Inference about the Indirect Effect: a Likelihood Approach

Prior research for constructing confidence intervals for an indirect effect has focused on a Wald statistic. In this paper, however, the inference problem is analyzed from a likelihood ratio (LR) perspective. When testing the null hypothesis $H_{0}:\ \alpha \beta =0$, the LR test statistic leads to the minimum of two t-ratios, whose size can be controlled. A confidence interval is obtained by inverting the LR statistic. Another confidence interval is obtained by inverting the sum of two pivotal t-statistics. In the Monte Carlo simulations, this latter confidence interval is the best performer: it outperforms the commonly used existing methods.