A group-based approach to the least squares regression for handling multicollinearity from strongly correlated variables

Multicollinearity due to strongly correlated predictor variables is a long-standing problem in regression analysis. It leads to difficulties in parameter estimation, inference, variable selection and prediction for the least squares regression. To deal with these difficulties, we propose a group-based approach to the least squares regression centered on the collective impact of the strongly correlated variables. We discuss group effects of such variables that represent their collective impact, and present the group-based approach through real and simulated data examples. We also give a condition more precise than what is available in the literature under which predictions by the least squares estimated model are accurate. This approach is a natural way of working with multicollinearity which resolves the difficulties without altering the least squares method. It has several advantages over alternative methods such as ridge regression and principal component regression.Comment: 36 pages, 1 figur

Discouraging Use of Benzodiazepines for Anxiety and Insomnia

Benzodiazepines are commonly prescribed for anxiety and insomnia because patients respond quickly to them. Although they are meant to be short-term solutions, patients often use them for more than ten years. Long-term use is associated with tolerance, dependence, rebound anxiety and insomnia, painful withdrawal symptoms, and higher rates of falls and motor vehicle accidents. The purpose of this project is to educate patients about the dangers of using benzodiazepines and encourage consideration of safe alternative therapies for anxiety and insomnia. Results suggest that patient education in the form of a handout may effectively discourage new benzodiazepine users from continuing or starting benzodiazepine treatment. However, this is not be the case for long-term users of benzodiazepines who have become dependent and require more aggressive intervention. Preventing initiation of benzodiazepine therapy for people who have never used them before may be an effective way to address the growing benzodiazepine epidemic.https://scholarworks.uvm.edu/fmclerk/1440/thumbnail.jp

Average group effect of strongly correlated predictor variables is estimable

It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an average of these parameters can be extremely accurately estimated. We find this average and briefly discuss its applications in the least squares regression.Comment: 1

Bounds on coverage probabilities of the empirical likelihood ratio confidence regions

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed

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