R/results_mvn_std_mc.wishart_ci.R
results_mvn_std_mc.wishart_ci.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Standardized - Complete Data - Monte Carlo Method Confidence Intervals from Estimates Derived from Simulated Covariances Using the Wishart Distribution
results_mvn_std_mc.wishart_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 functions:
results_mvn_std_fit.sem,
results_mvn_std_mc.mvn.delta_ci,
results_mvn_std_mc.mvn.sem_ci,
results_mvn_std_mc.mvn.tb_ci,
results_mvn_std_nb_ci,
results_mvn_std_pb.mvn_ci
data(results_mvn_std_mc.wishart_ci, package = "jeksterslabRmedsimple") head(results_mvn_std_mc.wishart_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 0.5097527 0.02015538 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.5097172 0.02858985 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.5096705 0.04077573 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.5088352 0.04576523 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.5091470 0.05313231 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.5075375 0.06575368 #> reps ci_0.05 ci_0.5 ci_2.5 ci_97.5 ci_99.5 ci_99.95 #> 1 20000 0.4448127 0.4584175 0.4704474 0.5494504 0.5622355 0.5769892 #> 2 20000 0.4179896 0.4371421 0.4540604 0.5661241 0.5844819 0.6058012 #> 3 20000 0.3795368 0.4065660 0.4304494 0.5903192 0.6169877 0.6481469 #> 4 20000 0.3631569 0.3932965 0.4199636 0.5994380 0.6296015 0.6650509 #> 5 20000 0.3401789 0.3752023 0.4060860 0.6144693 0.6499171 0.6916290 #> 6 20000 0.2983888 0.3419317 0.3800736 0.6380992 0.6828507 0.7360715 #> zero_hit_99.9 zero_hit_99 zero_hit_95 len_99.9 len_99 len_95 #> 1 0 0 0 0.1321764 0.1038180 0.07900298 #> 2 0 0 0 0.1878116 0.1473398 0.11206370 #> 3 0 0 0 0.2686101 0.2104217 0.15986983 #> 4 0 0 0 0.3018941 0.2363050 0.17947437 #> 5 0 0 0 0.3514501 0.2747148 0.20838328 #> 6 0 0 0 0.4376827 0.3409190 0.25802561 #> shape_99.9 shape_99 shape_95 theta_hit_99.9 theta_hit_99 theta_hit_95 #> 1 1.036064 1.022513 1.010064 0.9990 0.9894 0.9478 #> 2 1.048184 1.030333 1.013543 0.9990 0.9916 0.9504 #> 3 1.064820 1.041006 1.018062 0.9990 0.9890 0.9494 #> 4 1.073070 1.045394 1.019509 0.9992 0.9922 0.9476 #> 5 1.080749 1.051107 1.021950 0.9998 0.9922 0.9528 #> 6 1.093866 1.058896 1.024320 0.9988 0.9886 0.9542 #> theta_miss_99.9 theta_miss_99 theta_miss_95 theta power_99.9 power_99 #> 1 0.0010 0.0106 0.0522 0.509902 1 1 #> 2 0.0010 0.0084 0.0496 0.509902 1 1 #> 3 0.0010 0.0110 0.0506 0.509902 1 1 #> 4 0.0008 0.0078 0.0524 0.509902 1 1 #> 5 0.0002 0.0078 0.0472 0.509902 1 1 #> 6 0.0012 0.0114 0.0458 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 1 1 1 1 1 #> 2 0.065 1 1 1 1 1 #> 3 0.065 1 1 1 1 1 #> 4 0.065 1 1 1 0 0 #> 5 0.065 0 1 1 0 0 #> 6 0.065 1 1 1 1 1 #> moderate_95 strict_99.9 strict_99 strict_95 serlin_95 missing std #> 1 1 1 1 1 1 Complete Standardized #> 2 1 1 0 1 1 Complete Standardized #> 3 1 1 0 1 1 Complete Standardized #> 4 1 0 0 1 1 Complete Standardized #> 5 1 0 0 1 1 Complete Standardized #> 6 1 0 0 1 1 Complete Standardized #> Method n_label alpha_label beta_label taudot_label theta_label #> 1 MC.WISHART n: 1000 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 2 MC.WISHART n: 500 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 3 MC.WISHART n: 250 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 4 MC.WISHART n: 200 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 5 MC.WISHART n: 150 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 6 MC.WISHART n: 100 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71)#> 'data.frame': 531 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 0.51 0.51 0.509 0.509 ... #> $ se : num 0.0202 0.0286 0.0408 0.0458 0.0531 ... #> $ reps : num 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 ... #> $ ci_0.05 : num 0.445 0.418 0.38 0.363 0.34 ... #> $ ci_0.5 : num 0.458 0.437 0.407 0.393 0.375 ... #> $ ci_2.5 : num 0.47 0.454 0.43 0.42 0.406 ... #> $ ci_97.5 : num 0.549 0.566 0.59 0.599 0.614 ... #> $ ci_99.5 : num 0.562 0.584 0.617 0.63 0.65 ... #> $ ci_99.95 : num 0.577 0.606 0.648 0.665 0.692 ... #> $ zero_hit_99.9 : num 0 0 0 0 0 0 0.0006 0.0216 0.713 0 ... #> $ zero_hit_99 : num 0 0 0 0 0 ... #> $ zero_hit_95 : num 0 0 0 0 0 0 0 0.0004 0.12 0 ... #> $ len_99.9 : num 0.132 0.188 0.269 0.302 0.351 ... #> $ len_99 : num 0.104 0.147 0.21 0.236 0.275 ... #> $ len_95 : num 0.079 0.112 0.16 0.179 0.208 ... #> $ shape_99.9 : num 1.04 1.05 1.06 1.07 1.08 ... #> $ shape_99 : num 1.02 1.03 1.04 1.05 1.05 ... #> $ shape_95 : num 1.01 1.01 1.02 1.02 1.02 ... #> $ theta_hit_99.9 : num 0.999 0.999 0.999 0.999 1 ... #> $ theta_hit_99 : num 0.989 0.992 0.989 0.992 0.992 ... #> $ theta_hit_95 : num 0.948 0.95 0.949 0.948 0.953 ... #> $ theta_miss_99.9 : num 0.001 0.001 0.001 0.0008 0.0002 0.0012 0.0018 0.001 0 0.0006 ... #> $ theta_miss_99 : num 0.0106 0.0084 0.011 0.0078 0.0078 0.0114 0.0092 0.008 0.0076 0.0106 ... #> $ theta_miss_95 : num 0.0522 0.0496 0.0506 0.0524 0.0472 0.0458 0.0488 0.0514 0.0464 0.0536 ... #> $ 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 1 1 1 1 0 1 0 1 0 1 ... #> $ liberal_99 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ liberal_95 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ moderate_99.9 : num 1 1 1 0 0 1 0 1 0 0 ... #> $ moderate_99 : num 1 1 1 0 0 1 1 0 0 1 ... #> $ moderate_95 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ strict_99.9 : num 1 1 1 0 0 0 0 1 0 0 ... #> $ strict_99 : num 1 0 0 0 0 0 1 0 0 1 ... #> $ strict_95 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ serlin_95 : num 1 1 1 1 1 1 1 1 1 1 ... #> $ missing : chr "Complete" "Complete" "Complete" "Complete" ... #> $ std : chr "Standardized" "Standardized" "Standardized" "Standardized" ... #> $ Method : chr "MC.WISHART" "MC.WISHART" "MC.WISHART" "MC.WISHART" ... #> $ 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)" ...