R/results_mvn_mar_fit.sem.R
results_mvn_mar_fit.sem.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Data Missing at Random - Fit Structural Equation Modeling with Full Information Maximum Likelihood
results_mvn_mar_fit.sem
A data frame with the following variables
Simulation task identification number.
Sample size.
Monte Carlo replications.
Population slope of path from x to y \(\left( \dot{\tau} \right)\).
Population slope of path from m to y \(\left( \beta \right)\).
Population slope of path from x to m \(\left( \alpha \right)\).
Population indirect effect of x on y through m \(\left( \alpha \beta \right)\).
Population variance of x \(\left( \sigma_{x}^{2} \right)\).
Population error variance of m \(\left( \sigma_{\varepsilon_{m}}^{2} \right)\).
Population error variance of y \(\left( \sigma_{\varepsilon_{y}}^{2} \right)\).
Population mean of x \(\left( \mu_x \right)\).
Population intercept of m \(\left( \delta_m \right)\).
Population intercept of y \(\left( \delta_y \right)\).
Mean of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Mean of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Mean of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Mean of estimated error variance of y \(\left( \hat{\sigma}_{\varepsilon_{y}}^{2} \right)\).
Mean of estimated error variance of m \(\left( \hat{\sigma}_{\varepsilon_{m}}^{2} \right)\).
Mean of estimated intercept of y \(\left( \hat{\delta}_y \right)\).
Mean of estimated intercept of m \(\left( \hat{\delta}_{m} \right)\).
Mean of estimated mean of x \(\left( \hat{\mu}_x \right)\).
Mean of estimated variance of x \(\left( \hat{\sigma}_{x}^{2} \right)\).
Mean of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Mean of estimated standard error of \(\hat{\dot{\tau}}\).
Mean of estimated standard error of \(\hat{\beta}\).
Mean of estimated standard error of \(\hat{\alpha}\).
Mean of estimated standard error of error variance of y \(\left( \hat{\sigma}_{\varepsilon_{y}}^{2} \right)\).
Mean of estimated standard error of error variance of m \(\left( \hat{\sigma}_{\varepsilon_{m}}^{2} \right)\).
Mean of estimated standard error of \(\hat{\delta}_{y}\).
Mean of estimated standard error of \(\hat{\delta}_{m}\).
Mean of estimated standard error of mean of x \(\left( \hat{\mu}_x \right)\).
Mean of estimated standard error of variance of x \(\left( \hat{\sigma}_{x}^{2} \right)\).
Population parameter \(\alpha \beta\).
Variance of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Variance of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Variance of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Variance of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Standard deviation of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Standard deviation of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Standard deviation of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Standard deviation of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Skewness of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Skewness of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Skewness of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Skewness of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Excess kurtosis of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Excess kurtosis of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Excess kurtosis of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Excess kurtosis of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Bias of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Bias of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Bias of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Bias of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Mean square error of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Mean square error of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Mean square error of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Mean square error of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Root mean square error of estimated slope of path from x to y \(\left( \hat{\dot{\tau}} \right)\).
Root mean square error of estimated slope of path from m to y \(\left( \hat{\beta} \right)\).
Root mean square error of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Root mean square error of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
Type of missingness.
Standardized vs. unstandardize indirect effect.
Method used. Fit in this case.
Sample size labels.
\(\alpha\) labels.
\(\beta\) labels.
\(\dot{\tau}\) labels.
\(\theta\) labels.
The simple mediation model is given by $$ y_i = \delta_y + \dot{\tau} x_i + \beta m_i + \varepsilon_{y_{i}} $$
$$ m_i = \delta_m + \alpha x_i + \varepsilon_{m_{i}} $$
The parameters for the mean structure are $$ \boldsymbol{\theta}_{\text{mean structure}} = \left\{ \mu_x, \delta_m, \delta_y \right\} . $$
The parameters for the covariance structure are $$ \boldsymbol{\theta}_{\text{covariance structure}} = \left\{ \dot{\tau}, \beta, \alpha, \sigma_{x}^{2}, \sigma_{\varepsilon_{m}}^{2}, \sigma_{\varepsilon_{y}}^{2} \right\} . $$
Other results:
results_beta_fit.ols,
results_beta_ols_mc.mvn_ci,
results_exp_fit.ols,
results_exp_ols_mc.mvn_ci,
results_mvn_fit.ols,
results_mvn_fit.sem,
results_mvn_mar_mc.mvn_ci,
results_mvn_mar_nb.fiml_ci,
results_mvn_mar_pb.mvn_ci,
results_mvn_mcar_fit.sem,
results_mvn_mcar_mc.mvn_ci,
results_mvn_mcar_nb.fiml_ci,
results_mvn_mcar_pb.mvn_ci,
results_mvn_mnar_fit.sem,
results_mvn_mnar_mc.mvn_ci,
results_mvn_mnar_nb.fiml_ci,
results_mvn_nb_ci,
results_mvn_ols_mc.mvn_ci,
results_mvn_pb.mvn_ci,
results_mvn_sem_mc.mvn_ci,
results_vm_mod_fit.ols,
results_vm_mod_fit.sem.mlr,
results_vm_mod_nb_ci,
results_vm_mod_ols_mc.mvn_ci,
results_vm_mod_pb.mvn_ci,
results_vm_mod_sem_mc.mvn_ci,
results_vm_sev_fit.ols,
results_vm_sev_fit.sem.mlr,
results_vm_sev_nb_ci,
results_vm_sev_ols_mc.mvn_ci,
results_vm_sev_pb.mvn_ci,
results_vm_sev_sem_mc.mvn_ci
#> taskid n reps taudot beta alpha alphabeta sigma2x #> 1 1 1000 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> 2 2 500 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> 3 3 250 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> 4 4 200 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> 5 5 150 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> 6 6 100 5000 0.1414214 0.7140742 0.7140742 0.509902 225 #> sigma2epsilonm sigma2epsilony mux deltam deltay taudothat betahat #> 1 110.2721 73.3221 100 28.59258 14.45045 0.1414260 0.7137673 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.1409499 0.7148095 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.1401230 0.7146896 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.1414218 0.7136926 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.1396104 0.7158172 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.1413558 0.7151024 #> alphahat sigma2hatepsilonyhat sigma2hatepsilonmhat deltayhat deltamhat #> 1 0.7141745 73.01513 109.9969 14.48432 28.58664 #> 2 0.7143421 72.80894 109.9272 14.42782 28.56011 #> 3 0.7148084 72.37036 109.4090 14.52343 28.53316 #> 4 0.7138078 72.27085 109.1216 14.49037 28.62329 #> 5 0.7133967 71.91072 109.0001 14.44591 28.65565 #> 6 0.7127444 70.87726 108.1219 14.36521 28.73572 #> muxhat sigma2xhat alphahatbetahat sehattaudothat sehatbetahat #> 1 99.98946 224.8061 0.5097503 0.02703004 0.02677294 #> 2 99.99608 224.3217 0.5106244 0.03826467 0.03786975 #> 3 99.99378 223.7906 0.5108821 0.05420430 0.05364264 #> 4 100.01707 223.9122 0.5094888 0.06061902 0.06007959 #> 5 100.00703 224.1021 0.5106098 0.07003157 0.06939276 #> 6 99.97942 222.2889 0.5097006 0.08580449 0.08501304 #> sehatalphahat sehatsigma2hatepsilonyhat sehatsigma2hatepsilonmhat #> 1 0.02266661 3.369566 5.080972 #> 2 0.03211208 4.753836 7.184120 #> 3 0.04545640 6.690855 10.122137 #> 4 0.05079364 7.473200 11.289776 #> 5 0.05870156 8.597321 13.038434 #> 6 0.07214009 10.399328 15.858868 #> sehatdeltayhat sehatdeltamhat sehatmuxhat sehatsigma2xhat theta #> 1 2.039974 2.285887 0.4782237 10.23399 0.509902 #> 2 2.887520 3.238622 0.6758314 14.45166 0.509902 #> 3 4.089004 4.584221 0.9550587 20.40569 0.509902 #> 4 4.579133 5.123392 1.0682802 22.83352 0.509902 #> 5 5.284461 5.920408 1.2345463 26.41008 0.509902 #> 6 6.489903 7.272914 1.5070481 32.13121 0.509902 #> taudothat_var betahat_var alphahat_var alphahatbetahat_var taudothat_sd #> 1 0.0007491382 0.0007466344 0.0005081424 0.000636272 0.02737039 #> 2 0.0014494313 0.0014506762 0.0010272934 0.001272479 0.03807140 #> 3 0.0030208904 0.0029767530 0.0020783865 0.002609268 0.05496263 #> 4 0.0038075545 0.0036312014 0.0025952660 0.003224645 0.06170538 #> 5 0.0049440387 0.0048740335 0.0034625020 0.004209257 0.07031386 #> 6 0.0077938812 0.0073962789 0.0052320464 0.006498411 0.08828296 #> betahat_sd alphahat_sd alphahatbetahat_sd taudothat_skew betahat_skew #> 1 0.02732461 0.02254201 0.02522443 -0.068675862 0.008968774 #> 2 0.03808774 0.03205142 0.03567183 -0.010340650 -0.018482411 #> 3 0.05455963 0.04558932 0.05108100 -0.064735954 0.042430148 #> 4 0.06025945 0.05094375 0.05678596 0.006402749 -0.030378817 #> 5 0.06981428 0.05884303 0.06487879 -0.020303208 0.037679829 #> 6 0.08600162 0.07233289 0.08061272 0.018582407 -0.023884808 #> alphahat_skew alphahatbetahat_skew taudothat_kurt betahat_kurt alphahat_kurt #> 1 -0.001654276 0.0903431 -0.026430447 0.01472061 -0.01730095 #> 2 0.021856796 0.1018975 -0.044886108 0.05091866 -0.01206637 #> 3 -0.038906590 0.1760290 -0.021622604 -0.09890091 0.02281177 #> 4 0.023571909 0.1264599 0.085301249 -0.09318891 -0.02498903 #> 5 0.041571866 0.1733952 0.007278609 0.02505435 0.20688924 #> 6 -0.016335263 0.2199734 0.184789832 0.04500088 0.02014943 #> alphahatbetahat_kurt taudothat_bias betahat_bias alphahat_bias #> 1 -0.0482224887 4.632720e-06 -0.0003069325 0.0001003454 #> 2 0.1392162788 -4.714514e-04 0.0007353072 0.0002679366 #> 3 -0.0136120138 -1.298356e-03 0.0006154008 0.0007342349 #> 4 0.0009262161 4.386264e-07 -0.0003815848 -0.0002664362 #> 5 -0.0556019209 -1.810991e-03 0.0017429847 -0.0006774935 #> 6 0.0168918296 -6.554108e-05 0.0010281860 -0.0013298149 #> alphahatbetahat_bias taudothat_mse betahat_mse alphahat_mse #> 1 -0.0001516459 0.0007489884 0.0007465792 0.0005080509 #> 2 0.0007224360 0.0014493637 0.0014509267 0.0010271597 #> 3 0.0009801403 0.0030219720 0.0029765364 0.0020785099 #> 4 -0.0004131067 0.0038067930 0.0036306208 0.0025948179 #> 5 0.0007078231 0.0049463296 0.0048760967 0.0034622685 #> 6 -0.0002013966 0.0077923267 0.0073958568 0.0052327684 #> alphahatbetahat_mse taudothat_rmse betahat_rmse alphahat_rmse #> 1 0.0006361677 0.02736765 0.02732360 0.02253998 #> 2 0.0012727466 0.03807051 0.03809103 0.03204933 #> 3 0.0026097069 0.05497247 0.05455764 0.04559068 #> 4 0.0032241709 0.06169921 0.06025463 0.05093936 #> 5 0.0042089162 0.07033015 0.06982905 0.05884104 #> 6 0.0064971514 0.08827416 0.08599917 0.07233788 #> alphahatbetahat_rmse missing std Method n_label alpha_label #> 1 0.02522237 MAR.10 Unstandardized fit.sem n: 1000 α: 0.71 #> 2 0.03567557 MAR.10 Unstandardized fit.sem n: 500 α: 0.71 #> 3 0.05108529 MAR.10 Unstandardized fit.sem n: 250 α: 0.71 #> 4 0.05678178 MAR.10 Unstandardized fit.sem n: 200 α: 0.71 #> 5 0.06487616 MAR.10 Unstandardized fit.sem n: 150 α: 0.71 #> 6 0.08060491 MAR.10 Unstandardized fit.sem n: 100 α: 0.71 #> beta_label taudot_label theta_label #> 1 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 2 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 3 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 4 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 5 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 6 β: 0.71 τ̇: 0.14 0.51(0.71,0.71)#> 'data.frame': 1593 obs. of 69 variables: #> $ taskid : num 1 2 3 4 5 6 7 8 9 10 ... #> $ n : num 1000 500 250 200 150 100 75 50 20 1000 ... #> $ reps : num 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 ... #> $ taudot : num 0.141 0.141 0.141 0.141 0.141 ... #> $ beta : num 0.714 0.714 0.714 0.714 0.714 ... #> $ alpha : num 0.714 0.714 0.714 0.714 0.714 ... #> $ alphabeta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ sigma2x : num 225 225 225 225 225 225 225 225 225 225 ... #> $ sigma2epsilonm : num 110 110 110 110 110 ... #> $ sigma2epsilony : num 73.3 73.3 73.3 73.3 73.3 ... #> $ mux : num 100 100 100 100 100 100 100 100 100 100 ... #> $ deltam : num 28.6 28.6 28.6 28.6 28.6 ... #> $ deltay : num 14.5 14.5 14.5 14.5 14.5 ... #> $ taudothat : num 0.141 0.141 0.14 0.141 0.14 ... #> $ betahat : num 0.714 0.715 0.715 0.714 0.716 ... #> $ alphahat : num 0.714 0.714 0.715 0.714 0.713 ... #> $ sigma2hatepsilonyhat : num 73 72.8 72.4 72.3 71.9 ... #> $ sigma2hatepsilonmhat : num 110 110 109 109 109 ... #> $ deltayhat : num 14.5 14.4 14.5 14.5 14.4 ... #> $ deltamhat : num 28.6 28.6 28.5 28.6 28.7 ... #> $ muxhat : num 100 100 100 100 100 ... #> $ sigma2xhat : num 225 224 224 224 224 ... #> $ alphahatbetahat : num 0.51 0.511 0.511 0.509 0.511 ... #> $ sehattaudothat : num 0.027 0.0383 0.0542 0.0606 0.07 ... #> $ sehatbetahat : num 0.0268 0.0379 0.0536 0.0601 0.0694 ... #> $ sehatalphahat : num 0.0227 0.0321 0.0455 0.0508 0.0587 ... #> $ sehatsigma2hatepsilonyhat: num 3.37 4.75 6.69 7.47 8.6 ... #> $ sehatsigma2hatepsilonmhat: num 5.08 7.18 10.12 11.29 13.04 ... #> $ sehatdeltayhat : num 2.04 2.89 4.09 4.58 5.28 ... #> $ sehatdeltamhat : num 2.29 3.24 4.58 5.12 5.92 ... #> $ sehatmuxhat : num 0.478 0.676 0.955 1.068 1.235 ... #> $ sehatsigma2xhat : num 10.2 14.5 20.4 22.8 26.4 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ taudothat_var : num 0.000749 0.001449 0.003021 0.003808 0.004944 ... #> $ betahat_var : num 0.000747 0.001451 0.002977 0.003631 0.004874 ... #> $ alphahat_var : num 0.000508 0.001027 0.002078 0.002595 0.003463 ... #> $ alphahatbetahat_var : num 0.000636 0.001272 0.002609 0.003225 0.004209 ... #> $ taudothat_sd : num 0.0274 0.0381 0.055 0.0617 0.0703 ... #> $ betahat_sd : num 0.0273 0.0381 0.0546 0.0603 0.0698 ... #> $ alphahat_sd : num 0.0225 0.0321 0.0456 0.0509 0.0588 ... #> $ alphahatbetahat_sd : num 0.0252 0.0357 0.0511 0.0568 0.0649 ... #> $ taudothat_skew : num -0.0687 -0.0103 -0.0647 0.0064 -0.0203 ... #> $ betahat_skew : num 0.00897 -0.01848 0.04243 -0.03038 0.03768 ... #> $ alphahat_skew : num -0.00165 0.02186 -0.03891 0.02357 0.04157 ... #> $ alphahatbetahat_skew : num 0.0903 0.1019 0.176 0.1265 0.1734 ... #> $ taudothat_kurt : num -0.02643 -0.04489 -0.02162 0.0853 0.00728 ... #> $ betahat_kurt : num 0.0147 0.0509 -0.0989 -0.0932 0.0251 ... #> $ alphahat_kurt : num -0.0173 -0.0121 0.0228 -0.025 0.2069 ... #> $ alphahatbetahat_kurt : num -0.048222 0.139216 -0.013612 0.000926 -0.055602 ... #> $ taudothat_bias : num 4.63e-06 -4.71e-04 -1.30e-03 4.39e-07 -1.81e-03 ... #> $ betahat_bias : num -0.000307 0.000735 0.000615 -0.000382 0.001743 ... #> $ alphahat_bias : num 0.0001 0.000268 0.000734 -0.000266 -0.000677 ... #> $ alphahatbetahat_bias : num -0.000152 0.000722 0.00098 -0.000413 0.000708 ... #> $ taudothat_mse : num 0.000749 0.001449 0.003022 0.003807 0.004946 ... #> $ betahat_mse : num 0.000747 0.001451 0.002977 0.003631 0.004876 ... #> $ alphahat_mse : num 0.000508 0.001027 0.002079 0.002595 0.003462 ... #> $ alphahatbetahat_mse : num 0.000636 0.001273 0.00261 0.003224 0.004209 ... #> $ taudothat_rmse : num 0.0274 0.0381 0.055 0.0617 0.0703 ... #> $ betahat_rmse : num 0.0273 0.0381 0.0546 0.0603 0.0698 ... #> $ alphahat_rmse : num 0.0225 0.032 0.0456 0.0509 0.0588 ... #> $ alphahatbetahat_rmse : num 0.0252 0.0357 0.0511 0.0568 0.0649 ... #> $ missing : chr "MAR.10" "MAR.10" "MAR.10" "MAR.10" ... #> $ std : chr "Unstandardized" "Unstandardized" "Unstandardized" "Unstandardized" ... #> $ Method : chr "fit.sem" "fit.sem" "fit.sem" "fit.sem" ... #> $ n_label : Factor w/ 9 levels "n: 20","n: 50",..: 9 8 7 6 5 4 3 2 1 9 ... #> $ alpha_label : Factor w/ 4 levels "α: 0.00","α: 0.38",..: 4 4 4 4 4 4 4 4 4 4 ... #> $ beta_label : Factor w/ 4 levels "β: 0.00","β: 0.38",..: 4 4 4 4 4 4 4 4 4 4 ... #> $ taudot_label : Factor w/ 4 levels "τ̇: 0.00","τ̇: 0.14",..: 2 2 2 2 2 2 2 2 2 1 ... #> $ theta_label : chr "0.51(0.71,0.71)" "0.51(0.71,0.71)" "0.51(0.71,0.71)" "0.51(0.71,0.71)" ...