A Study of Effects of MultiCollinearity in the Multivariable Analysis
Wonsuk Yoo, Robert Mayberry, Sejong Bae, Karan Singh, Qinghua (Peter), James W. Lillard Jr.

Abstract
A multivariable analysis is the most popular approach when investigating associations between risk factors and disease. However, efficiency of multivariable analysis highly depends on correlation structure among predictive variables. When the covariates in the model are not independent one another, collinearity/multicollinearity problems arise in the analysis, which leads to biased estimation. This work aims to perform a simulation study with various scenarios of different collinearity structures to investigate the effects of collinearity under various correlation structures amongst predictive and explanatory variables and to compare these results with existing guidelines to decide harmful collinearity. Three correlation scenarios among predictor variables are considered: (1) bivariate collinear structure as the most simple collinearity case, (2) multivariate collinear structure where an explanatory variable is correlated with two other covariates, (3) a more realistic scenario when an independent variable can be expressed by various functions including the other variables.

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