A SAS Monte Carlo Program for Confidence Intervals of the Mediated Effect

Introduction: Prevention researchers are often interested in understanding the presence and magnitude of the effects that mediate the relationship between prevention programs and their outcomes.  Also, many researchers are now calculating confidence intervals for estimated effects, as confidence intervals provide more detailed information about the effect than the binary outcome of a significance test.  Although estimation of these mediated effects is usually straightforward, estimation of standard errors and confidence intervals is more complicated, as the mediated effect does not always follow a normal distribution.  More accurate methods can be used that accommodate the distribution of the product for confidence interval estimation. There are a now a variety of methods available for two-path mediated effects. For more complicated chains of mediation with three or more paths, there are fewer options. This study describes and applies a SAS program that calculates Monte Carlo confidence limits for a mediated path that includes any number of mediators.

Methods: The SAS Monte Carlo program computes the confidence limits and significance tests for any number of coefficients in the mediated effect. The user enters the values of the coefficients and the covariance matrix among the coefficients and the program conducts Monte Carlo sampling to create confidence limits for the mediated effect. The SAS program was applied to several existing data sets and a simulation study compared the Monte Carlo method to distribution of the product and normal theory methods based on Type I error rates, power, and coverage.

Results: The program was used to compute confidence intervals for several existing three path mediated effects.  The results of the program were comparable to other method but the program is easier to use for three or more path mediated effects than other options.

Conclusions: The SAS program presented here has potential to provide accurate confidence intervals for mediated effects comprised of any number of paths.   The input to the program, coefficients and covariance matrix of coefficients, makes it easier to use than other options.