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有中介的调节模型的拓展及其效应量

本站小编 Free考研考试/2022-01-01
刘红云1,2, 袁克海3,4(), 甘凯宇1
1北京师范大学心理学部, 北京 100875
2北京师范大学心理学部应用实验心理北京市重点实验室, 北京 100875
3南京邮电大学理学院, 南京 210023
4美国圣母大学心理系, 印第安纳州46556, 美国
收稿日期:2020-06-25出版日期:2021-03-25发布日期:2021-01-27
通讯作者:袁克海E-mail:kyuan@nd.edu

基金资助:* 国家自然科学基金项目资助(31971029);国家自然科学基金项目资助(32071091)

Two-level mediated moderation models with single level data
and new measures of effect sizes

LIU Hongyun1,2, YUAN Ke-Hai3,4(), GAN Kaiyu1
1Faculty of Psychology, Beijing Normal University, Beijing 100875, China
2Beijing Key Laboratory of Applied Experimental Psychology, Faculty of Psychology, Beijing Normal University, Beijing 100875, China
3School of Science of Nanjing University of Posts and Telecommunications, Nanjing, 210023, China
4Department of Psychology, University of Notre Dame, IN 46556, USA
Received:2020-06-25Online:2021-03-25Published:2021-01-27
Contact:YUAN Ke-Hai E-mail:kyuan@nd.edu






摘要/Abstract


摘要： 传统的有中介的调节(mediated moderation, meMO)模型关于误差方差齐性的假设经常被违背, 应用研究中也缺乏测量meMO效应大小的指标。对于单层数据, 本文借助于两层建模的思想, 提出了一种可用于处理方差非齐性的两层有中介的调节(2meMO)模型; 给出了用于测量meMO分析中总调节效应、直接调节效应和有中介调节效应大小的效应量。通过Monte Carlo模拟研究, 比较了meMO和2meMO模型在参数和效应量估计上的表现。并通过实际案例解释了2meMO模型的应用以及效应量的计算和解释。



图1有中介的调节效应的概念模型(粗体线表示有中介的调节效应)
图1有中介的调节效应的概念模型(粗体线表示有中介的调节效应)



图2拓展的有中介的调节(2meMO)分析对应的分层统计模型(粗体线表示有中介的调节路径)
图2拓展的有中介的调节(2meMO)分析对应的分层统计模型(粗体线表示有中介的调节路径)



图3拓展的有中介的调节(2meMO)分析对应的合并统计模型(粗体线表示有中介的调节路径)
图3拓展的有中介的调节(2meMO)分析对应的合并统计模型(粗体线表示有中介的调节路径)


表1模拟设计条件对应的效应量真值
${{\gamma }_{c1}}$ 0 0.2 0.4
$\sigma _{uc}^{2}$ 0 0.25 0.5 0 0.25 0.5 0 0.25 0.5
$\phi _{MO\_tot}^{\left( f \right)}$ 1 1 1 0.6622 0.6622 0.6622 0.4475 0.4475 0.4475
$\phi _{MO\_dir}^{\left( f \right)}$ 1 1 1 0.3378 0.3378 0.3378 0.1381 0.1381 0.1381
$\phi _{meMO}^{\left( f \right)}$ 0 0 0 0.0541 0.0541 0.0541 0.0884 0.0884 0.0884
${{\phi }_{MO\_tot}}$ 1 0.1379 0.7410 0.6622 0.2128 0.1268 0.4475 0.2402 0.1641
${{\phi }_{MO\_dir}}$ 1 0.1379 0.7410 0.3378 0.1086 0.0647 0.1381 0.0741 0.0507
${{\phi }_{meMO}}$ 0 0 0 0.0541 0.0174 0.0103 0.0884 0.0474 0.0324

表1模拟设计条件对应的效应量真值
${{\gamma }_{c1}}$ 0 0.2 0.4
$\sigma _{uc}^{2}$ 0 0.25 0.5 0 0.25 0.5 0 0.25 0.5
$\phi _{MO\_tot}^{\left( f \right)}$ 1 1 1 0.6622 0.6622 0.6622 0.4475 0.4475 0.4475
$\phi _{MO\_dir}^{\left( f \right)}$ 1 1 1 0.3378 0.3378 0.3378 0.1381 0.1381 0.1381
$\phi _{meMO}^{\left( f \right)}$ 0 0 0 0.0541 0.0541 0.0541 0.0884 0.0884 0.0884
${{\phi }_{MO\_tot}}$ 1 0.1379 0.7410 0.6622 0.2128 0.1268 0.4475 0.2402 0.1641
${{\phi }_{MO\_dir}}$ 1 0.1379 0.7410 0.3378 0.1086 0.0647 0.1381 0.0741 0.0507
${{\phi }_{meMO}}$ 0 0 0 0.0541 0.0174 0.0103 0.0884 0.0474 0.0324


表2两种模型得到的${{\gamma }_{meMO}}$的偏差, 均方误差, 95%可信区间覆盖率和拒绝率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 meMO 2meMO
100 200 500 1000 100 200 500 1000
Bias 0 0 0 0.002 0.001 0.000 -0.001 0.002 0.001 0.000 -0.001
0.25 0 -0.002 -0.001 0.000 0.001 -0.001 -0.001 0.000 0.001
0.5 0 0.003 0.000 0.001 -0.001 0.003 0.000 0.001 -0.001
0.2 0 0.08 -0.002 -0.002 0.000 0.001 -0.002 -0.002 0.000 0.001
0.25 0.08 -0.006 0.000 0.000 0.000 -0.006 0.000 0.000 0.000
0.5 0.08 -0.002 0.002 -0.002 0.001 -0.001 0.000 -0.002 0.002
0.4 0 0.16 0.000 0.001 0.001 0.000 0.000 0.001 0.001 0.000
0.25 0.16 -0.004 -0.001 0.002 0.000 -0.004 -0.001 0.002 0.000
0.5 0.16 -0.002 -0.004 0.000 0.002 -0.002 -0.003 0.001 0.002
MSE 0 0 0 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.5 0 0.004 0.002 0.001 0.000 0.004 0.002 0.001 0.000
0.2 0 0.08 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0.08 0.004 0.002 0.001 0.000 0.003 0.002 0.001 0.000
0.5 0.08 0.005 0.002 0.001 0.001 0.005 0.002 0.001 0.000
0.4 0 0.16 0.004 0.002 0.001 0.000 0.004 0.002 0.001 0.000
0.25 0.16 0.005 0.002 0.001 0.000 0.005 0.002 0.001 0.000
0.5 0.16 0.006 0.003 0.001 0.001 0.005 0.003 0.001 0.001
覆盖率 0 0 0 0.952 0.942 0.942 0.942 0.952 0.956 0.944 0.940
0.25 0 0.908 0.920 0.918 0.872 0.940 0.956 0.942 0.932
0.5 0 0.912 0.874 0.852 0.870 0.948 0.952 0.936 0.948
0.2 0 0.08 0.962 0.950 0.966 0.924 0.968 0.954 0.972 0.926
0.25 0.08 0.920 0.918 0.922 0.908 0.930 0.944 0.956 0.946
0.5 0.08 0.894 0.882 0.884 0.882 0.928 0.946 0.936 0.944
0.4 0 0.16 0.960 0.948 0.958 0.950 0.962 0.950 0.958 0.946
0.25 0.16 0.935 0.937 0.930 0.933 0.960 0.948 0.942 0.962
0.5 0.16 0.926 0.928 0.896 0.882 0.946 0.954 0.940 0.940
拒绝率 0 0 0 0.048 0.058 0.058 0.058 0.048 0.044 0.056 0.060
0.25 0 0.092 0.080 0.082 0.129 0.060 0.044 0.058 0.068
0.5 0 0.088 0.126 0.148 0.130 0.052 0.048 0.064 0.052
0.2 0 0.08 0.438 0.762 0.998 1.000 0.399 0.760 0.996 1.000
0.25 0.08 0.390 0.650 0.970 1.000 0.314 0.606 0.950 1.000
0.5 0.08 0.362 0.600 0.882 0.994 0.269 0.488 0.838 0.990
0.4 0 0.16 0.938 1.000 1.000 1.000 0.926 1.000 1.000 1.000
0.25 0.16 0.834 0.996 1.000 1.000 0.808 0.952 1.000 1.000
0.5 0.16 0.794 0.970 1.000 1.000 0.730 0.964 1.000 1.000

表2两种模型得到的${{\gamma }_{meMO}}$的偏差, 均方误差, 95%可信区间覆盖率和拒绝率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 meMO 2meMO
100 200 500 1000 100 200 500 1000
Bias 0 0 0 0.002 0.001 0.000 -0.001 0.002 0.001 0.000 -0.001
0.25 0 -0.002 -0.001 0.000 0.001 -0.001 -0.001 0.000 0.001
0.5 0 0.003 0.000 0.001 -0.001 0.003 0.000 0.001 -0.001
0.2 0 0.08 -0.002 -0.002 0.000 0.001 -0.002 -0.002 0.000 0.001
0.25 0.08 -0.006 0.000 0.000 0.000 -0.006 0.000 0.000 0.000
0.5 0.08 -0.002 0.002 -0.002 0.001 -0.001 0.000 -0.002 0.002
0.4 0 0.16 0.000 0.001 0.001 0.000 0.000 0.001 0.001 0.000
0.25 0.16 -0.004 -0.001 0.002 0.000 -0.004 -0.001 0.002 0.000
0.5 0.16 -0.002 -0.004 0.000 0.002 -0.002 -0.003 0.001 0.002
MSE 0 0 0 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.5 0 0.004 0.002 0.001 0.000 0.004 0.002 0.001 0.000
0.2 0 0.08 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0.08 0.004 0.002 0.001 0.000 0.003 0.002 0.001 0.000
0.5 0.08 0.005 0.002 0.001 0.001 0.005 0.002 0.001 0.000
0.4 0 0.16 0.004 0.002 0.001 0.000 0.004 0.002 0.001 0.000
0.25 0.16 0.005 0.002 0.001 0.000 0.005 0.002 0.001 0.000
0.5 0.16 0.006 0.003 0.001 0.001 0.005 0.003 0.001 0.001
覆盖率 0 0 0 0.952 0.942 0.942 0.942 0.952 0.956 0.944 0.940
0.25 0 0.908 0.920 0.918 0.872 0.940 0.956 0.942 0.932
0.5 0 0.912 0.874 0.852 0.870 0.948 0.952 0.936 0.948
0.2 0 0.08 0.962 0.950 0.966 0.924 0.968 0.954 0.972 0.926
0.25 0.08 0.920 0.918 0.922 0.908 0.930 0.944 0.956 0.946
0.5 0.08 0.894 0.882 0.884 0.882 0.928 0.946 0.936 0.944
0.4 0 0.16 0.960 0.948 0.958 0.950 0.962 0.950 0.958 0.946
0.25 0.16 0.935 0.937 0.930 0.933 0.960 0.948 0.942 0.962
0.5 0.16 0.926 0.928 0.896 0.882 0.946 0.954 0.940 0.940
拒绝率 0 0 0 0.048 0.058 0.058 0.058 0.048 0.044 0.056 0.060
0.25 0 0.092 0.080 0.082 0.129 0.060 0.044 0.058 0.068
0.5 0 0.088 0.126 0.148 0.130 0.052 0.048 0.064 0.052
0.2 0 0.08 0.438 0.762 0.998 1.000 0.399 0.760 0.996 1.000
0.25 0.08 0.390 0.650 0.970 1.000 0.314 0.606 0.950 1.000
0.5 0.08 0.362 0.600 0.882 0.994 0.269 0.488 0.838 0.990
0.4 0 0.16 0.938 1.000 1.000 1.000 0.926 1.000 1.000 1.000
0.25 0.16 0.834 0.996 1.000 1.000 0.808 0.952 1.000 1.000
0.5 0.16 0.794 0.970 1.000 1.000 0.730 0.964 1.000 1.000


表3两种模型得到的效应量$\phi _{meMO}^{(f)}$估计的偏差, 均方误差, 95%可信区间覆盖率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 moME 2moME
100 200 500 1000 100 200 500 1000
Bias 0.2 0 0.054 0.014 0.006 0.002 0.002 0.015 0.006 0.003 0.002
0.25 0.054 0.015 0.009 0.004 0.001 0.016 0.010 0.004 0.001
0.5 0.054 0.023 0.013 0.003 0.003 0.022 0.012 0.003 0.003
0.4 0 0.088 0.003 0.001 0.001 0.001 0.004 0.001 0.001 0.001
0.25 0.088 0.000 0.001 0.002 -0.001 0.000 0.001 0.002 -0.001
0.5 0.088 0.001 -0.002 0.002 0.001 0.002 -0.002 0.001 0.001
MSE 0.2 0 0.054 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.25 0.054 0.003 0.002 0.001 0.000 0.003 0.002 0.001 0.000
0.5 0.054 0.004 0.002 0.001 0.001 0.003 0.002 0.001 0.000
0.4 0 0.088 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0.088 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.5 0.088 0.003 0.002 0.001 0.000 0.003 0.001 0.001 0.000
覆盖率 0.2 0 0.054 0.962 0.940 0.956 0.926 0.958 0.944 0.954 0.922
0.25 0.054 0.958 0.926 0.922 0.914 0.970 0.950 0.962 0.948
0.5 0.054 0.958 0.902 0.882 0.874 0.980 0.954 0.952 0.934
0.4 0 0.088 0.968 0.952 0.948 0.954 0.966 0.952 0.948 0.950
0.25 0.088 0.964 0.944 0.948 0.952 0.964 0.944 0.948 0.952
0.5 0.088 0.932 0.908 0.914 0.874 0.950 0.940 0.956 0.932

表3两种模型得到的效应量$\phi _{meMO}^{(f)}$估计的偏差, 均方误差, 95%可信区间覆盖率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 moME 2moME
100 200 500 1000 100 200 500 1000
Bias 0.2 0 0.054 0.014 0.006 0.002 0.002 0.015 0.006 0.003 0.002
0.25 0.054 0.015 0.009 0.004 0.001 0.016 0.010 0.004 0.001
0.5 0.054 0.023 0.013 0.003 0.003 0.022 0.012 0.003 0.003
0.4 0 0.088 0.003 0.001 0.001 0.001 0.004 0.001 0.001 0.001
0.25 0.088 0.000 0.001 0.002 -0.001 0.000 0.001 0.002 -0.001
0.5 0.088 0.001 -0.002 0.002 0.001 0.002 -0.002 0.001 0.001
MSE 0.2 0 0.054 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.25 0.054 0.003 0.002 0.001 0.000 0.003 0.002 0.001 0.000
0.5 0.054 0.004 0.002 0.001 0.001 0.003 0.002 0.001 0.000
0.4 0 0.088 0.002 0.001 0.000 0.000 0.002 0.001 0.000 0.000
0.25 0.088 0.003 0.001 0.001 0.000 0.003 0.001 0.001 0.000
0.5 0.088 0.003 0.002 0.001 0.000 0.003 0.001 0.001 0.000
覆盖率 0.2 0 0.054 0.962 0.940 0.956 0.926 0.958 0.944 0.954 0.922
0.25 0.054 0.958 0.926 0.922 0.914 0.970 0.950 0.962 0.948
0.5 0.054 0.958 0.902 0.882 0.874 0.980 0.954 0.952 0.934
0.4 0 0.088 0.968 0.952 0.948 0.954 0.966 0.952 0.948 0.950
0.25 0.088 0.964 0.944 0.948 0.952 0.964 0.944 0.948 0.952
0.5 0.088 0.932 0.908 0.914 0.874 0.950 0.940 0.956 0.932


表42meMO模型得到的效应量${{\phi }_{meMO}}$估计的偏差, 均方误差, 95%可信区间覆盖率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 100 200 500 1000
Bias 0 0 0 0.040 0.024 0.013 0.007
0.25 0 0.030 0.016 0.005 0.002
0.5 0 0.023 0.009 0.003 0.001
0.2 0 0.0541 -0.002 -0.005 -0.006 -0.004
0.25 0.0174 0.021 0.016 0.006 0.002
0.5 0.0104 0.020 0.010 0.002 0.002
0.4 0 0.0884 -0.009 -0.008 -0.005 -0.004
0.25 0.0474 0.013 0.011 0.006 0.002
0.5 0.0324 0.017 0.007 0.003 0.002
MSE 0 0 0 0.003 0.001 0.000 0.000
0.25 0 0.002 0.001 0.000 0.000
0.5 0 0.001 0.000 0.000 0.000
0.2 0 0.0541 0.002 0.001 0.000 0.000
0.25 0.0174 0.001 0.001 0.000 0.000
0.5 0.0104 0.001 0.001 0.000 0.000
0.4 0 0.0884 0.002 0.001 0.000 0.000
0.25 0.0474 0.002 0.001 0.000 0.000
0.5 0.0324 0.002 0.001 0.000 0.000
覆盖率 0.2 0 0.0541 0.932 0.936 0.948 0.922
0.25 0.0174 0.978 0.954 0.954 0.936
0.5 0.0104 0.976 0.964 0.940 0.948
0.4 0 0.0884 0.946 0.946 0.950 0.932
0.25 0.0474 0.962 0.946 0.936 0.936
0.5 0.0324 0.960 0.962 0.932 0.948

表42meMO模型得到的效应量${{\phi }_{meMO}}$估计的偏差, 均方误差, 95%可信区间覆盖率
评价指标 ${{\gamma }_{c1}}$ $\sigma _{uc}^{2}$ 真值 100 200 500 1000
Bias 0 0 0 0.040 0.024 0.013 0.007
0.25 0 0.030 0.016 0.005 0.002
0.5 0 0.023 0.009 0.003 0.001
0.2 0 0.0541 -0.002 -0.005 -0.006 -0.004
0.25 0.0174 0.021 0.016 0.006 0.002
0.5 0.0104 0.020 0.010 0.002 0.002
0.4 0 0.0884 -0.009 -0.008 -0.005 -0.004
0.25 0.0474 0.013 0.011 0.006 0.002
0.5 0.0324 0.017 0.007 0.003 0.002
MSE 0 0 0 0.003 0.001 0.000 0.000
0.25 0 0.002 0.001 0.000 0.000
0.5 0 0.001 0.000 0.000 0.000
0.2 0 0.0541 0.002 0.001 0.000 0.000
0.25 0.0174 0.001 0.001 0.000 0.000
0.5 0.0104 0.001 0.001 0.000 0.000
0.4 0 0.0884 0.002 0.001 0.000 0.000
0.25 0.0474 0.002 0.001 0.000 0.000
0.5 0.0324 0.002 0.001 0.000 0.000
覆盖率 0.2 0 0.0541 0.932 0.936 0.948 0.922
0.25 0.0174 0.978 0.954 0.954 0.936
0.5 0.0104 0.976 0.964 0.940 0.948
0.4 0 0.0884 0.946 0.946 0.950 0.932
0.25 0.0474 0.962 0.946 0.936 0.936
0.5 0.0324 0.960 0.962 0.932 0.948



图4家庭教育资源对社会经济地位与数学自我效能与数学成绩之间中介调节效应模型(粗体线表示有中介的调节效应)
图4家庭教育资源对社会经济地位与数学自我效能与数学成绩之间中介调节效应模型(粗体线表示有中介的调节效应)


表5meMO和2meMO模型参数估计结果
统计量 meMO 2meMO
后验均值 后验标准差 后验均值 后验标准差
路径系数
ESCS→HRES (${{\hat{\gamma }}_{M1}}$) 0.484*** 0.011 0.484*** 0.011
MEFF→MATH (${{\hat{\gamma }}_{c0}})$ 46.438*** 1.385 48.436*** 1.571
ESCS→MATH (${{\hat{\gamma }}_{d2}})$ 14.621*** 1.687 14.368*** 1.676
HRES→MATH (${{\hat{\gamma }}_{d1}})$ 3.492* 1.672 3.418* 1.644
ESCS×MEFF→MATH (${{\hat{\gamma }}_{c2}})$ -2.911* 1.501 -3.284* 1.640
HRES×MEFF→MATH (${{\hat{\gamma }}_{c1}})$ -4.171** 1.478 -4.471** 1.631
ESCS×MEFF→HRES×MEFF (${{\hat{\gamma }}_{M1}})$ 0.484*** 0.011 0.484*** 0.011
残差方差
$\sigma _{eM}^{2}$ 6197.923 160.921 5668.715 189.195
$\sigma _{eY}^{2}$ 0.749 0.019 0.749 0.019
$\sigma _{uc}^{2}$ - - 484.239 130.388
有中介调节meMO
${{\hat{\gamma }}_{M1}}{{\hat{\gamma }}_{c1}}$ -2.019 0.718 -2.165 0.791
效应量
${{\hat{\phi }}_{MO\_tot}}$ - - 0.059 0.032
${{\hat{\phi }}_{MO\_dir}}$ - - 0.025 0.022
${{\hat{\phi }}_{meMO}}$ - - 0.010 0.007
$\hat{\phi }_{MO\_tot}^{\left( f \right)}$ 0.623 0.193 0.637 0.192
$\hat{\phi }_{MO\_dir}^{\left( f \right)}$ 0.261 0.203 0.275 0.206
$\hat{\phi }_{meMO}^{\left( f \right)}$ 0.110 0.057 0.106 0.056

表5meMO和2meMO模型参数估计结果
统计量 meMO 2meMO
后验均值 后验标准差 后验均值 后验标准差
路径系数
ESCS→HRES (${{\hat{\gamma }}_{M1}}$) 0.484*** 0.011 0.484*** 0.011
MEFF→MATH (${{\hat{\gamma }}_{c0}})$ 46.438*** 1.385 48.436*** 1.571
ESCS→MATH (${{\hat{\gamma }}_{d2}})$ 14.621*** 1.687 14.368*** 1.676
HRES→MATH (${{\hat{\gamma }}_{d1}})$ 3.492* 1.672 3.418* 1.644
ESCS×MEFF→MATH (${{\hat{\gamma }}_{c2}})$ -2.911* 1.501 -3.284* 1.640
HRES×MEFF→MATH (${{\hat{\gamma }}_{c1}})$ -4.171** 1.478 -4.471** 1.631
ESCS×MEFF→HRES×MEFF (${{\hat{\gamma }}_{M1}})$ 0.484*** 0.011 0.484*** 0.011
残差方差
$\sigma _{eM}^{2}$ 6197.923 160.921 5668.715 189.195
$\sigma _{eY}^{2}$ 0.749 0.019 0.749 0.019
$\sigma _{uc}^{2}$ - - 484.239 130.388
有中介调节meMO
${{\hat{\gamma }}_{M1}}{{\hat{\gamma }}_{c1}}$ -2.019 0.718 -2.165 0.791
效应量
${{\hat{\phi }}_{MO\_tot}}$ - - 0.059 0.032
${{\hat{\phi }}_{MO\_dir}}$ - - 0.025 0.022
${{\hat{\phi }}_{meMO}}$ - - 0.010 0.007
$\hat{\phi }_{MO\_tot}^{\left( f \right)}$ 0.623 0.193 0.637 0.192
$\hat{\phi }_{MO\_dir}^{\left( f \right)}$ 0.261 0.203 0.275 0.206
$\hat{\phi }_{meMO}^{\left( f \right)}$ 0.110 0.057 0.106 0.056







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