Effects of multicollinearity on type I error rate and test power of binary logistic regression model: A simulation study

In this study, the effect of multicollinearity, which is defined as high correlation, on the type I error rate and test power of the binary logistic regression models were studied. To do this, one dependent variable that consists of 1 and 2 and four continuous independent variables that were randomly drawn from the standardized normal distribution were taken into consideration in the constructed binary logistic regression model. To calculate the type I error rates and test power, the simulation study was performed 100.000 times. The simulation study repeated for the sample sizes of 10, 20, 30 and 40 the various degrees of correlations, namely 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90%. In order to calculate test power, differences (δ) were created between population means by adding to the mean of the second population in standard deviation units as 0.5, 1.0, 1.5 and 2.0, respectively. The simulation runs exhibited that the increasing degree of multicollinearity among independent variables had no influence on type I error rates, provided that the sample size should not be smaller than 30. The power of the binary logistic regression was least affected by the increasing degrees of multicollinearity when the sample size is 10 and there is a 0.5δ difference between population means. The fact that there was a marked decline in test power with rising multicollinearity for all sample sizes clarified that the binary logistic regression was most powerful if there is no strong multicollinearity among independent variables when there is a 1.0δ difference between population means. The negative impact of the rising degrees of multicollinearity on the test power can be avoided if the number of observations is sufficiently large and if the populations were satisfactorily separated from each other.