R/results_mvn_mar_mc.mvn_ci.R
results_mvn_mar_mc.mvn_ci.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Data Missing at Random - Monte Carlo Method Confidence Intervals Structural Equation Modeling with Full Information Maximum Likelihood Parameter Estimates and Standard Errors
results_mvn_mar_mc.mvn_ci
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 the estimate of the indirect effect \(\left( \hat{\alpha} \hat{\beta} \right)\).
Mean of the estimate of standard error of the indirect effect \(\left( \hat{\alpha} \hat{\beta} \right)\).
Monte Carlo method of bootstrap replications.
Mean of the lower limit confidence interval for the 99.9% confidence interval.
Mean of the lower limit confidence interval for the 99% confidence interval.
Mean of the lower limit confidence interval for the 95% confidence interval.
Mean of the upper limit confidence interval for the 95% confidence interval.
Mean of the upper limit confidence interval for the 99% confidence interval.
Mean of the upper limit confidence interval for the 99.9% confidence interval.
Mean zero hit for the 99.9% confidence interval.
Mean zero hit for the 99% confidence interval.
Mean zero hit for the 95% confidence interval.
Mean confidence interval length for the 99.9% confidence interval.
Mean confidence interval length for the 99% confidence interval.
Mean confidence interval length for the 95% confidence interval.
Mean confidence interval shape for the 99.9% confidence interval.
Mean confidence interval shape for the 99% confidence interval.
Mean confidence interval shape for the 95% confidence interval.
Mean theta hit for the 99.9% confidence interval.
Mean theta hit for the 99% confidence interval.
Mean theta hit for the 95% confidence interval.
Mean theta miss for the 99.9% confidence interval.
Mean theta miss for the 99% confidence interval.
Mean theta miss for the 95% confidence interval.
Population parameter \(\alpha \beta\).
Mean power for the 99.9% confidence interval.
Mean power for the 99% confidence interval.
Mean power for the 95% confidence interval.
Lower limit of the liberal criteria for the 99.9% confidence interval.
Upper limit of the liberal criteria for the 99.9% confidence interval.
Lower limit of the moderate criteria for the 99.9% confidence interval.
Upper limit of the moderate criteria for the 99.9% confidence interval.
Lower limit of the strict criteria for the 99.9% confidence interval.
Upper limit of the strict criteria for the 99.9% confidence interval.
Lower limit of the liberal criteria for the 99% confidence interval.
Upper limit of the liberal criteria for the 99% confidence interval.
Lower limit of the moderate criteria for the 99% confidence interval.
Upper limit of the moderate criteria for the 99% confidence interval.
Lower limit of the strict criteria for the 99% confidence interval.
Upper limit of the strict criteria for the 99% confidence interval.
Lower limit of the liberal criteria for the 95% confidence interval.
Upper limit of the liberal criteria for the 95% confidence interval.
Lower limit of the moderate criteria for the 95% confidence interval.
Upper limit of the moderate criteria for the 95% confidence interval.
Lower limit of the strict criteria for the 95% confidence interval.
Upper limit of the strict criteria for the 95% confidence interval.
Lower limit of the Serlin criteria for the 95% confidence interval.
Upper limit of the Serlin criteria for the 95% confidence interval.
Logical. 1 if miss rate is inside the liberal robustness criteria for 99.9% confidence interval.
Logical. 1 if miss rate is inside the liberal robustness criteria for 99% confidence interval.
Logical. 1 if miss rate is inside the liberal robustness criteria for 95% confidence interval.
Logical. 1 if miss rate is inside the moderate robustness criteria for 99.9% confidence interval.
Logical. 1 if miss rate is inside the moderate robustness criteria for 99% confidence interval.
Logical. 1 if miss rate is inside the moderate robustness criteria for 95% confidence interval.
Logical. 1 if miss rate is inside the strict robustness criteria for 99.9% confidence interval.
Logical. 1 if miss rate is inside the strict robustness criteria for 99% confidence interval.
Logical. 1 if miss rate is inside the strict robustness criteria for 95% confidence interval.
Logical. 1 if miss rate is inside the Serlin robustness criteria for 95% confidence interval.
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_fit.sem,
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 simreps 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 est se #> 1 110.2721 73.3221 100 28.59258 14.45045 0.5097503 0.02506932 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.5106244 0.03554534 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.5108821 0.05046127 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.5094888 0.05642850 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.5106098 0.06536506 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.5097006 0.08038622 #> reps ci_0.05 ci_0.5 ci_2.5 ci_97.5 ci_99.5 ci_99.95 #> 1 20000 0.4305515 0.4468879 0.4614712 0.5597103 0.5759558 0.5947831 #> 2 20000 0.4000369 0.4225016 0.4426886 0.5819517 0.6054367 0.6328221 #> 3 20000 0.3572733 0.3877427 0.4154322 0.6131034 0.6474121 0.6877889 #> 4 20000 0.3389680 0.3725748 0.4031764 0.6241736 0.6629547 0.7087038 #> 5 20000 0.3154362 0.3534721 0.3882049 0.6441805 0.6898452 0.7438520 #> 6 20000 0.2744456 0.3192721 0.3606528 0.6753097 0.7328421 0.8014119 #> zero_hit_99.9 zero_hit_99 zero_hit_95 len_99.9 len_99 len_95 #> 1 0 0 0 0.1642316 0.1290679 0.09823906 #> 2 0 0 0 0.2327852 0.1829351 0.13926305 #> 3 0 0 0 0.3305155 0.2596694 0.19767111 #> 4 0 0 0 0.3697358 0.2903799 0.22099718 #> 5 0 0 0 0.4284158 0.3363732 0.25597560 #> 6 0 0 0 0.5269663 0.4135700 0.31465691 #> shape_99.9 shape_99 shape_95 theta_hit_99.9 theta_hit_99 theta_hit_95 #> 1 1.074322 1.053359 1.034923 0.9996 0.9900 0.9498 #> 2 1.105801 1.076169 1.050062 0.9992 0.9886 0.9460 #> 3 1.152635 1.109111 1.071164 0.9990 0.9902 0.9498 #> 4 1.169439 1.121360 1.079045 0.9990 0.9900 0.9438 #> 5 1.196459 1.141286 1.091628 0.9996 0.9914 0.9514 #> 6 1.242363 1.173002 1.111798 0.9988 0.9898 0.9454 #> theta_miss_99.9 theta_miss_99 theta_miss_95 theta power_99.9 power_99 #> 1 0.0004 0.0100 0.0502 0.509902 1 1 #> 2 0.0008 0.0114 0.0540 0.509902 1 1 #> 3 0.0010 0.0098 0.0502 0.509902 1 1 #> 4 0.0010 0.0100 0.0562 0.509902 1 1 #> 5 0.0004 0.0086 0.0486 0.509902 1 1 #> 6 0.0012 0.0102 0.0546 0.509902 1 1 #> power_95 liberal_ll_99.9 liberal_ul_99.9 moderate_ll_99.9 moderate_ul_99.9 #> 1 1 5e-04 0.0015 8e-04 0.0012 #> 2 1 5e-04 0.0015 8e-04 0.0012 #> 3 1 5e-04 0.0015 8e-04 0.0012 #> 4 1 5e-04 0.0015 8e-04 0.0012 #> 5 1 5e-04 0.0015 8e-04 0.0012 #> 6 1 5e-04 0.0015 8e-04 0.0012 #> strict_ll_99.9 strict_ul_99.9 liberal_ll_99 liberal_ul_99 moderate_ll_99 #> 1 9e-04 0.0011 0.005 0.015 0.008 #> 2 9e-04 0.0011 0.005 0.015 0.008 #> 3 9e-04 0.0011 0.005 0.015 0.008 #> 4 9e-04 0.0011 0.005 0.015 0.008 #> 5 9e-04 0.0011 0.005 0.015 0.008 #> 6 9e-04 0.0011 0.005 0.015 0.008 #> moderate_ul_99 strict_ll_99 strict_ul_99 liberal_ll_95 liberal_ul_95 #> 1 0.012 0.009 0.011 0.025 0.075 #> 2 0.012 0.009 0.011 0.025 0.075 #> 3 0.012 0.009 0.011 0.025 0.075 #> 4 0.012 0.009 0.011 0.025 0.075 #> 5 0.012 0.009 0.011 0.025 0.075 #> 6 0.012 0.009 0.011 0.025 0.075 #> moderate_ll_95 moderate_ul_95 strict_ll_95 strict_ul_95 serlin_ll_95 #> 1 0.04 0.06 0.045 0.055 0.035 #> 2 0.04 0.06 0.045 0.055 0.035 #> 3 0.04 0.06 0.045 0.055 0.035 #> 4 0.04 0.06 0.045 0.055 0.035 #> 5 0.04 0.06 0.045 0.055 0.035 #> 6 0.04 0.06 0.045 0.055 0.035 #> serlin_ul_95 liberal_99.9 liberal_99 liberal_95 moderate_99.9 moderate_99 #> 1 0.065 0 1 1 0 1 #> 2 0.065 1 1 1 0 1 #> 3 0.065 1 1 1 1 1 #> 4 0.065 1 1 1 1 1 #> 5 0.065 0 1 1 0 1 #> 6 0.065 1 1 1 1 1 #> moderate_95 strict_99.9 strict_99 strict_95 serlin_95 missing std #> 1 1 0 1 1 1 MAR.10 Unstandardized #> 2 1 0 0 1 1 MAR.10 Unstandardized #> 3 1 1 1 1 1 MAR.10 Unstandardized #> 4 1 1 1 0 1 MAR.10 Unstandardized #> 5 1 0 0 1 1 MAR.10 Unstandardized #> 6 1 0 1 1 1 MAR.10 Unstandardized #> Method n_label alpha_label beta_label taudot_label theta_label #> 1 MC.MAR.10 n: 1000 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 2 MC.MAR.10 n: 500 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 3 MC.MAR.10 n: 250 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 4 MC.MAR.10 n: 200 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 5 MC.MAR.10 n: 150 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 6 MC.MAR.10 n: 100 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71)#> 'data.frame': 1593 obs. of 79 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 ... #> $ simreps : 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 ... #> $ est : num 0.51 0.511 0.511 0.509 0.511 ... #> $ se : num 0.0251 0.0355 0.0505 0.0564 0.0654 ... #> $ reps : num 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 ... #> $ ci_0.05 : num 0.431 0.4 0.357 0.339 0.315 ... #> $ ci_0.5 : num 0.447 0.423 0.388 0.373 0.353 ... #> $ ci_2.5 : num 0.461 0.443 0.415 0.403 0.388 ... #> $ ci_97.5 : num 0.56 0.582 0.613 0.624 0.644 ... #> $ ci_99.5 : num 0.576 0.605 0.647 0.663 0.69 ... #> $ ci_99.95 : num 0.595 0.633 0.688 0.709 0.744 ... #> $ zero_hit_99.9 : num 0 0 0 0 0 ... #> $ zero_hit_99 : num 0 0 0 0 0 ... #> $ zero_hit_95 : num 0 0 0 0 0 0 0 0.0004 0.113 0 ... #> $ len_99.9 : num 0.164 0.233 0.331 0.37 0.428 ... #> $ len_99 : num 0.129 0.183 0.26 0.29 0.336 ... #> $ len_95 : num 0.0982 0.1393 0.1977 0.221 0.256 ... #> $ shape_99.9 : num 1.07 1.11 1.15 1.17 1.2 ... #> $ shape_99 : num 1.05 1.08 1.11 1.12 1.14 ... #> $ shape_95 : num 1.03 1.05 1.07 1.08 1.09 ... #> $ theta_hit_99.9 : num 1 0.999 0.999 0.999 1 ... #> $ theta_hit_99 : num 0.99 0.989 0.99 0.99 0.991 ... #> $ theta_hit_95 : num 0.95 0.946 0.95 0.944 0.951 ... #> $ theta_miss_99.9 : num 0.0004 0.0008 0.001 0.001 0.0004 0.0012 0.0014 0.0028 0.0022 0.0012 ... #> $ theta_miss_99 : num 0.01 0.0114 0.0098 0.01 0.0086 0.0102 0.0144 0.013 0.0208 0.0096 ... #> $ theta_miss_95 : num 0.0502 0.054 0.0502 0.0562 0.0486 0.0546 0.0582 0.0552 0.0734 0.0478 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ power_99.9 : num 1 1 1 1 1 ... #> $ power_99 : num 1 1 1 1 1 ... #> $ power_95 : num 1 1 1 1 1 ... #> $ liberal_ll_99.9 : num 5e-04 5e-04 5e-04 5e-04 5e-04 5e-04 5e-04 5e-04 5e-04 5e-04 ... #> $ liberal_ul_99.9 : num 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 ... #> $ moderate_ll_99.9: num 8e-04 8e-04 8e-04 8e-04 8e-04 8e-04 8e-04 8e-04 8e-04 8e-04 ... #> $ moderate_ul_99.9: num 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 0.0012 ... #> $ strict_ll_99.9 : num 9e-04 9e-04 9e-04 9e-04 9e-04 9e-04 9e-04 9e-04 9e-04 9e-04 ... #> $ strict_ul_99.9 : num 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 ... #> $ liberal_ll_99 : num 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 ... #> $ liberal_ul_99 : num 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 ... #> $ moderate_ll_99 : num 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 ... #> $ moderate_ul_99 : num 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 ... #> $ strict_ll_99 : num 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 ... #> $ strict_ul_99 : num 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 ... #> $ liberal_ll_95 : num 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 ... #> $ liberal_ul_95 : num 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 ... #> $ moderate_ll_95 : num 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 ... #> $ moderate_ul_95 : num 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 ... #> $ strict_ll_95 : num 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 ... #> $ strict_ul_95 : num 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 ... #> $ serlin_ll_95 : num 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 ... #> $ serlin_ul_95 : num 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.065 ... #> $ liberal_99.9 : num 0 1 1 1 0 1 1 0 0 1 ... #> $ liberal_99 : num 1 1 1 1 1 1 1 1 0 1 ... #> $ liberal_95 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ moderate_99.9 : num 0 0 1 1 0 1 0 0 0 1 ... #> $ moderate_99 : num 1 1 1 1 1 1 0 0 0 1 ... #> $ moderate_95 : num 1 1 1 1 1 1 1 1 0 1 ... #> $ strict_99.9 : num 0 0 1 1 0 0 0 0 0 0 ... #> $ strict_99 : num 1 0 1 1 0 1 0 0 0 1 ... #> $ strict_95 : num 1 1 1 0 1 1 0 0 0 1 ... #> $ serlin_95 : num 1 1 1 1 1 1 1 1 0 1 ... #> $ missing : chr "MAR.10" "MAR.10" "MAR.10" "MAR.10" ... #> $ std : chr "Unstandardized" "Unstandardized" "Unstandardized" "Unstandardized" ... #> $ Method : chr "MC.MAR.10" "MC.MAR.10" "MC.MAR.10" "MC.MAR.10" ... #> $ 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)" ...