R/results_mvn_mcar_fit.sem.R
results_mvn_mcar_fit.sem.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Data Missing Completely at Random - Fit Structural Equation Modeling with Full Information Maximum Likelihood
results_mvn_mcar_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_fit.sem,
results_mvn_mar_mc.mvn_ci,
results_mvn_mar_nb.fiml_ci,
results_mvn_mar_pb.mvn_ci,
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 0.1413377 0.7137186 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.1408221 0.7147600 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.1405409 0.7145688 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.1417030 0.7134980 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.1403691 0.7150701 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.1414344 0.7148332 #> alphahat sigma2hatepsilonyhat sigma2hatepsilonmhat deltayhat deltamhat #> 1 0.7142413 73.05431 110.0008 14.49972 28.58045 #> 2 0.7143788 72.77972 109.9600 14.44492 28.55669 #> 3 0.7147745 72.40440 109.3915 14.49501 28.53760 #> 4 0.7142609 72.32439 109.0662 14.48209 28.58014 #> 5 0.7138515 71.92993 108.9935 14.44756 28.61204 #> 6 0.7132623 70.95014 107.9770 14.38005 28.68347 #> muxhat sigma2xhat alphahatbetahat sehattaudothat sehatbetahat #> 1 99.98685 224.7991 0.5097591 0.02690692 0.02671163 #> 2 99.99639 224.3624 0.5106129 0.03806872 0.03776345 #> 3 99.99342 223.9090 0.5107630 0.05395747 0.05352989 #> 4 100.01528 223.9065 0.5096472 0.06039913 0.05997298 #> 5 100.00534 223.9056 0.5104204 0.06976699 0.06924354 #> 6 99.98423 222.4398 0.5099510 0.08548692 0.08491387 #> sehatalphahat sehatsigma2hatepsilonyhat sehatsigma2hatepsilonmhat #> 1 0.02255466 3.367895 5.055749 #> 2 0.03195789 4.748435 7.150904 #> 3 0.04522360 6.687463 10.071823 #> 4 0.05053010 7.473407 11.234645 #> 5 0.05844535 8.593604 12.976012 #> 6 0.07174193 10.399274 15.774196 #> sehatdeltayhat sehatdeltamhat sehatmuxhat sehatsigma2xhat theta #> 1 2.023994 2.280327 0.4781233 10.18394 0.509902 #> 2 2.864068 3.231251 0.6756859 14.38011 0.509902 #> 3 4.058441 4.572183 0.9550603 20.31891 0.509902 #> 4 4.543835 5.109703 1.0681447 22.72947 0.509902 #> 5 5.249581 5.909551 1.2338337 26.26622 0.509902 #> 6 6.440353 7.251769 1.5073719 32.01916 0.509902 #> taudothat_var betahat_var alphahat_var alphahatbetahat_var taudothat_sd #> 1 0.0007373544 0.0007416698 0.0004994931 0.000625310 0.02715427 #> 2 0.0014214482 0.0014216055 0.0010302003 0.001256809 0.03770210 #> 3 0.0029726990 0.0029169233 0.0020430692 0.002549786 0.05452246 #> 4 0.0036758261 0.0036045125 0.0025513149 0.003164866 0.06062859 #> 5 0.0049210007 0.0047894146 0.0034464842 0.004199369 0.07014984 #> 6 0.0076905892 0.0073422901 0.0051376260 0.006494707 0.08769600 #> betahat_sd alphahat_sd alphahatbetahat_sd taudothat_skew betahat_skew #> 1 0.02723361 0.02234934 0.02500620 -0.043470005 0.008815481 #> 2 0.03770418 0.03209673 0.03545150 -0.033854393 -0.012309664 #> 3 0.05400855 0.04520032 0.05049541 -0.044450509 0.063820015 #> 4 0.06003759 0.05051054 0.05625714 0.024349207 -0.036056157 #> 5 0.06920560 0.05870676 0.06480254 -0.054375832 0.018891200 #> 6 0.08568716 0.07167723 0.08058975 0.005909009 -0.016336674 #> alphahat_skew alphahatbetahat_skew taudothat_kurt betahat_kurt alphahat_kurt #> 1 -0.0161490053 0.0934668 -0.043051637 -0.08034023 -0.06596364 #> 2 0.0109439175 0.1030841 -0.099898404 0.01573027 0.03777718 #> 3 -0.0645809891 0.1675816 -0.005116577 -0.01773557 -0.04310960 #> 4 0.0072980694 0.1228973 0.075822578 -0.08396863 -0.07432525 #> 5 0.0424863192 0.2310179 0.024658525 -0.06071015 0.17648857 #> 6 0.0008588112 0.2211760 0.149059816 0.08525317 0.01052623 #> alphahatbetahat_kurt taudothat_bias betahat_bias alphahat_bias #> 1 -0.023160490 -8.369687e-05 -0.0003556120 0.0001670921 #> 2 0.142039345 -5.992720e-04 0.0006858482 0.0003045899 #> 3 -0.032795552 -8.805053e-04 0.0004945915 0.0007002703 #> 4 0.007187065 2.816209e-04 -0.0005761514 0.0001866855 #> 5 -0.050187734 -1.052262e-03 0.0009959407 -0.0002226742 #> 6 0.025468427 1.302436e-05 0.0007589917 -0.0008118437 #> alphahatbetahat_bias taudothat_mse betahat_mse alphahat_mse #> 1 -1.428436e-04 0.000737214 0.0007416479 0.0004994211 #> 2 7.109738e-04 0.001421523 0.0014217916 0.0010300870 #> 3 8.610298e-04 0.002972880 0.0029165846 0.0020431509 #> 4 -2.547753e-04 0.003675170 0.0036041236 0.0025508395 #> 5 5.184353e-04 0.004921124 0.0047894486 0.0034458445 #> 6 4.908433e-05 0.007689051 0.0073413977 0.0051372575 #> alphahatbetahat_mse taudothat_rmse betahat_rmse alphahat_rmse #> 1 0.0006252054 0.02715168 0.02723321 0.02234773 #> 2 0.0012570628 0.03770309 0.03770665 0.03209497 #> 3 0.0025500177 0.05452412 0.05400541 0.04520123 #> 4 0.0031642975 0.06062318 0.06003435 0.05050584 #> 5 0.0041987979 0.07015072 0.06920584 0.05870132 #> 6 0.0064934106 0.08768724 0.08568196 0.07167466 #> alphahatbetahat_rmse missing std Method n_label alpha_label #> 1 0.02500411 MCAR.10 Unstandardized fit.sem n: 1000 α: 0.71 #> 2 0.03545508 MCAR.10 Unstandardized fit.sem n: 500 α: 0.71 #> 3 0.05049770 MCAR.10 Unstandardized fit.sem n: 250 α: 0.71 #> 4 0.05625209 MCAR.10 Unstandardized fit.sem n: 200 α: 0.71 #> 5 0.06479813 MCAR.10 Unstandardized fit.sem n: 150 α: 0.71 #> 6 0.08058170 MCAR.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 0.141 0.142 0.14 ... #> $ betahat : num 0.714 0.715 0.715 0.713 0.715 ... #> $ alphahat : num 0.714 0.714 0.715 0.714 0.714 ... #> $ sigma2hatepsilonyhat : num 73.1 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 28.6 ... #> $ muxhat : num 100 100 100 100 100 ... #> $ sigma2xhat : num 225 224 224 224 224 ... #> $ alphahatbetahat : num 0.51 0.511 0.511 0.51 0.51 ... #> $ sehattaudothat : num 0.0269 0.0381 0.054 0.0604 0.0698 ... #> $ sehatbetahat : num 0.0267 0.0378 0.0535 0.06 0.0692 ... #> $ sehatalphahat : num 0.0226 0.032 0.0452 0.0505 0.0584 ... #> $ sehatsigma2hatepsilonyhat: num 3.37 4.75 6.69 7.47 8.59 ... #> $ sehatsigma2hatepsilonmhat: num 5.06 7.15 10.07 11.23 12.98 ... #> $ sehatdeltayhat : num 2.02 2.86 4.06 4.54 5.25 ... #> $ sehatdeltamhat : num 2.28 3.23 4.57 5.11 5.91 ... #> $ sehatmuxhat : num 0.478 0.676 0.955 1.068 1.234 ... #> $ sehatsigma2xhat : num 10.2 14.4 20.3 22.7 26.3 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ taudothat_var : num 0.000737 0.001421 0.002973 0.003676 0.004921 ... #> $ betahat_var : num 0.000742 0.001422 0.002917 0.003605 0.004789 ... #> $ alphahat_var : num 0.000499 0.00103 0.002043 0.002551 0.003446 ... #> $ alphahatbetahat_var : num 0.000625 0.001257 0.00255 0.003165 0.004199 ... #> $ taudothat_sd : num 0.0272 0.0377 0.0545 0.0606 0.0701 ... #> $ betahat_sd : num 0.0272 0.0377 0.054 0.06 0.0692 ... #> $ alphahat_sd : num 0.0223 0.0321 0.0452 0.0505 0.0587 ... #> $ alphahatbetahat_sd : num 0.025 0.0355 0.0505 0.0563 0.0648 ... #> $ taudothat_skew : num -0.0435 -0.0339 -0.0445 0.0243 -0.0544 ... #> $ betahat_skew : num 0.00882 -0.01231 0.06382 -0.03606 0.01889 ... #> $ alphahat_skew : num -0.0161 0.0109 -0.0646 0.0073 0.0425 ... #> $ alphahatbetahat_skew : num 0.0935 0.1031 0.1676 0.1229 0.231 ... #> $ taudothat_kurt : num -0.04305 -0.0999 -0.00512 0.07582 0.02466 ... #> $ betahat_kurt : num -0.0803 0.0157 -0.0177 -0.084 -0.0607 ... #> $ alphahat_kurt : num -0.066 0.0378 -0.0431 -0.0743 0.1765 ... #> $ alphahatbetahat_kurt : num -0.02316 0.14204 -0.0328 0.00719 -0.05019 ... #> $ taudothat_bias : num -8.37e-05 -5.99e-04 -8.81e-04 2.82e-04 -1.05e-03 ... #> $ betahat_bias : num -0.000356 0.000686 0.000495 -0.000576 0.000996 ... #> $ alphahat_bias : num 0.000167 0.000305 0.0007 0.000187 -0.000223 ... #> $ alphahatbetahat_bias : num -0.000143 0.000711 0.000861 -0.000255 0.000518 ... #> $ taudothat_mse : num 0.000737 0.001422 0.002973 0.003675 0.004921 ... #> $ betahat_mse : num 0.000742 0.001422 0.002917 0.003604 0.004789 ... #> $ alphahat_mse : num 0.000499 0.00103 0.002043 0.002551 0.003446 ... #> $ alphahatbetahat_mse : num 0.000625 0.001257 0.00255 0.003164 0.004199 ... #> $ taudothat_rmse : num 0.0272 0.0377 0.0545 0.0606 0.0702 ... #> $ betahat_rmse : num 0.0272 0.0377 0.054 0.06 0.0692 ... #> $ alphahat_rmse : num 0.0223 0.0321 0.0452 0.0505 0.0587 ... #> $ alphahatbetahat_rmse : num 0.025 0.0355 0.0505 0.0563 0.0648 ... #> $ missing : chr "MCAR.10" "MCAR.10" "MCAR.10" "MCAR.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)" ...