ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2013, Vol. 45 ›› Issue (12): 1431-1442.doi: 10.3724/SP.J.1041.2013.01431

• 论文 • 上一篇    下一篇



  1. (1北京师范大学心理学院应用实验心理北京市重点实验室; 2中国基础教育质量评价与提升协同创新中心; 3北京师范大学教育学部, 北京 100875)
  • 收稿日期:2013-01-16 出版日期:2013-12-25 发布日期:2013-12-25
  • 通讯作者: 张丹慧
  • 基金资助:

    国家自然科学基金(31100759); 全国教育科学“十二五”规划教育部重点课题(GFA111001)资助。

Mediation Analysis for Ordinal Outcome Variables

LIU Hongyun;LUO Fang;ZHANG Yu;ZHANG Danhui   

  1. (1 Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, Beijing 100875, China) (2 National Cooperative Innovation Center for Assessment and Improvement of Basic Education Quality, Beijing Normal University, Beijing 100875, China) (3 Faculty of Education, Beijing Normal University, Beijing 100875, China)
  • Received:2013-01-16 Online:2013-12-25 Published:2013-12-25
  • Contact: ZHANG Danhui


本文聚焦于因变量为等级数据的中介效应模型, 通过模拟研究比较了Logistic回归与通常线性回归的差别, 并比较了这两种分析框架下常用的系数乘积法和系数差异法的优劣, 同时考察了因变量类别数对估计结果的影响。研究结果表明:对因变量为等级数据的中介效应模型, 应使用Logistic回归进行分析, 如果使用了通常线性回归分析, 会导致中介效应低估、标准误低估、置信区间对真值覆盖比例偏低等问题。对于等级因变量的中介效应估计, 系数乘积法得到的结果优于系数差异法, 随着等级数的增加Logistic回归与通常线性回归的差别越来越小, 当因变量的类别数较多(5及以上)时, 可考虑使用通常线性回归的分析方法。最后通过一个实例说明了该方法的应用。

关键词: 中介效应分析, 等级数据, 蒙特卡洛模拟


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.

Key words: mediation analysis, ordinal variable, Monte Carlo simulation