Data Generation

The following presents an example of how to use the functions in this package to simulate a data set, perform a multivariate amputation, and multiple imputations. See the individual function documentation for more information.

The most basic mediation model involves three variables, \(X\), \(M\), and \(Y\) whose associations are expressed in the following equations

\[\begin{equation} Y = \delta_{Y} + \tau^{\prime}{X} + \beta{M} + \varepsilon_{Y}, \end{equation}\]

\[\begin{equation} M = \delta_{M} + \alpha X + \varepsilon_{M}, \end{equation}\]

where \(\alpha\) represents the effect of the independent variable \(X\) on the mediator variable \(M\); \(\beta\) represents the effect of the mediator variable \(M\) on the dependent variable \(Y\); \(\tau^{\prime}\) represents the effect of the independent variable \(X\) on the dependent variable \(Y\), adjusting for the mediator variable \(M\); \(\delta_{M}\) and \(\delta_{Y}\) are intercepts; and \(\varepsilon_{M}\) and \(\varepsilon_{Y}\) are stochastic error terms. The direct effect, \(\tau^{\prime}\), which is the change in the dependent variable corresponding to one unit change in the independent variable, while the mediator variable is held constant, can be contrasted with the indirect effect (the product of \(\alpha\) and \(\beta\) or \(\alpha \beta\)), which represents the change in the dependent variable via the mediator if the independent variable increases by one unit. See MacKinnon (2008) for more information on the simple mediation model.

Mplus

Mplus Version 8.8 Demo for GNU/Linux was used in the study. Note that this version is equivalent to the commercial release except for the limitations on the number of variables that can be used in the analysis. See https://www.statmodel.com/demo.shtml for more details on the limitations and installation instructions.

The functions in this package will work on other versions of Mplus in various platforms. However, for compatibility, we recommend the use of Mplus Version 8.8 Demo for GNU/Linux. The functions in this package require the user to specify the path to the Mplus binary as the argument mplus_bin. For example, the default location of the Mplus demo binary in GNU/Linux is /opt/mplusdemo/mpdemo.

NOTE: For complete reproducibility of the software stack, we recommend the use of manmcmedmiss.sif described in the Containers article.

Arguments

library(manMCMedMiss)

Variable	Value	Notes
m	100	Number of imputations.
mplus_bin	“/opt/mplusdemo/mpdemo”	Path to Mplus binary.

NOTE: If you are using manmcmedmiss-rocker or manmcmedmiss.sif described in the Containers article, set mplus_bin = "mpdemo".

Parameters

Variable	Value	Notes
n	50	\(n\)
tauprime	0.14142135623731	\(\tau^{\prime}\)
alpha	0.714074191775111	\(\alpha\)
beta	0.714074191775111	\(\beta\)

Data

Generation

Generate sample data with complete observations.

set.seed(42)
data_complete <- GenData(
  n = n,
  tauprime = tauprime,
  beta = beta,
  alpha = alpha
)
knitr::kable(head(data_complete))

x	m	y
1.4335508	0.8481267	1.4611211
-0.8011428	-0.7484141	0.0080208
1.0207058	0.4294871	-0.4326847
0.9993171	-0.0979391	0.8558379
0.3465149	0.5793515	0.1654108
0.0522852	-0.1740765	-0.1570564

Amputation

Generate sample data with missing values using the multivariate amputation approach proposed by Schouten et al. (2018).

data_missing <- AmputeData(
  data_complete,
  mech = "MAR",
  prop = 0.10
)
knitr::kable(head(data_missing))

x	m	y
1.4335508	0.8481267	1.4611211
NA	NA	0.0080208
1.0207058	0.4294871	-0.4326847
0.9993171	-0.0979391	0.8558379
0.3465149	NA	NA
0.0522852	-0.1740765	-0.1570564

Imputation

Perform multiple imputations following Asparouhov and Muthen (2010) using Mplus.

data_mi <- ImputeData(
  data_missing,
  m = m,
  mplus_bin = mplus_bin
)

Show the first two complete data sets.

data_mi[1:2]
#> [[1]]
#>        V1     V2     V3
#> 1   1.434  0.848  1.461
#> 2   0.314  1.330  0.008
#> 3   1.021  0.429 -0.433
#> 4   0.999 -0.098  0.856
#> 5   0.347 -1.297 -0.918
#> 6   0.052 -0.174 -0.157
#> 7   1.615  1.449  1.051
#> 8  -0.046 -0.062 -0.147
#> 9   0.284  2.270  1.068
#> 10  0.095 -0.139 -0.117
#> 11  0.947  1.283  1.299
#> 12  2.081  2.076  2.053
#> 13 -0.951 -1.229 -1.578
#> 14  0.414 -0.305 -0.831
#> 15 -0.595  0.517 -0.325
#> 16  1.167  0.525  0.065
#> 17 -0.117 -0.151 -0.500
#> 18 -1.594 -3.507 -2.044
#> 19 -1.758 -1.980 -2.873
#> 20  1.510  1.084  1.010
#> 21 -0.889  0.348 -0.338
#> 22 -1.694 -1.179 -1.979
#> 23  0.168 -0.293 -0.322
#> 24  0.509  1.598  1.149
#> 25  1.374  1.481  1.899
#> 26 -0.117 -0.351 -0.689
#> 27  0.112 -0.157 -0.639
#> 28 -1.445 -1.066 -2.284
#> 29  1.132  0.955  0.381
#> 30 -1.085 -0.494 -0.186
#> 31  1.183  0.020  0.082
#> 32  0.703  0.780  0.431
#> 33  1.504  0.955  1.670
#> 34 -0.506 -0.913 -0.223
#> 35 -0.049  0.185  1.217
#> 36 -1.265 -1.343 -2.046
#> 37 -0.795 -0.664 -0.676
#> 38 -0.741 -1.155 -0.403
#> 39 -1.665 -2.245 -2.620
#> 40  0.433 -0.071 -0.242
#> 41  0.860  0.015 -0.278
#> 42 -0.612  0.018 -0.410
#> 43  0.946  0.756  0.368
#> 44  0.055 -0.876 -1.112
#> 45 -1.764 -0.982 -1.002
#> 46  0.030  0.174  0.959
#> 47 -1.297 -0.437 -0.505
#> 48  0.499  1.706  1.667
#> 49 -0.284 -0.640 -0.236
#> 50  0.815  0.857  0.113
#> 
#> [[2]]
#>        V1     V2     V3
#> 1   1.434  0.848  1.461
#> 2  -0.601  0.203  0.008
#> 3   1.021  0.429 -0.433
#> 4   0.999 -0.098  0.856
#> 5   0.347 -0.841 -0.182
#> 6   0.052 -0.174 -0.157
#> 7   1.615  1.449  1.051
#> 8  -0.046 -0.062 -0.147
#> 9   0.284  2.270  2.325
#> 10  0.095 -0.139 -0.117
#> 11  0.947  1.283  1.299
#> 12  2.081  2.076  2.053
#> 13 -0.951 -1.229 -1.578
#> 14  0.414 -0.305 -0.831
#> 15 -0.595  0.517 -0.325
#> 16  1.167  0.525  0.065
#> 17 -0.117 -0.151 -0.500
#> 18 -1.594 -3.507 -2.044
#> 19 -1.758 -1.980 -2.873
#> 20  1.510  1.084  1.010
#> 21 -0.889  0.348 -0.338
#> 22 -1.694 -1.179 -1.979
#> 23  0.168 -0.293 -0.322
#> 24  0.509  1.598  1.149
#> 25  1.374  1.531  1.899
#> 26 -0.117 -0.351 -0.689
#> 27  0.112 -0.157 -0.639
#> 28 -1.445 -1.066 -2.284
#> 29  0.196  0.955  0.381
#> 30 -1.085 -0.494 -0.186
#> 31  1.183  0.020  0.082
#> 32  0.703  0.780  0.431
#> 33  0.404  0.955  0.476
#> 34 -0.506 -0.913 -0.223
#> 35 -0.049  0.185  1.217
#> 36 -1.265 -1.343 -2.046
#> 37 -0.795 -0.664 -0.676
#> 38 -0.741 -1.155 -0.403
#> 39 -1.665 -2.245 -2.620
#> 40  0.433 -0.071 -0.242
#> 41  0.860  0.015 -0.278
#> 42 -0.612  0.018 -0.410
#> 43  0.946  0.756  0.368
#> 44  0.055 -0.876 -1.112
#> 45 -1.764 -0.982 -1.002
#> 46  0.030  0.174  0.959
#> 47 -1.297 -0.437 -0.505
#> 48  0.499  1.706  1.667
#> 49 -0.284 -0.640 -0.236
#> 50  0.815  0.857  0.113

References

Asparouhov, T., & Muthen, B. (2010). Multiple imputation with Mplus. Retrieved from http://www.statmodel.com/download/Imputations7.pdf

MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. Lawrence Erlbaum Associates.

Schouten, R. M., Lugtig, P. and Vink, G. (2018). Generating missing values for simulation purposes: A multivariate amputation procedure. Journal of Statistical Computation and Simulation, 88(15), 1909–1930. https://doi.org/10.1080/00949655.2018.1491577

Ivan Jacob Agaloos Pesigan