SEM-Based Methods to Form Confidence Intervals for Indirect Effect: Still Applicable Given Nonnormality, under Certain Conditions

SEM-based approach using likelihood-based confidence interval (LBCI) has been proposed to form confidence intervals for unstandardized and standardized indirect effect in mediation models. However, when used with the maximum likelihood estimation, this approach requires that the variables are multivariate normally distributed. This can affect the LBCIs of unstandardized and standardized effect differently. In the present study, the robustness of this approach when the predictor is not normally distributed but the error terms are conditionally normal, which does not violate the distributional assumption of ordinary least squares (OLS) estimation, is compared to three other approaches, namely nonparametric bootstrapping and two variants of LBCI, LBCI assuming the predictor is fixed (LBCI-Fixed-X), and LBCI based on ADF estimation (LBCI-ADF). A simulation study was conducted using a simple mediation model, manipulating the distribution of the predictor. LBCI and LBCI-Fixed-X had suboptimal performance when the distributions had high kurtosis and the population indirect effects were medium to large. In some conditions, the problem was severe even when the sample size was large. LBCI-ADF and nonparametric bootstrapping had coverage probabilities close to the nominal value in nearly all conditions. Implications of these findings in the context of this special case of nonnormal data were discussed.