R/results_mvn_std_fit.sem.R
results_mvn_std_fit.sem.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Standardized - Complete Data - Fit Structural Equation Modeling
results_mvn_std_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 factor loading xlatent ~ x \( \left( \lambda_x \right)\). Numerically equivalent to the standard deviation of x.
Mean of estimated factor loading mlatent ~ m \( \left( \lambda_m \right)\). Numerically equivalent to the standard deviation of m.
Mean of estimated factor loading ylatent ~ y \( \left( \lambda_y \right)\). Numerically equivalent to the standard deviation of y.
Mean of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Mean of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Mean of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Mean of estimated error variance of y \(\left( \hat{\sigma}_{\varepsilon_{y_{\mathrm{latent}}}}^{2} \right)\).
Mean of estimated error variance of m \(\left( \hat{\sigma}_{\varepsilon_{m_{\mathrm{latent}}}}^{2} \right)\).
Mean of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Mean of estimated standard error of estimated factor loading xlatent ~ x \( \left( \lambda_x \right)\).
Mean of estimated standard error of estimated factor loading mlatent ~ m \( \left( \lambda_m \right)\).
Mean of estimated standard error of estimated factor loading ylatent ~ y \( \left( \lambda_y \right)\).
Mean of estimated standard error of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Mean of estimated standard error of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Mean of estimated standard error of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Mean of estimated standard error of estimated error variance of y \(\left( \hat{\sigma}_{\varepsilon_{y_{\mathrm{latent}}}}^{2} \right)\).
Mean of estimated standard error of estimated error variance of m \(\left( \hat{\sigma}_{\varepsilon_{m_{\mathrm{latent}}}}^{2} \right)\).
Population parameter \(\alpha^{\prime} \beta^{\prime}\).
Variance of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Variance of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Variance of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Variance of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Standard deviation of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Standard deviation of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Standard deviation of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Standard deviation of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Skewness of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Skewness of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Skewness of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Skewness of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Excess kurtosis of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Excess kurtosis of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Excess kurtosis of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Excess kurtosis of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Bias of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Bias of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Bias of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Bias of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Mean square error of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Mean square error of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Mean square error of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Mean square error of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Root mean square error of estimated standardized slope of path from x to y \(\left( \hat{\dot{\tau}}^{\prime} \right)\).
Root mean square error of estimated standardized slope of path from m to y \(\left( \hat{\beta}^{\prime} \right)\).
Root mean square error of estimated standardized slope of path from x to m \(\left( \hat{\alpha}^{\prime} \right)\).
Root mean square error of estimated standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
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 standardized simple mediation model is given by the following measurement model and regression model.
Measurement model $$x_{\mathrm{latent}} = \lambda_x x$$ $$m_{\mathrm{latent}} = \lambda_m m$$ $$y_{\mathrm{latent}} = \lambda_y y$$
Regression model $$y_{\mathrm{latent}} = \dot{\tau}^{\prime} x_{\mathrm{latent}} + \beta^{\prime} m_{\mathrm{latent}} + \varepsilon_{y_{\mathrm{latent}}}$$ $$m_{\mathrm{latent}} = \alpha^{\prime} x_{\mathrm{latent}} + \varepsilon_{m_{\mathrm{latent}}}$$
The measurement errors in the measurement model are fixed to 0
The variance of \(x_{\mathrm{latent}}\) \(\left( \sigma_{x_{\mathrm{latent}}}^{2} \right)\) is fixed to 1
The error variance \(\varepsilon_{y_{\mathrm{latent}}}\) \(\left( \sigma_{\varepsilon_{y_{\mathrm{latent}}}}^{2} \right)\) is constrained to \(1 - \dot{\tau}^{\prime 2} - \beta^{\prime 2} - 2 \dot{\tau}^{\prime} \beta^{\prime} \alpha^{\prime}\)
The error variance \(\varepsilon_{m_{\mathrm{latent}}}\) \(\left( \sigma_{\varepsilon_{m_{\mathrm{latent}}}}^{2} \right)\) is constrained to \(1 - \alpha^{\prime 2}\)
Other results functions:
results_mvn_std_mc.mvn.delta_ci,
results_mvn_std_mc.mvn.sem_ci,
results_mvn_std_mc.mvn.tb_ci,
results_mvn_std_mc.wishart_ci,
results_mvn_std_nb_ci,
results_mvn_std_pb.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 lambdaxhat lambdamhat #> 1 110.2721 73.3221 100 28.59258 14.45045 14.99682 14.99604 #> 2 110.2721 73.3221 100 28.59258 14.45045 14.98600 14.99539 #> 3 110.2721 73.3221 100 28.59258 14.45045 14.97718 14.98918 #> 4 110.2721 73.3221 100 28.59258 14.45045 14.98542 14.97894 #> 5 110.2721 73.3221 100 28.59258 14.45045 14.99102 14.98701 #> 6 110.2721 73.3221 100 28.59258 14.45045 14.95107 14.94404 #> lambdayhat taudothatprime betahatprime alphahatprime #> 1 14.99034 0.1414578 0.7139323 0.7139719 #> 2 14.99440 0.1411358 0.7143124 0.7135210 #> 3 14.98096 0.1404725 0.7141806 0.7135072 #> 4 14.98061 0.1414693 0.7129967 0.7134799 #> 5 14.99074 0.1402090 0.7142253 0.7126436 #> 6 14.95413 0.1412288 0.7132173 0.7112758 #> sigma2hatepsilonylatenthat sigma2hatepsilonmlatenthat #> 1 0.3256446 0.4900060 #> 2 0.3251026 0.4904095 #> 3 0.3252494 0.4899523 #> 4 0.3254487 0.4897328 #> 5 0.3245309 0.4904784 #> 6 0.3235455 0.4916015 #> alphahatprimebetahatprime sehatlambdaxhat sehatlambdamhat sehatlambdayhat #> 1 0.5097527 0.3355070 0.3354895 0.3353618 #> 2 0.5097172 0.4743735 0.4746708 0.4746396 #> 3 0.5096705 0.6711434 0.6716813 0.6713130 #> 4 0.5088352 0.7511514 0.7508265 0.7509101 #> 5 0.5091470 0.8684063 0.8681740 0.8683904 #> 6 0.5075375 1.0625261 1.0620267 1.0627440 #> sehattaudothatprime sehatbetahatprime sehatalphahatprime #> 1 0.02576605 0.02245830 0.01550310 #> 2 0.03641655 0.03173574 0.02195374 #> 3 0.05159899 0.04498726 0.03104947 #> 4 0.05775610 0.05039795 0.03471624 #> 5 0.06662204 0.05809759 0.04018155 #> 6 0.08155141 0.07116570 0.04940781 #> sehatsigma2hatepsilonylatenthat sehatsigma2hatepsilonmlatenthat theta #> 1 0.01690933 0.02211606 0.5097527 #> 2 0.02387715 0.03126803 0.5097172 #> 3 0.03376401 0.04413620 0.5096705 #> 4 0.03775479 0.04929495 0.5088352 #> 5 0.04348097 0.05688682 0.5091470 #> 6 0.05310154 0.06958516 0.5075375 #> taudothatprime_var betahatprime_var alphahatprime_var #> 1 0.0006765683 0.0005125293 0.0002382753 #> 2 0.0013108209 0.0010147296 0.0004784026 #> 3 0.0027542679 0.0021202151 0.0009553470 #> 4 0.0033998350 0.0025756886 0.0012138294 #> 5 0.0044614394 0.0033572898 0.0016609980 #> 6 0.0070212492 0.0053137170 0.0024857559 #> alphahatprimebetahatprime_var taudothatprime_sd betahatprime_sd #> 1 0.0004089400 0.02601093 0.02263911 #> 2 0.0008046243 0.03620526 0.03185482 #> 3 0.0016709913 0.05248112 0.04604579 #> 4 0.0020655565 0.05830810 0.05075124 #> 5 0.0027337293 0.06679401 0.05794212 #> 6 0.0042524901 0.08379289 0.07289525 #> alphahatprime_sd alphahatprimebetahatprime_sd taudothatprime_skew #> 1 0.01543617 0.02022226 -0.08016860 #> 2 0.02187242 0.02836590 -0.02011559 #> 3 0.03090869 0.04087776 -0.06340355 #> 4 0.03484005 0.04544839 0.01295206 #> 5 0.04075534 0.05228508 -0.06025688 #> 6 0.04985736 0.06521112 0.01914667 #> betahatprime_skew alphahatprime_skew alphahatprimebetahatprime_skew #> 1 0.01821502 -0.1325749 0.08541397 #> 2 -0.06742260 -0.2405970 0.07537900 #> 3 -0.04031865 -0.2454082 0.07949310 #> 4 -0.12926391 -0.2982075 0.04872285 #> 5 -0.10885205 -0.3948730 0.08538548 #> 6 -0.17048198 -0.4276851 0.10997593 #> taudothatprime_kurt betahatprime_kurt alphahatprime_kurt #> 1 -0.065562688 -0.002103488 0.04593218 #> 2 -0.041339758 0.034103986 0.26807077 #> 3 0.002509797 -0.079877730 0.10945641 #> 4 -0.012580299 -0.036065080 0.21823388 #> 5 -0.014274742 -0.106420642 0.36145210 #> 6 0.138175012 0.165840008 0.34622429 #> alphahatprimebetahatprime_kurt taudothatprime_bias betahatprime_bias #> 1 0.06785356 3.648768e-05 -0.0001419363 #> 2 0.04669690 -2.855642e-04 0.0002382454 #> 3 0.01241305 -9.488710e-04 0.0001064572 #> 4 -0.01095826 4.791579e-05 -0.0010775156 #> 5 -0.05953854 -1.212322e-03 0.0001510672 #> 6 0.01427716 -1.925288e-04 -0.0008568647 #> alphahatprime_bias alphahatprimebetahatprime_bias taudothatprime_mse #> 1 -0.0001023370 -0.0001492751 0.0006764343 #> 2 -0.0005532081 -0.0001847031 0.0013106402 #> 3 -0.0005670046 -0.0002314656 0.0027546174 #> 4 -0.0005942854 -0.0010667177 0.0033991573 #> 5 -0.0014305566 -0.0007549720 0.0044620169 #> 6 -0.0027983921 -0.0023644560 0.0070198820 #> betahatprime_mse alphahatprime_mse alphahatprimebetahatprime_mse #> 1 0.0005124469 0.0002382381 0.0004088805 #> 2 0.0010145834 0.0004786130 0.0008044975 #> 3 0.0021198024 0.0009554774 0.0016707107 #> 4 0.0025763345 0.0012139398 0.0020662812 #> 5 0.0033566412 0.0016627123 0.0027337526 #> 6 0.0053133885 0.0024930898 0.0042572302 #> taudothatprime_rmse betahatprime_rmse alphahatprime_rmse #> 1 0.02600835 0.02263729 0.01543496 #> 2 0.03620277 0.03185253 0.02187723 #> 3 0.05248445 0.04604131 0.03091080 #> 4 0.05830229 0.05075761 0.03484164 #> 5 0.06679833 0.05793653 0.04077637 #> 6 0.08378474 0.07289299 0.04993085 #> alphahatprimebetahatprime_rmse missing std Method n_label #> 1 0.02022079 Complete Standardized fit.sem n: 1000 #> 2 0.02836366 Complete Standardized fit.sem n: 500 #> 3 0.04087433 Complete Standardized fit.sem n: 250 #> 4 0.04545637 Complete Standardized fit.sem n: 200 #> 5 0.05228530 Complete Standardized fit.sem n: 150 #> 6 0.06524745 Complete Standardized fit.sem n: 100 #> alpha_label beta_label taudot_label theta_label #> 1 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 2 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 3 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 4 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 5 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71) #> 6 α: 0.71 β: 0.71 τ̇: 0.14 0.51(0.71,0.71)#> 'data.frame': 531 obs. of 67 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 ... #> $ lambdaxhat : num 15 15 15 15 15 ... #> $ lambdamhat : num 15 15 15 15 15 ... #> $ lambdayhat : num 15 15 15 15 15 ... #> $ taudothatprime : num 0.141 0.141 0.14 0.141 0.14 ... #> $ betahatprime : num 0.714 0.714 0.714 0.713 0.714 ... #> $ alphahatprime : num 0.714 0.714 0.714 0.713 0.713 ... #> $ sigma2hatepsilonylatenthat : num 0.326 0.325 0.325 0.325 0.325 ... #> $ sigma2hatepsilonmlatenthat : num 0.49 0.49 0.49 0.49 0.49 ... #> $ alphahatprimebetahatprime : num 0.51 0.51 0.51 0.509 0.509 ... #> $ sehatlambdaxhat : num 0.336 0.474 0.671 0.751 0.868 ... #> $ sehatlambdamhat : num 0.335 0.475 0.672 0.751 0.868 ... #> $ sehatlambdayhat : num 0.335 0.475 0.671 0.751 0.868 ... #> $ sehattaudothatprime : num 0.0258 0.0364 0.0516 0.0578 0.0666 ... #> $ sehatbetahatprime : num 0.0225 0.0317 0.045 0.0504 0.0581 ... #> $ sehatalphahatprime : num 0.0155 0.022 0.031 0.0347 0.0402 ... #> $ sehatsigma2hatepsilonylatenthat: num 0.0169 0.0239 0.0338 0.0378 0.0435 ... #> $ sehatsigma2hatepsilonmlatenthat: num 0.0221 0.0313 0.0441 0.0493 0.0569 ... #> $ theta : num 0.51 0.51 0.51 0.509 0.509 ... #> $ taudothatprime_var : num 0.000677 0.001311 0.002754 0.0034 0.004461 ... #> $ betahatprime_var : num 0.000513 0.001015 0.00212 0.002576 0.003357 ... #> $ alphahatprime_var : num 0.000238 0.000478 0.000955 0.001214 0.001661 ... #> $ alphahatprimebetahatprime_var : num 0.000409 0.000805 0.001671 0.002066 0.002734 ... #> $ taudothatprime_sd : num 0.026 0.0362 0.0525 0.0583 0.0668 ... #> $ betahatprime_sd : num 0.0226 0.0319 0.046 0.0508 0.0579 ... #> $ alphahatprime_sd : num 0.0154 0.0219 0.0309 0.0348 0.0408 ... #> $ alphahatprimebetahatprime_sd : num 0.0202 0.0284 0.0409 0.0454 0.0523 ... #> $ taudothatprime_skew : num -0.0802 -0.0201 -0.0634 0.013 -0.0603 ... #> $ betahatprime_skew : num 0.0182 -0.0674 -0.0403 -0.1293 -0.1089 ... #> $ alphahatprime_skew : num -0.133 -0.241 -0.245 -0.298 -0.395 ... #> $ alphahatprimebetahatprime_skew : num 0.0854 0.0754 0.0795 0.0487 0.0854 ... #> $ taudothatprime_kurt : num -0.06556 -0.04134 0.00251 -0.01258 -0.01427 ... #> $ betahatprime_kurt : num -0.0021 0.0341 -0.0799 -0.0361 -0.1064 ... #> $ alphahatprime_kurt : num 0.0459 0.2681 0.1095 0.2182 0.3615 ... #> $ alphahatprimebetahatprime_kurt : num 0.0679 0.0467 0.0124 -0.011 -0.0595 ... #> $ taudothatprime_bias : num 3.65e-05 -2.86e-04 -9.49e-04 4.79e-05 -1.21e-03 ... #> $ betahatprime_bias : num -0.000142 0.000238 0.000106 -0.001078 0.000151 ... #> $ alphahatprime_bias : num -0.000102 -0.000553 -0.000567 -0.000594 -0.001431 ... #> $ alphahatprimebetahatprime_bias : num -0.000149 -0.000185 -0.000231 -0.001067 -0.000755 ... #> $ taudothatprime_mse : num 0.000676 0.001311 0.002755 0.003399 0.004462 ... #> $ betahatprime_mse : num 0.000512 0.001015 0.00212 0.002576 0.003357 ... #> $ alphahatprime_mse : num 0.000238 0.000479 0.000955 0.001214 0.001663 ... #> $ alphahatprimebetahatprime_mse : num 0.000409 0.000804 0.001671 0.002066 0.002734 ... #> $ taudothatprime_rmse : num 0.026 0.0362 0.0525 0.0583 0.0668 ... #> $ betahatprime_rmse : num 0.0226 0.0319 0.046 0.0508 0.0579 ... #> $ alphahatprime_rmse : num 0.0154 0.0219 0.0309 0.0348 0.0408 ... #> $ alphahatprimebetahatprime_rmse : num 0.0202 0.0284 0.0409 0.0455 0.0523 ... #> $ missing : chr "Complete" "Complete" "Complete" "Complete" ... #> $ std : chr "Standardized" "Standardized" "Standardized" "Standardized" ... #> $ 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)" ...