Mediation Analysis for Ordinal Outcome Variables

Abstract

Statistical mediation analyses have been widely used to investigate the mechanism of mediating effects, in which mediator M mediates the effect of independent variable X on dependent variable Y. For the last 25 years, the causal steps approach as described by, for example, Baron and Kenny(1986) had dominated and become the standard procedure for statistical mediation analyses. However, most of the research in these statistical mediation analyses were conducted with the dependent variable being continuous. In this article, basing on the methods of MacKinnon(1993, 2007), we examined a more appropriate procedure of categorical data analysis rather than that for continuous data in the examination of mediation models when the outcome variable is binary or ordinal. We believed that the logistic regression should be used to analyze categorical data, while the ordinal line regression is more appropriate for analyses involving continuous data.Two approaches have been usually used in the analyses of mediation effect: one involving the examination of the product of coefficient while the other involving of the comparison of the difference of the respective coefficients. In this study, therefore, we compared the performance of these two methods with the logistic regression and the ordinal line regression respectively, using the Monte Carlo simulation method. These methods were compared with respective to three factors, namely, sample size, size of mediation effects, and the number of categories in the outcome variable. These factors were systematically varied in the simulations with: i) sample size at 50, 100, 200, 500 and 1000; ii)the number of categories in the outcome variable set at 2, 3 and 5; and 3) the standard regression coefficients of a, b and c′ set at 0, 0.14, 0.39 and 0.59respectively generating of 63 combinations of the coefficient combinations(the all 0.59 was dropped due to improper solution). So, a total of 5 sample size ×3 categories of outcome variables × 63 regression coefficient combinations = 945 combination of conditions were generated. Mplus 6.0 was used to generate the simulated data sets, and 500 replicates were used in each of the conditions. Each data set was analyzed using all of the statistical approach mentioned above. The performance of these analytical approaches was then evaluated according to six criteria, namely,(1) convergence rates,(2) the precision of the mediation effects estimates,(3) the precision of standard error estimates,(4)the coverage rates of the CIs,(5) the test power, and(6) Type I error rates. Results showed that firstly, for the mediating model with binary or ordinal outcome variable, the approach using product of coefficient always performed better than the approach using the difference of coefficients irrespective of whether the logistic regression was used or not. Secondly, the ordinal regression for analyzing continuous variables produced lower precision of estimates, poorer performance in statistical tests and an underestimation of SE, as compared with the logistic regression. However, as the number of categories of outcome variable increased, the ordinal regression for continuous variables could be an acceptable alternative with a decrease in the RMSE and estimated standard errors of the mediation effect, and an increase in the statistical power. In conclusion, the approach using the product of coefficients with the logistic regression is the recommended method for mediation analyses of categorical data. We also provide examples to demonstrate the procedures for the implementation of the tests.