Background
Methods
Aim
Simulation set up
Continuous mediator | Dichotomous mediator prevalence | |||
---|---|---|---|---|
0.1 | 0.3 | 0.5 | ||
Multiple regression/SEM | ||||
crude | 0.360 | 0.360 | 0.360 | 0.360 |
y-standardization | 0.168 | 0.098 | 0.097 | 0.096 |
Full-standardization | 0.196 | 0.048 | 0.044 | 0.048 |
Standardized logistic solution | 0.360 | NA | NA | NA |
Potential outcomes framework | 0.360 | 0.047 | 0.087 | 0.081 |
Performance measures
Real-life data examples
Methods for statistical mediation analysis
Multiple regression and SEM
Potential outcomes framework
Results
Simulation study
Multiple regression and SEM | Potential outcomes | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Crude | y-standardization | Full-standardization | Standardized logistic solution | ||||||||
Y prev
|
bias
|
MSE
|
bias
|
MSE
|
bias
|
MSE
|
bias
|
MSE
|
bias
|
MSE
| |
0.5 | Indirect effect | −0.001 | 0.002 | ||||||||
ab | −0.001 | 0.002 | −0.001 | 0.000 | −0.000 | 0.001 | −0.001 | 0.002 | |||
c-c’ | −0.068 | 0.006 | −0.008 | 0.000 | −0.036 | 0.002 | −0.021 | 0.003 | |||
Proportion mediated | 0.003 | 0.003 | |||||||||
ab/(ab + c’) | 0.003 | 0.003 | 0.003 | 0.003 | 0.065 | 0.009 | 0.003 | 0.003 | |||
ab/c | 0.032 | 0.005 | 0.009 | 0.003 | 0.073 | 0.010 | 0.011 | 0.003 | |||
1-(c’/c) | −0.044 | 0.004 | − 0.008 | 0.003 | −0.008 | 0.003 | −0.010 | 0.003 | |||
0.3 | Indirect effect | 0.000 | 0.003 | ||||||||
ab | 0.000 | 0.003 | −0.000 | 0.000 | −0.000 | 0.001 | 0.000 | 0.003 | |||
c-c’ | −0.061 | 0.005 | −0.005 | 0.001 | −0.033 | 0.002 | −0.012 | 0.003 | |||
Proportion mediated | 0.001 | 0.004 | |||||||||
ab/(ab + c’) | 0.001 | 0.004 | 0.001 | 0.004 | 0.064 | 0.010 | 0.001 | 0.004 | |||
ab/c | 0.027 | 0.005 | 0.005 | 0.004 | 0.069 | 0.010 | 0.006 | 0.004 | |||
1-(c’/c) | −0.041 | 0.005 | −0.006 | 0.004 | −0.006 | 0.004 | −0.007 | 0.004 | |||
0.1 | Indirect effect | 0.003 | 0.006 | ||||||||
ab | 0.003 | 0.006 | 0.001 | 0.001 | 0.001 | 0.001 | 0.003 | 0.006 | |||
c-c’ | −0.036 | 0.005 | 0.005 | 0.001 | −0.023 | 0.002 | 0.016 | 0.003 | |||
Proportion mediated | 0.006 | 0.008 | |||||||||
ab/(ab + c’) | 0.006 | 0.008 | 0.006 | 0.008 | 0.070 | 0.017 | 0.006 | 0.008 | |||
ab/c | 0.023 | 0.010 | 0.002 | 0.008 | 0.065 | 0.015 | 0.001 | 0.008 | |||
1-(c’/c) | −0.020 | 0.008 | 0.011 | 0.009 | 0.011 | 0.009 | 0.013 | 0.009 |
Multiple regression and SEM | Potential outcomes | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Crude | y-standardization | Full-standardization | ||||||||
M prev
|
Y prev
|
bias
|
MSE
|
bias
|
MSE
|
bias
|
MSE
|
bias
|
MSE
| |
0.5 | 0.5 | Indirect effect | 0.000 | 0.000 | ||||||
ab | 0.002 | 0.008 | 0.000 | 0.001 | 0.000 | 0.000 | ||||
c-c’ | −0.287 | 0.083 | −0.054 | 0.003 | 0.006 | 0.000 | ||||
Proportion mediated | 0.001 | 0.001 | ||||||||
ab/(ab + c’) | −0.003 | 0.005 | −0.136 | 0.021 | −0.235 | 0.057 | ||||
ab/c | 0.167 | 0.048 | −0.096 | 0.014 | −0.236 | 0.057 | ||||
1-(c’/c) | −0.266 | 0.072 | −0.254 | 0.066 | −0.254 | 0.066 | ||||
0.3 | Indirect effect | −0.001 | 0.000 | |||||||
ab | 0.003 | 0.010 | −0.001 | 0.001 | 0.000 | 0.000 | ||||
c-c’ | −0.288 | 0.083 | −0.055 | 0.003 | 0.007 | 0.000 | ||||
Proportion mediated | 0.001 | 0.001 | ||||||||
ab/(ab + c’) | −0.004 | 0.006 | −0.136 | 0.022 | −0.235 | 0.057 | ||||
ab/c | 0.168 | 0.054 | −0.095 | 0.016 | −0.235 | 0.057 | ||||
1-(c’/c) | −0.265 | 0.071 | −0.254 | 0.066 | −0.254 | 0.066 | ||||
0.1 | Indirect effect | 0.002 | 0.001 | |||||||
ab | 0.016 | 0.021 | −0.003 | 0.001 | 0.002 | 0.000 | ||||
c-c’ | −0.284 | 0.081 | −0.052 | 0.003 | −0.004 | 0.000 | ||||
Proportion mediated | 0.004 | 0.002 | ||||||||
ab/(ab + c’) | −0.001 | 0.012 | −0.132 | 0.024 | −0.230 | 0.056 | ||||
ab/c | 0.187 | 0.087 | −0.087 | 0.021 | −0.231 | 0.057 | ||||
1-(c’/c) | −0.261 | 0.070 | −0.248 | 0.064 | −0.248 | 0.064 | ||||
0.3 | 0.5 | Indirect effect | −0.001 | 0.001 | ||||||
ab | −0.001 | 0.020 | −0.001 | 0.001 | −0.000 | 0.000 | ||||
c-c’ | −0.299 | 0.081 | −0.062 | 0.003 | − 0.009 | 0.000 | ||||
Proportion mediated | −0.001 | 0.001 | ||||||||
ab/(ab + c’) | −0.006 | 0.013 | −0.138 | 0.025 | −0.247 | 0.062 | ||||
ab/c | 0.171 | 0.086 | −0.093 | 0.022 | −0.246 | 0.062 | ||||
1-(c’/c) | −0.283 | 0.070 | −0.272 | 0.066 | −0.272 | 0.066 | ||||
0.3 | Indirect effect | −0.001 | 0.001 | |||||||
ab | −0.001 | 0.011 | −0.001 | 0.001 | 0.000 | 0.000 | ||||
c-c’ | −0.294 | 0.087 | −0.060 | 0.004 | −0.007 | 0.000 | ||||
Proportion mediated | 0.001 | 0.001 | ||||||||
ab/(ab + c’) | −0.003 | 0.007 | −0.135 | 0.022 | −0.244 | 0.061 | ||||
ab/c | 0.176 | 0.061 | −0.090 | 0.016 | −0.244 | 0.061 | ||||
1-(c’/c) | −0.274 | 0.076 | − 0.264 | 0.071 | −0.264 | 0.071 | ||||
0.1 | Indirect effect | 0.003 | 0.001 | |||||||
ab | 0.012 | 0.010 | 0.002 | 0.001 | 0.001 | 0.000 | ||||
c-c’ | −0.283 | 0.090 | −0.054 | 0.004 | −0.001 | 0.000 | ||||
Proportion mediated | 0.004 | 0.003 | ||||||||
ab/(ab + c’) | −0.004 | 0.006 | − 0.134 | 0.022 | −0.242 | 0.062 | ||||
ab/c | 0.179 | 0.054 | −0.090 | 0.015 | −0.244 | 0.062 | ||||
1-(c’/c) | −0.260 | 0.081 | −0.252 | 0.075 | −0.252 | 0.075 | ||||
0.1 | 0.5 | Indirect effect | 0.004 | 0.001 | ||||||
ab | 0.013 | 0.026 | 0.002 | 0.002 | −0.018 | 0.000 | ||||
c-c’ | −0.333 | 0.111 | −0.082 | 0.007 | −0.032 | 0.001 | ||||
Proportion mediated | 0.004 | 0.001 | ||||||||
ab/(ab + c’) | −0.006 | 0.011 | −0.137 | 0.025 | −0.284 | 0.082 | ||||
ab/c | 0.223 | 0.113 | −0.066 | 0.020 | −0.281 | 0.081 | ||||
1-(c’/c) | −0.332 | 0.111 | −0.326 | 0.107 | −0.326 | 0.107 | ||||
0.3 | Indirect effect | 0.003 | 0.001 | |||||||
ab | 0.009 | 0.025 | 0.002 | 0.002 | −0.018 | 0.000 | ||||
c-c’ | −0.328 | 0.108 | −0.080 | 0.006 | −0.030 | 0.001 | ||||
Proportion mediated | 0.005 | 0.001 | ||||||||
ab/(ab + c’) | −0.005 | 0.013 | −0.135 | 0.025 | −0.283 | 0.082 | ||||
ab/c | 0.225 | 0.121 | −0.065 | 0.022 | −0.281 | 0.081 | ||||
1-(c’/c) | −0.323 | 0.105 | −0.318 | 0.102 | −0.318 | 0.102 | ||||
0.1 | Indirect effect | 0.003 | 0.001 | |||||||
ab | 0.002 | 0.033 | −0.001 | 0.002 | −0.018 | 0.001 | ||||
c-c’ | −0.319 | 0.102 | −0.076 | 0.006 | −0.026 | 0.001 | ||||
Proportion mediated | 0.003 | 0.002 | ||||||||
ab/(ab + c’) | −0.024 | 0.027 | −0.145 | 0.033 | −0.286 | 0.084 | ||||
ab/c | 0.193 | 0.130 | −0.081 | 0.031 | −0.285 | 0.084 | ||||
1-(c’/c) | −0.310 | 0.098 | −0.307 | 0.096 | −0.307 | 0.096 |
Multiple regression and SEM | Potential outcomesa | |||||
---|---|---|---|---|---|---|
Crude | y-standardization | Full-standardization | Standardized logistic solutionb | |||
Situation 1 M continuous Y dichotomous | Total effect (c) | −0.20 | −0.11 | −0.20 | −0.21 | −0.21 |
a coefficientd | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | |
b coefficient | −0.04 | −0.02 | −0.23 | −0.04 | −0.04 | |
Direct effect (c’) | −0.19 | −0.10 | −0.18 | −0.19 | −0.19 | |
Indirect effect | −0.03 | |||||
ab | −0.03 | −0.01 | −0.15 | −0.03 | ||
c-c’ | −0.02 | −0.01 | −0.02 | −0.02 | ||
Proportion mediated | 0.12 | |||||
ab/(ab + c’) | 0.12 | 0.12 | 0.47 | 0.12 | ||
ab/c | 0.13 | 0.12 | 0.77 | 0.12 | ||
1-(c’/c) | 0.09 | 0.11 | 0.11 | 0.11 | ||
Situation 2 M dichotomous Y dichotomous | Total effect (c) | −0.20 | −0.11 | −0.20 | NA | −0.21 |
a coefficient | 0.11 | 0.06 | 0.11 | NA | 0.11 | |
b coefficient | −0.60 | −0.32 | −0.16 | NA | −0.60 | |
Direct effect (c’) | −0.19 | −0.10 | −0.19 | NA | −0.19 | |
Indirect effect | −0.01 | |||||
ab | −0.06 | −0.02 | −0.02 | NA | ||
c-c’ | −0.01 | −0.01 | −0.01 | NA | ||
Proportion mediated | 0.07 | |||||
ab/(ab + c’) | 0.25 | 0.16 | 0.09 | NA | ||
ab/c | 0.32 | 0.17 | 0.09 | NA | ||
1-(c’/c) | 0.06 | 0.07 | 0.07 | NA |