semmcci: Methods (MC)

library(semmcci)
library(lavaan)

Data

summary(df)
#>        X                   M                   Y           
#>  Min.   :-3.199558   Min.   :-3.371276   Min.   :-3.61432  
#>  1st Qu.:-0.636035   1st Qu.:-0.692640   1st Qu.:-0.66146  
#>  Median : 0.011377   Median : 0.007125   Median :-0.04726  
#>  Mean   :-0.003207   Mean   :-0.023968   Mean   :-0.01677  
#>  3rd Qu.: 0.651951   3rd Qu.: 0.647363   3rd Qu.: 0.62640  
#>  Max.   : 3.470910   Max.   : 2.963216   Max.   : 3.09950
colMeans(df)
#>            X            M            Y 
#> -0.003206987 -0.023968103 -0.016774294
var(df)
#>           X         M         Y
#> X 1.0600162 0.5108780 0.5069458
#> M 0.5108780 0.9996606 0.6272104
#> Y 0.5069458 0.6272104 0.9837255

Model Specification

model <- "
  Y ~ cp * X + b * M
  M ~ a * X
  indirect := a * b
  direct := cp
  total := cp + (a * b)
"

Model Fitting

fit <- sem(data = df, model = model)

Monte Carlo Confidence Intervals

unstd <- MC(fit, R = 20000L, alpha = 0.05)

Methods

print

print(unstd)
#> Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2333 0.0264 20000 0.1819 0.2849
#> b        0.5082 0.0272 20000 0.4553 0.5613
#> a        0.4820 0.0264 20000 0.4302 0.5340
#> Y~~Y     0.5462 0.0244 20000 0.4979 0.5944
#> M~~M     0.7527 0.0339 20000 0.6858 0.8187
#> X~~X     1.0590 0.0000 20000 1.0590 1.0590
#> indirect 0.2449 0.0187 20000 0.2094 0.2831
#> direct   0.2333 0.0264 20000 0.1819 0.2849
#> total    0.4782 0.0265 20000 0.4261 0.5306

summary

summary(unstd)
#> Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2333 0.0264 20000 0.1819 0.2849
#> b        0.5082 0.0272 20000 0.4553 0.5613
#> a        0.4820 0.0264 20000 0.4302 0.5340
#> Y~~Y     0.5462 0.0244 20000 0.4979 0.5944
#> M~~M     0.7527 0.0339 20000 0.6858 0.8187
#> X~~X     1.0590 0.0000 20000 1.0590 1.0590
#> indirect 0.2449 0.0187 20000 0.2094 0.2831
#> direct   0.2333 0.0264 20000 0.1819 0.2849
#> total    0.4782 0.0265 20000 0.4261 0.5306

coef

coef(unstd)
#>        cp         b         a      Y~~Y      M~~M      X~~X  indirect    direct 
#> 0.2333230 0.5081833 0.4819530 0.5461589 0.7526879 1.0589562 0.2449205 0.2333230 
#>     total 
#> 0.4782435

vcov

vcov(unstd)
#>                     cp             b             a         Y~~Y          M~~M
#> cp        6.975724e-04 -3.570594e-04  1.739434e-06 2.065846e-06 -4.029921e-06
#> b        -3.570594e-04  7.379603e-04 -7.450590e-06 1.744389e-06  6.618803e-06
#> a         1.739434e-06 -7.450590e-06  6.982971e-04 8.322624e-06 -5.021764e-06
#> Y~~Y      2.065846e-06  1.744389e-06  8.322624e-06 5.962836e-04  4.504744e-06
#> M~~M     -4.029921e-06  6.618803e-06 -5.021764e-06 4.504744e-06  1.148370e-03
#> X~~X      0.000000e+00  0.000000e+00  0.000000e+00 0.000000e+00  0.000000e+00
#> indirect -1.708943e-04  3.516821e-04  3.515320e-04 4.920373e-06  3.808621e-07
#> direct    6.975724e-04 -3.570594e-04  1.739434e-06 2.065846e-06 -4.029921e-06
#> total     5.266782e-04 -5.377290e-06  3.532714e-04 6.986219e-06 -3.649059e-06
#>          X~~X      indirect        direct         total
#> cp          0 -1.708943e-04  6.975724e-04  5.266782e-04
#> b           0  3.516821e-04 -3.570594e-04 -5.377290e-06
#> a           0  3.515320e-04  1.739434e-06  3.532714e-04
#> Y~~Y        0  4.920373e-06  2.065846e-06  6.986219e-06
#> M~~M        0  3.808621e-07 -4.029921e-06 -3.649059e-06
#> X~~X        0  0.000000e+00  0.000000e+00  0.000000e+00
#> indirect    0  3.486997e-04 -1.708943e-04  1.778055e-04
#> direct      0 -1.708943e-04  6.975724e-04  5.266782e-04
#> total       0  1.778055e-04  5.266782e-04  7.044836e-04

confint

confint(unstd, level = 0.95)
#>              2.5 %    97.5 %
#> cp       0.1819362 0.2849104
#> b        0.4552649 0.5613296
#> a        0.4301663 0.5339651
#> Y~~Y     0.4979155 0.5944224
#> M~~M     0.6857891 0.8187138
#> X~~X     1.0589562 1.0589562
#> indirect 0.2093636 0.2830510
#> direct   0.1819362 0.2849104
#> total    0.4261341 0.5305578

Standardized Monte Carlo Confidence Intervals

fit <- sem(data = df, model = model, fixed.x = FALSE)
unstd <- MC(fit, R = 20000L, alpha = 0.05)

std <- MCStd(unstd, alpha = 0.05)

Methods

print

print(std)
#> Standardized Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2422 0.0266 20000 0.1897 0.2941
#> b        0.5123 0.0247 20000 0.4636 0.5605
#> a        0.4963 0.0240 20000 0.4476 0.5416
#> Y~~Y     0.5558 0.0236 20000 0.5089 0.6015
#> M~~M     0.7537 0.0238 20000 0.7066 0.7996
#> X~~X     1.0000 0.0000 20000 1.0000 1.0000
#> indirect 0.2542 0.0177 20000 0.2199 0.2891
#> direct   0.2422 0.0266 20000 0.1897 0.2941
#> total    0.4964 0.0239 20000 0.4477 0.5417

summary

summary(std)
#> Standardized Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2422 0.0266 20000 0.1897 0.2941
#> b        0.5123 0.0247 20000 0.4636 0.5605
#> a        0.4963 0.0240 20000 0.4476 0.5416
#> Y~~Y     0.5558 0.0236 20000 0.5089 0.6015
#> M~~M     0.7537 0.0238 20000 0.7066 0.7996
#> X~~X     1.0000 0.0000 20000 1.0000 1.0000
#> indirect 0.2542 0.0177 20000 0.2199 0.2891
#> direct   0.2422 0.0266 20000 0.1897 0.2941
#> total    0.4964 0.0239 20000 0.4477 0.5417

coef

coef(std)
#>        cp         b         a      Y~~Y      M~~M      X~~X  indirect    direct 
#> 0.2422015 0.5122827 0.4962890 0.5557501 0.7536972 1.0000000 0.2542403 0.2422015 
#>     total 
#> 0.4964418

vcov

vcov(std)
#>                     cp             b             a          Y~~Y          M~~M
#> cp        7.091899e-04 -4.651025e-04  8.245583e-06 -1.168207e-04 -8.275421e-06
#> b        -4.651025e-04  6.083075e-04  2.339914e-05 -3.134309e-04 -2.305571e-05
#> a         8.245583e-06  2.339914e-05  5.769659e-04 -1.801830e-04 -5.706892e-04
#> Y~~Y     -1.168207e-04 -3.134309e-04 -1.801830e-04  5.569665e-04  1.782647e-04
#> M~~M     -8.275421e-06 -2.305571e-05 -5.706892e-04  1.782647e-04  5.651409e-04
#> X~~X      3.525000e-20 -4.147947e-20 -9.499398e-21  1.914120e-20  8.545081e-21
#> indirect -2.265255e-04  3.136098e-04  3.069966e-04 -2.474505e-04 -3.036457e-04
#> direct    7.091899e-04 -4.651025e-04  8.245583e-06 -1.168207e-04 -8.275421e-06
#> total     4.826644e-04 -1.514927e-04  3.152422e-04 -3.642712e-04 -3.119212e-04
#>                   X~~X      indirect        direct         total
#> cp        3.525000e-20 -2.265255e-04  7.091899e-04  4.826644e-04
#> b        -4.147947e-20  3.136098e-04 -4.651025e-04 -1.514927e-04
#> a        -9.499398e-21  3.069966e-04  8.245583e-06  3.152422e-04
#> Y~~Y      1.914120e-20 -2.474505e-04 -1.168207e-04 -3.642712e-04
#> M~~M      8.545081e-21 -3.036457e-04 -8.275421e-06 -3.119212e-04
#> X~~X      1.182796e-32 -2.533127e-20  3.525000e-20  9.918728e-21
#> indirect -2.533127e-20  3.130369e-04 -2.265255e-04  8.651139e-05
#> direct    3.525000e-20 -2.265255e-04  7.091899e-04  4.826644e-04
#> total     9.918728e-21  8.651139e-05  4.826644e-04  5.691757e-04

confint

confint(std, level = 0.95)
#>              2.5 %    97.5 %
#> cp       0.1896616 0.2941122
#> b        0.4635708 0.5604860
#> a        0.4476424 0.5416327
#> Y~~Y     0.5089400 0.6015440
#> M~~M     0.7066340 0.7996163
#> X~~X     1.0000000 1.0000000
#> indirect 0.2198992 0.2890635
#> direct   0.1896616 0.2941122
#> total    0.4477209 0.5416757

References

Pesigan, I. J. A., & Cheung, S. F. (2023). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods, 56(3), 1678–1696. https://doi.org/10.3758/s13428-023-02114-4

Ivan Jacob Agaloos Pesigan

2025-01-13

Data

Model Specification

Model Fitting

Monte Carlo Confidence Intervals

Methods

print

summary

coef

vcov

confint

Standardized Monte Carlo Confidence Intervals

Methods

print

summary

coef

vcov

confint

References