An improved model averaging scheme for logistic regression

Prospects for predictive modeling of transition cow diseases

Transition cow diseases can negatively impact animal welfare and reduce dairy herd profitability. Transition cow disease incidence has remained relatively stable over time despite monitoring and management efforts aimed to reduce the risk of developing diseases. Dairy cattle disease risk is monitored by assessing multiple factors, including certain biomarker test results, health records, feed intake, body condition score, and milk production. However, these factors, which are used to make herd management decisions, are often reviewed separately without considering the correlation between them. In addition, the biomarkers that are currently used for monitoring may not be representative of the complex physiological changes that occur during the transition period. Predictive modeling, which uses data to predict future or current outcomes, is a method that can be used to combine the most predictive variables and their interactions efficiently. The use of an effective predictive model with relevant predictors for transition cow diseases will result in better targeted interventions, and therefore lower disease incidence. This review will discuss predictive modeling methods and candidate variables in the context of transition cow diseases. The next step is to investigate novel biomarkers and statistical methods that are best suited for the prediction of transition cow diseases.

Model selection based on resampling approaches for cluster longitudinal data with missingness in outcomes

In medical and health studies, longitudinal and cluster longitudinal data are often collected, where the response variable of interest is observed repeatedly over time and along with a set of covariates. Model selection becomes an active research topic but has not been explored largely due to the complex correlation structure of the data set. To address this important issue, in this paper, we concentrate on model selection of cluster longitudinal data especially when data are subject to missingness. Motivated from the expected weighted quadratic loss of a given model, data perturbation and bootstrapping methods are used to estimate the loss and then the model that has the smallest expected loss is selected as the best model. To justify the proposed model selection method, we provide various numerical assessments and a real application regarding the asthma data set is also analyzed for illustration.

Estimating the Probability of Rare Events Occurring Using a Local Model Averaging

In statistical applications, logistic regression is a popular method for analyzing binary data accompanied by explanatory variables. But when one of the two outcomes is rare, the estimation of model parameters has been shown to be severely biased and hence estimating the probability of rare events occurring based on a logistic regression model would be inaccurate. In this article, we focus on estimating the probability of rare events occurring based on logistic regression models. Instead of selecting a best model, we propose a local model averaging procedure based on a data perturbation technique applied to different information criteria to obtain different probability estimates of rare events occurring. Then an approximately unbiased estimator of Kullback-Leibler loss is used to choose the best one among them. We design complete simulations to show the effectiveness of our approach. For illustration, a necrotizing enterocolitis (NEC) data set is analyzed.

A Generic Path Algorithm for Regularized Statistical Estimation

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints lead to the popular lasso, fused-lasso, and other generalized ℓ₁ penalized regression methods. In this article we follow a recent idea by Wu (2011, 2012) and propose an exact path solver based on ordinary differential equations (EPSODE) that works for any convex loss function and can deal with generalized ℓ₁ penalties as well as more complicated regularization such as inequality constraints encountered in shape-restricted regressions and nonparametric density estimation. Non-asymptotic error bounds for the equality regularized estimates are derived. In practice, the EPSODE can be coupled with AIC, BIC, C_p or cross-validation to select an optimal tuning parameter, or provides a convenient model space for performing model averaging or aggregation. Our applications to generalized ℓ₁ regularized generalized linear models, shape-restricted regressions, Gaussian graphical models, and nonparametric density estimation showcase the potential of the EPSODE algorithm.