When Two Wrongs Make a Right: The Opposing Effects of Ignoring Measurement Error and Omitting Confounders in the Same Single Mediator Model

The single mediator model is commonly used by prevention researchers and other behavioral and social scientists to investigate how prevention interventions change outcome variables such as risky behaviors. The single mediator model seems quite simple at first glance since it only contains three variables, but there are many assumptions that must be met in order for the estimates of the mediated effect to be unbiased. Two commonly violated assumptions are that the mediator, M, is measured without error and that no confounding variables of the relation between M and the outcome variable, Y, are omitted from the model. When the independent variable X is measured without error, such as when X is random assignment to treatment conditions, but M is measured with error, the effect on the model is the estimate of the b path is attenuated. The lower the reliability of M, the more b is underestimated. When a confounding variable C that explains all or part of the relation between M and Y is omitted from the model, the effect on the model is the estimate of the b path will be positively biased. This is due to the effect of C not being partialled out of b such that the larger the relation between C, M, and Y, the more b will be overestimated. When M is measured with error and C is omitted from the model, both of these effects are present. Due to the opposing effects on the estimate of b, that is measurement error in M underestimates b while omitting C overestimates b, for any specific set of data b could be over or underestimated. The overall effect on the estimate of b is dependent on the reliability of M and the size of the effect of C on M. This also leads to the situation where, for certain values, the effects of violating the two assumptions are equal and opposite so that the estimate of b is unbiased. The current study investigates the effect of reliability and the size of the omitted effect on bias in b and calculates for which parameter values the two effects cancel each other out to provide an unbiased estimate of b. The results are presented in terms of effect sizes and situations where this could occur are discussed. An empirical example is then provided to illustrate the results. Finally, implications, limitations, and future directions are discussed.