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 0.1817 0.2846
#> b        0.5082 0.0272 20000 0.4551 0.5611
#> 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 0.2093 0.2825
#> direct   0.2333 0.0264 20000 0.1817 0.2846
#> total    0.4782 0.0267 20000 0.4257 0.5303

summary

summary(unstd)
#> Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2333 0.0264 20000 0.1817 0.2846
#> b        0.5082 0.0272 20000 0.4551 0.5611
#> 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 0.2093 0.2825
#> direct   0.2333 0.0264 20000 0.1817 0.2846
#> total    0.4782 0.0267 20000 0.4257 0.5303

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        6.957832e-04 -3.569537e-04  7.335055e-06 -1.863172e-06 -6.369651e-06
#> b        -3.569537e-04  7.397495e-04 -2.175751e-06 -1.959388e-06  4.413204e-06
#> a         7.335055e-06 -2.175751e-06  6.982971e-04  8.322624e-06 -5.021764e-06
#> Y~~Y     -1.863172e-06 -1.959388e-06  8.322624e-06  5.962836e-04  4.504744e-06
#> M~~M     -6.369651e-06  4.413204e-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 -1.680080e-04  3.551166e-04  3.538576e-04  3.161695e-06 -4.149403e-07
#> direct    6.957832e-04 -3.569537e-04  7.335055e-06 -1.863172e-06 -6.369651e-06
#> total     5.277753e-04 -1.837106e-06  3.611927e-04  1.298523e-06 -6.784591e-06
#>          X~~X      indirect        direct         total
#> cp          0 -1.680080e-04  6.957832e-04  5.277753e-04
#> b           0  3.551166e-04 -3.569537e-04 -1.837106e-06
#> a           0  3.538576e-04  7.335055e-06  3.611927e-04
#> Y~~Y        0  3.161695e-06 -1.863172e-06  1.298523e-06
#> M~~M        0 -4.149403e-07 -6.369651e-06 -6.784591e-06
#> X~~X        0  0.000000e+00  0.000000e+00  0.000000e+00
#> indirect    0  3.513668e-04 -1.680080e-04  1.833588e-04
#> direct      0 -1.680080e-04  6.957832e-04  5.277753e-04
#> total       0  1.833588e-04  5.277753e-04  7.111341e-04

confint

confint(unstd, level = 0.95)
#>              2.5 %    97.5 %
#> cp       0.1816910 0.2845601
#> b        0.4551497 0.5611403
#> a        0.4301663 0.5339651
#> Y~~Y     0.4979155 0.5944224
#> M~~M     0.6857891 0.8187138
#> X~~X     1.0589562 1.0589562
#> indirect 0.2093133 0.2824762
#> direct   0.1816910 0.2845601
#> total    0.4256765 0.5303385

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      3.561808e-20 -4.381808e-20 -1.616684e-20  2.411689e-20  1.517962e-20
#> 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        3.561808e-20 -2.265255e-04  7.091899e-04  4.826644e-04
#> b        -4.381808e-20  3.136098e-04 -4.651025e-04 -1.514927e-04
#> a        -1.616684e-20  3.069966e-04  8.245583e-06  3.152422e-04
#> Y~~Y      2.411689e-20 -2.474505e-04 -1.168207e-04 -3.642712e-04
#> M~~M      1.517962e-20 -3.036457e-04 -8.275421e-06 -3.119212e-04
#> X~~X      1.185138e-32 -3.008102e-20  3.561808e-20  5.537064e-21
#> indirect -3.008102e-20  3.130369e-04 -2.265255e-04  8.651139e-05
#> direct    3.561808e-20 -2.265255e-04  7.091899e-04  4.826644e-04
#> total     5.537064e-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. (2024). 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

2026-03-01

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