R/results_mvn_std_mc.mvn.tb_ci.R
results_mvn_std_mc.mvn.tb_ci.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Standardized - Complete Data - Monte Carlo Method Confidence Intervals with Ordinary Least Squares Parameter Estimates and Text Book Standard Errors
results_mvn_std_mc.mvn.tb_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.wishart_ci,
results_mvn_std_nb_ci,
results_mvn_std_pb.mvn_ci
data(results_mvn_std_mc.mvn.tb_ci, package = "jeksterslabRmedsimple") head(results_mvn_std_mc.mvn.tb_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 0.02431591 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.5097172 0.03445055 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.5096705 0.04895972 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.5088352 0.05484020 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.5091470 0.06352323 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.5075375 0.07822482 #> reps ci_0.05 ci_0.5 ci_2.5 ci_97.5 ci_99.5 ci_99.95 #> 1 20000 0.4327711 0.4487478 0.4629157 0.5582022 0.5739348 0.5921700 #> 2 20000 0.4023668 0.4242207 0.4438261 0.5788073 0.6015502 0.6280971 #> 3 20000 0.3602739 0.3900214 0.4169744 0.6087593 0.6420116 0.6809235 #> 4 20000 0.3428435 0.3756049 0.4054337 0.6202122 0.6578149 0.7020165 #> 5 20000 0.3192109 0.3561926 0.3900673 0.6388075 0.6830039 0.7351267 #> 6 20000 0.2781580 0.3219507 0.3623546 0.6685742 0.7244878 0.7911298 #> zero_hit_99.9 zero_hit_99 zero_hit_95 len_99.9 len_99 len_95 #> 1 0 0 0 0.1593989 0.1251870 0.09528651 #> 2 0 0 0 0.2257303 0.1773294 0.13498123 #> 3 0 0 0 0.3206496 0.2519903 0.19178488 #> 4 0 0 0 0.3591730 0.2822100 0.21477844 #> 5 0 0 0 0.4159159 0.3268113 0.24874018 #> 6 0 0 0 0.5129718 0.4025371 0.30621959 #> shape_99.9 shape_99 shape_95 theta_hit_99.9 theta_hit_99 theta_hit_95 #> 1 1.071310 1.052270 1.034537 0.9998 0.9978 0.9826 #> 2 1.103506 1.074355 1.048670 0.9998 0.9972 0.9844 #> 3 1.147203 1.106434 1.069178 1.0000 0.9982 0.9798 #> 4 1.164872 1.118683 1.077397 0.9998 0.9982 0.9846 #> 5 1.191037 1.137280 1.089214 1.0000 0.9992 0.9826 #> 6 1.238473 1.170077 1.109810 0.9998 0.9976 0.9810 #> theta_miss_99.9 theta_miss_99 theta_miss_95 theta power_99.9 power_99 #> 1 2e-04 0.0022 0.0174 0.509902 1 1 #> 2 2e-04 0.0028 0.0156 0.509902 1 1 #> 3 0e+00 0.0018 0.0202 0.509902 1 1 #> 4 2e-04 0.0018 0.0154 0.509902 1 1 #> 5 0e+00 0.0008 0.0174 0.509902 1 1 #> 6 2e-04 0.0024 0.0190 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 0 0 0 0 #> 2 0.065 0 0 0 0 0 #> 3 0.065 0 0 0 0 0 #> 4 0.065 0 0 0 0 0 #> 5 0.065 0 0 0 0 0 #> 6 0.065 0 0 0 0 0 #> moderate_95 strict_99.9 strict_99 strict_95 serlin_95 missing std #> 1 0 0 0 0 0 Complete Standardized #> 2 0 0 0 0 0 Complete Standardized #> 3 0 0 0 0 0 Complete Standardized #> 4 0 0 0 0 0 Complete Standardized #> 5 0 0 0 0 0 Complete Standardized #> 6 0 0 0 0 0 Complete Standardized #> Method n_label alpha_label beta_label taudot_label theta_label #> 1 MC.TB n: 1000 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 2 MC.TB n: 500 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 3 MC.TB n: 250 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 4 MC.TB n: 200 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 5 MC.TB n: 150 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 6 MC.TB 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 0.0243 0.0345 0.049 0.0548 0.0635 ... #> $ reps : num 20000 20000 20000 20000 20000 20000 20000 20000 20000 20000 ... #> $ ci_0.05 : num 0.433 0.402 0.36 0.343 0.319 ... #> $ ci_0.5 : num 0.449 0.424 0.39 0.376 0.356 ... #> $ ci_2.5 : num 0.463 0.444 0.417 0.405 0.39 ... #> $ ci_97.5 : num 0.558 0.579 0.609 0.62 0.639 ... #> $ ci_99.5 : num 0.574 0.602 0.642 0.658 0.683 ... #> $ ci_99.95 : num 0.592 0.628 0.681 0.702 0.735 ... #> $ 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 ... #> $ len_99.9 : num 0.159 0.226 0.321 0.359 0.416 ... #> $ len_99 : num 0.125 0.177 0.252 0.282 0.327 ... #> $ len_95 : num 0.0953 0.135 0.1918 0.2148 0.2487 ... #> $ shape_99.9 : num 1.07 1.1 1.15 1.16 1.19 ... #> $ shape_99 : num 1.05 1.07 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 1 1 1 1 ... #> $ theta_hit_99 : num 0.998 0.997 0.998 0.998 0.999 ... #> $ theta_hit_95 : num 0.983 0.984 0.98 0.985 0.983 ... #> $ theta_miss_99.9 : num 2e-04 2e-04 0e+00 2e-04 0e+00 2e-04 4e-04 2e-04 4e-04 0e+00 ... #> $ theta_miss_99 : num 0.0022 0.0028 0.0018 0.0018 0.0008 0.0024 0.003 0.0024 0.0038 0.0016 ... #> $ theta_miss_95 : num 0.0174 0.0156 0.0202 0.0154 0.0174 0.019 0.0192 0.0236 0.0252 0.0232 ... #> $ 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 0 0 0 0 0 0 0 0 0 ... #> $ liberal_99 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ liberal_95 : num 0 0 0 0 0 0 0 0 1 0 ... #> $ moderate_99.9 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ moderate_99 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ moderate_95 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ strict_99.9 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ strict_99 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ strict_95 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ serlin_95 : num 0 0 0 0 0 0 0 0 0 0 ... #> $ missing : chr "Complete" "Complete" "Complete" "Complete" ... #> $ std : chr "Standardized" "Standardized" "Standardized" "Standardized" ... #> $ Method : chr "MC.TB" "MC.TB" "MC.TB" "MC.TB" ... #> $ 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)" ...