Multicollinearity and Measurement Error in Structural Equation Models: Implications for Theory Testing

The literature on structural equation models is unclear on whether and when multicollinearity may pose problems in theory testing (Type II errors). Two Monte Carlo simulation experiments show that multicollinearity can cause problems under certain conditions, specifically: (1) when multicollinearity is extreme, Type II error rates are generally unacceptably high (over 80%), (2) when multicollinearity is between 0.6 and 0.8, Type II error rates can be substantial (greater than 50% and frequently above 80%) if composite reliability is weak, explained variance ($R^{2}$) is low, and sample size is relatively small. However, as reliability improves (0.80 or higher), explained variance $R^{2}$ reaches 0.75, and sample becomes relatively large, Type II error rates become negligible. (3) When multicollinearity is between 0.4 and 0.5, Type II error rates tend to be quite small, except when reliability is weak, $R^{2}$ is low, and sample size is small, in which case error rates can still be high (greater than 50%). Methods for detecting and correcting multicollinearity are briefly discussed. However, since multicollinearity is difficult to manage after the fact, researchers should avoid problems by carefully managing the factors known to mitigate multicollinearity problems (particularly measurement error).