Number of predictors and multicollinearity: What are their effects on error and bias in regression? - Lavery, Matthew Ryan; Acharya, Parul; Sivo, Stephen A.; Xu, Lihua (Communications in statistics. Simulation and computation, 2019)
The present Monte Carlo simulation study adds to the literature by analyzing parameter bias, rates of Type I and Type II error, and variance inflation factor (VIF) values produced under various multicollinearity conditions by multiple regressions with two, four, and six predictors. Findings indicate multicollinearity is unrelated to Type I error, but increases Type II error. Investigation of bias suggests that multicollinearity increases the variability in parameter bias, while leading to overall underestimation of parameters. Collinearity also increases VIF. In the case of all diagnostics however, increasing the number of predictors interacts with multicollinearity to compound observed problems.