报告问题：Collinearity andLγPenalty Models
Department of Epidemiology,
MichiganState University, East Lansing, MI 48824
主持人：王汉生副教授 ，伟易博治理学院商务统计与经济计量系
摘要：Collinearity is one major problem in statistical regression analysis. It often occurs when a large number of risk factors are included as independent variables to explain the response or dependent variable. It presents major challenges for model-based estimation and prediction. Examples of collinearity can be found in many areas, including health economics, finance, social studies, biomedical and environmental research. Even since penalty model was introduced, it has received increasing attention in regression analysis,
especially with the recent development of Lasso penalty (Tibshirani 1996) for variable selection.
In this talk, I will briefly review collinearity problem, its impact on model parameter estimation and prediction. I will then talk about penalty models, and focus on a special penalty model, theLγpenalty with penalty function ∑|βj|γ. It includes ridge regression (γ=2) and the Lasso (γ=1) as special cases. I will give details on their properties and methods. Finally, I will present an interesting data set from social studies to demonstrate how smoothing (a special type penalty) can be used in dealing with linearly dependent covariates in regression analysis. Although this data set was obtained in social studies, same type of data can be obtained in economic studies and management science to address economic or management issues. Thus our method applies to many different areas, including public health, social studies, economics and management science.
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