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 0.4299 0.5337
#> 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 0.0188 20000 0.2094 0.2831
#> direct   0.2333 0.0264 20000 0.1817 0.2846
#> total    0.4782 0.0264 20000 0.4262 0.5295

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 0.4299 0.5337
#> 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 0.0188 20000 0.2094 0.2831
#> direct   0.2333 0.0264 20000 0.1817 0.2846
#> total    0.4782 0.0264 20000 0.4262 0.5295

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 -1.760619e-04  3.579324e-04  3.559548e-04 -5.050361e-06  4.668854e-06
#> direct    6.957832e-04 -3.569537e-04 -7.335055e-06 -1.863172e-06 -6.369651e-06
#> total     5.197213e-04  9.786539e-07  3.486198e-04 -6.913533e-06 -1.700796e-06
#>          X~~X      indirect        direct         total
#> cp          0 -1.760619e-04  6.957832e-04  5.197213e-04
#> b           0  3.579324e-04 -3.569537e-04  9.786539e-07
#> a           0  3.559548e-04 -7.335055e-06  3.486198e-04
#> Y~~Y        0 -5.050361e-06 -1.863172e-06 -6.913533e-06
#> M~~M        0  4.668854e-06 -6.369651e-06 -1.700796e-06
#> X~~X        0  0.000000e+00  0.000000e+00  0.000000e+00
#> indirect    0  3.540809e-04 -1.760619e-04  1.780190e-04
#> direct      0 -1.760619e-04  6.957832e-04  5.197213e-04
#> total       0  1.780190e-04  5.197213e-04  6.977403e-04

confint

confint(unstd, level = 0.95)
#>              2.5 %    97.5 %
#> cp       0.1816910 0.2845601
#> b        0.4551497 0.5611403
#> a        0.4299410 0.5337397
#> Y~~Y     0.4979155 0.5944224
#> M~~M     0.6857891 0.8187138
#> X~~X     1.0589562 1.0589562
#> indirect 0.2094303 0.2831318
#> direct   0.1816910 0.2845601
#> total    0.4262403 0.5294621

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 0.0268 20000 0.1895 0.2942
#> b        0.5123 0.0246 20000 0.4640 0.5609
#> a        0.4963 0.0240 20000 0.4476 0.5416
#> Y~~Y     0.5558 0.0235 20000 0.5094 0.6017
#> 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 0.2200 0.2889
#> direct   0.2422 0.0268 20000 0.1895 0.2942
#> total    0.4964 0.0240 20000 0.4483 0.5422

summary

summary(std)
#> Standardized Monte Carlo Confidence Intervals
#>             est     se     R   2.5%  97.5%
#> cp       0.2422 0.0268 20000 0.1895 0.2942
#> b        0.5123 0.0246 20000 0.4640 0.5609
#> a        0.4963 0.0240 20000 0.4476 0.5416
#> Y~~Y     0.5558 0.0235 20000 0.5094 0.6017
#> 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 0.2200 0.2889
#> direct   0.2422 0.0268 20000 0.1895 0.2942
#> total    0.4964 0.0240 20000 0.4483 0.5422

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        7.191848e-04 -4.667519e-04  6.123858e-06 -1.242838e-04 -6.255887e-06
#> b        -4.667519e-04  6.043972e-04  2.231523e-05 -3.063863e-04 -2.203165e-05
#> a         6.123858e-06  2.231523e-05  5.769659e-04 -1.767496e-04 -5.706892e-04
#> Y~~Y     -1.242838e-04 -3.063863e-04 -1.767496e-04  5.545463e-04  1.749864e-04
#> M~~M     -6.255887e-06 -2.203165e-05 -5.706892e-04  1.749864e-04  5.651409e-04
#> X~~X      3.417802e-20 -4.198085e-20 -1.927269e-20  2.384949e-20  1.827301e-20
#> indirect -2.284289e-04  3.111062e-04  3.064863e-04 -2.421852e-04 -3.031584e-04
#> direct    7.191848e-04 -4.667519e-04  6.123858e-06 -1.242838e-04 -6.255887e-06
#> total     4.907559e-04 -1.556457e-04  3.126101e-04 -3.664690e-04 -3.094143e-04
#>                   X~~X      indirect        direct         total
#> cp        3.417802e-20 -2.284289e-04  7.191848e-04  4.907559e-04
#> b        -4.198085e-20  3.111062e-04 -4.667519e-04 -1.556457e-04
#> a        -1.927269e-20  3.064863e-04  6.123858e-06  3.126101e-04
#> Y~~Y      2.384949e-20 -2.421852e-04 -1.242838e-04 -3.664690e-04
#> M~~M      1.827301e-20 -3.031584e-04 -6.255887e-06 -3.094143e-04
#> X~~X      1.183659e-32 -3.060614e-20  3.417802e-20  3.571876e-21
#> indirect -3.060614e-20  3.115388e-04 -2.284289e-04  8.310990e-05
#> direct    3.417802e-20 -2.284289e-04  7.191848e-04  4.907559e-04
#> total     3.571876e-21  8.310990e-05  4.907559e-04  5.738658e-04

confint

confint(std, level = 0.95)
#>              2.5 %    97.5 %
#> cp       0.1894519 0.2941807
#> b        0.4640480 0.5609003
#> a        0.4476424 0.5416327
#> Y~~Y     0.5094295 0.6016893
#> M~~M     0.7066340 0.7996163
#> X~~X     1.0000000 1.0000000
#> indirect 0.2199734 0.2889152
#> direct   0.1894519 0.2941807
#> total    0.4482508 0.5421569

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

2024-10-22

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