a method for dimension reduction and graphics in regression

Sliced average variance estimation (SAVE) is a method for constructing sufficient summary plots in regressions with many predictors. The summary plots are designed to capture all the information about the response that is available from the predictors, and do not require a model for their construction. They can be particularly helpful for guiding the choice of a first model. Methodological aspects of SAVE are studied in this article.