The statistical methods for variable selection and prediction could be challenging when missing covariates exist. Although multiple imputation (MI) is a universally accepted technique for solving missing data problem, how to combine the MI results for variable selection is not quite clear, because different imputations may result in different selections. The widely applied variable selection methods include the sparse partial least-squares (SPLS) method and the penalized least-squares method, e.g. the elastic net (ENet) method. In this paper, we propose an MI-based weighted elastic net (MI-WENet) method that is based on stacked MI data and a weighting scheme for each observation in the stacked data set. In the MI-WENet method, MI accounts for sampling and imputation uncertainty for missing values, and the weight accounts for the observed information. Extensive numerical simulations are carried out to compare the proposed MI-WENet method with the other competing alternatives, such as the SPLS and ENet. In addition, we applied the MIWENet method to examine the predictor variables for the endothelial function that can be characterized by median effective dose (ED50) and maximum effect (Emax) in an ex-vivo phenylephrine-induced extension and acetylcholine-induced relaxation experiment.

Consumer responses to the COVID-19 pandemic have varied widely. Thus, marketers need to understand consumer segments based on pandemic-related responses and behaviors. Through two studies conducted 9 months apart, we find that consumers shift from three segments in Study 1-the Apprehensive, the Prepared, and the Dismissive, to two segments in Study 2-the Dedicated and the Dismissive. The Apprehensive feel particularly threatened of the virus.The Prepared and the Dedicated perceive a lower susceptibility but still take the health threat seriously.The Dismissive downplay the threat and exhibit more negative reactions to mitigation measures. We also demonstrate between-segment downstream response differences. While the Apprehensive and the Prepared/Dedicated exhibit positive attitude toward companies enforcing guidelines, the Apprehensive engage in the most panic buying, hoarding, and stockpiling. The Dedicated also express greater stress and less life satisfaction than the Dismissive. The findings offer theoretical and practical implications for pandemic-related consumer responses.

Although single-index models have been extensively studied, the monotonicity of the link function f in the single-index model is rarely studied. In many situations, it is desirable that f is monotonic, which results in a monotonic single-index model that can be very useful in economics and biometrics. In this article, we propose a monotonic single-index model in which the link function is constructed using penalized I-splines along with constraints on coefficients to achieve monotonicity of the link function f. An algorithm to estimate the single-index parameters and the link function is developed, and the sandwich estimate of the variance of the index parameters is provided. We propose to apply this monotonic single-index model to estimate the dose-response surface and assess drug interactions while considering the variability of the observed data. An extensive simulation study was carried out to evaluate the performance of the proposed monotonic single-index model. A case study is provided to illustrate the application of the proposed model to estimate the dose-response surface and assess drug interactions. Both the simulation and case study show that the proposed monotonic single-index model works very well.

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Wan, Yubing, "Penalized regressions for variable selection model, single index model and an analysis of mass spectrometry data." (2014) The focus of this dissertation is to develop statistical methods, under the frame-