Statistical mediation analysis allows researchers to identify the most important mediating constructs in the causal process studied. Identifying specific mediators is especially relevant when the hypothesized mediating construct consists of multiple related facets. The general definition of the construct and its facets might relate differently to an outcome. However, current methods do not allow researchers to study the relationships between general and specific aspects of a construct to an outcome simultaneously. This study proposes a bifactor measurement model for the mediating construct as a way to parse variance and represent the general aspect and specific facets of a construct simultaneously. Monte Carlo simulation results are presented to help determine the properties of mediated effect estimation when the mediator has a bifactor structure and a specific facet of a construct is the true mediator. This study also investigates the conditions when researchers can detect the mediated effect when the multidimensionality of the mediator is ignored and treated as unidimensional. Simulation results indicated that the mediation model with a bifactor mediator measurement model had "unbiased" and "adequate" power to detect the mediated effect with a sample size greater than 500 and medium a- and b-paths. Also, results indicate that parameter bias and detection of the mediated effect in both the data-generating model and the misspecified model varies as a function of the amount of facet variance represented in the mediation model. This study contributes to the largely unexplored area of measurement issues in statistical mediation analysis.