R/results_mvn_mnar_fit.sem.R
results_mvn_mnar_fit.sem.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Data Missing Not at Random - Fit Structural Equation Modeling with Full Information Maximum Likelihood
results_mvn_mnar_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_fit.sem,
results_mvn_mcar_mc.mvn_ci,
results_mvn_mcar_nb.fiml_ci,
results_mvn_mcar_pb.mvn_ci,
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 0.1420547 0.7118208 #> 2 110.2721 73.3221 100 28.59258 14.45045 0.1416713 0.7128435 #> 3 110.2721 73.3221 100 28.59258 14.45045 0.1412600 0.7124383 #> 4 110.2721 73.3221 100 28.59258 14.45045 0.1419425 0.7119408 #> 5 110.2721 73.3221 100 28.59258 14.45045 0.1399029 0.7140467 #> 6 110.2721 73.3221 100 28.59258 14.45045 0.1424385 0.7129992 #> alphahat sigma2hatepsilonyhat sigma2hatepsilonmhat deltayhat deltamhat #> 1 0.7138168 72.77888 109.7068 14.59096 28.64999 #> 2 0.7140328 72.53022 109.6717 14.52675 28.61966 #> 3 0.7149039 72.15701 109.1739 14.61217 28.55374 #> 4 0.7139991 72.02668 108.7282 14.58746 28.63133 #> 5 0.7135543 71.64014 108.7152 14.56664 28.66918 #> 6 0.7128174 70.67251 107.7989 14.44055 28.75395 #> muxhat sigma2xhat alphahatbetahat sehattaudothat sehatbetahat sehatalphahat #> 1 99.79201 221.7040 0.5081001 0.02702592 0.02677978 0.02276036 #> 2 99.79992 221.2482 0.5090037 0.03821957 0.03784621 0.03223983 #> 3 99.79758 220.7112 0.5093317 0.05421408 0.05365902 0.04565663 #> 4 99.82359 220.9606 0.5083697 0.06062860 0.06011252 0.05097045 #> 5 99.81303 221.0913 0.5094734 0.06999836 0.06935580 0.05892744 #> 6 99.79187 219.6016 0.5082635 0.08578844 0.08504769 0.07238571 #> sehatsigma2hatepsilonyhat sehatsigma2hatepsilonmhat sehatdeltayhat #> 1 3.359227 5.060715 2.039539 #> 2 4.736466 7.157161 2.885220 #> 3 6.672515 10.087803 4.087489 #> 4 7.450732 11.237046 4.574201 #> 5 8.563409 12.984031 5.282757 #> 6 10.365974 15.796292 6.484950 #> sehatdeltamhat sehatmuxhat sehatsigma2xhat theta taudothat_var #> 1 2.291937 0.4749091 10.07265 0.509902 0.0007498757 #> 2 3.246792 0.6710784 14.22138 0.509902 0.0014532182 #> 3 4.597618 0.9483271 20.08454 0.509902 0.0030320208 #> 4 5.133640 1.0611083 22.48576 0.509902 0.0036966258 #> 5 5.934765 1.2261962 26.00649 0.509902 0.0050244946 #> 6 7.287765 1.4978797 31.68997 0.509902 0.0077162607 #> betahat_var alphahat_var alphahatbetahat_var taudothat_sd betahat_sd #> 1 0.0007462264 0.0005141942 0.0006319245 0.02738386 0.02731715 #> 2 0.0014810272 0.0010507598 0.0013003055 0.03812110 0.03848412 #> 3 0.0029773463 0.0021022382 0.0026021318 0.05506379 0.05456506 #> 4 0.0035902810 0.0026027907 0.0031995684 0.06079988 0.05991895 #> 5 0.0049274645 0.0035631624 0.0043013122 0.07088367 0.07019590 #> 6 0.0074232554 0.0053456337 0.0065717106 0.08784225 0.08615832 #> alphahat_sd alphahatbetahat_sd taudothat_skew betahat_skew alphahat_skew #> 1 0.02267585 0.02513811 -0.069279585 0.020310188 -0.0098413118 #> 2 0.03241543 0.03605975 -0.037065907 0.024286364 0.0005119987 #> 3 0.04585017 0.05101109 -0.006362018 0.041007472 -0.0570699310 #> 4 0.05101755 0.05656473 0.005128559 -0.040424142 0.0270907718 #> 5 0.05969223 0.06558439 -0.018514216 0.032700479 0.0483308332 #> 6 0.07311384 0.08106609 -0.012443085 0.008928038 0.0024196352 #> alphahatbetahat_skew taudothat_kurt betahat_kurt alphahat_kurt #> 1 0.09635024 0.009128894 -0.03084708 -0.06161469 #> 2 0.11064814 -0.047427586 0.01183849 0.02112707 #> 3 0.14330137 0.066480386 -0.07851001 -0.03712479 #> 4 0.13975451 -0.078309466 -0.17018959 -0.03090081 #> 5 0.19520874 -0.023944163 -0.07447710 0.17198651 #> 6 0.24760695 0.158033020 0.03256190 0.10036361 #> alphahatbetahat_kurt taudothat_bias betahat_bias alphahat_bias #> 1 -0.01858671 0.0006333781 -2.253435e-03 -2.574296e-04 #> 2 0.14037793 0.0002499749 -1.230645e-03 -4.143718e-05 #> 3 -0.10029081 -0.0001613391 -1.635896e-03 8.297574e-04 #> 4 0.05470845 0.0005211488 -2.133431e-03 -7.508839e-05 #> 5 -0.04375008 -0.0015184509 -2.749503e-05 -5.198647e-04 #> 6 0.02106093 0.0010171919 -1.074963e-03 -1.256816e-03 #> alphahatbetahat_bias taudothat_mse betahat_mse alphahat_mse #> 1 -0.0018018201 0.0007501269 0.0007511552 0.0005141576 #> 2 -0.0008982690 0.0014529900 0.0014822455 0.0010505514 #> 3 -0.0005702690 0.0030314405 0.0029794270 0.0021025062 #> 4 -0.0015322616 0.0036961580 0.0035941144 0.0026022757 #> 5 -0.0004285314 0.0050257954 0.0049264797 0.0035627200 #> 6 -0.0016384134 0.0077157521 0.0074229263 0.0053461441 #> alphahatbetahat_mse taudothat_rmse betahat_rmse alphahat_rmse #> 1 0.0006350447 0.02738844 0.02740721 0.02267504 #> 2 0.0013008523 0.03811811 0.03849994 0.03241221 #> 3 0.0026019366 0.05505852 0.05458413 0.04585309 #> 4 0.0032012763 0.06079604 0.05995093 0.05101251 #> 5 0.0043006356 0.07089284 0.07018889 0.05968853 #> 6 0.0065730807 0.08783935 0.08615641 0.07311733 #> alphahatbetahat_rmse missing std Method n_label alpha_label #> 1 0.02520009 MNAR.10 Unstandardized fit.sem n: 1000 α: 0.71 #> 2 0.03606733 MNAR.10 Unstandardized fit.sem n: 500 α: 0.71 #> 3 0.05100918 MNAR.10 Unstandardized fit.sem n: 250 α: 0.71 #> 4 0.05657982 MNAR.10 Unstandardized fit.sem n: 200 α: 0.71 #> 5 0.06557923 MNAR.10 Unstandardized fit.sem n: 150 α: 0.71 #> 6 0.08107454 MNAR.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 0.142 0.142 0.141 0.142 0.14 ... #> $ betahat : num 0.712 0.713 0.712 0.712 0.714 ... #> $ alphahat : num 0.714 0.714 0.715 0.714 0.714 ... #> $ sigma2hatepsilonyhat : num 72.8 72.5 72.2 72 71.6 ... #> $ sigma2hatepsilonmhat : num 110 110 109 109 109 ... #> $ deltayhat : num 14.6 14.5 14.6 14.6 14.6 ... #> $ deltamhat : num 28.6 28.6 28.6 28.6 28.7 ... #> $ muxhat : num 99.8 99.8 99.8 99.8 99.8 ... #> $ sigma2xhat : num 222 221 221 221 221 ... #> $ alphahatbetahat : num 0.508 0.509 0.509 0.508 0.509 ... #> $ sehattaudothat : num 0.027 0.0382 0.0542 0.0606 0.07 ... #> $ sehatbetahat : num 0.0268 0.0378 0.0537 0.0601 0.0694 ... #> $ sehatalphahat : num 0.0228 0.0322 0.0457 0.051 0.0589 ... #> $ sehatsigma2hatepsilonyhat: num 3.36 4.74 6.67 7.45 8.56 ... #> $ sehatsigma2hatepsilonmhat: num 5.06 7.16 10.09 11.24 12.98 ... #> $ sehatdeltayhat : num 2.04 2.89 4.09 4.57 5.28 ... #> $ sehatdeltamhat : num 2.29 3.25 4.6 5.13 5.93 ... #> $ sehatmuxhat : num 0.475 0.671 0.948 1.061 1.226 ... #> $ sehatsigma2xhat : num 10.1 14.2 20.1 22.5 26 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ taudothat_var : num 0.00075 0.00145 0.00303 0.0037 0.00502 ... #> $ betahat_var : num 0.000746 0.001481 0.002977 0.00359 0.004927 ... #> $ alphahat_var : num 0.000514 0.001051 0.002102 0.002603 0.003563 ... #> $ alphahatbetahat_var : num 0.000632 0.0013 0.002602 0.0032 0.004301 ... #> $ taudothat_sd : num 0.0274 0.0381 0.0551 0.0608 0.0709 ... #> $ betahat_sd : num 0.0273 0.0385 0.0546 0.0599 0.0702 ... #> $ alphahat_sd : num 0.0227 0.0324 0.0459 0.051 0.0597 ... #> $ alphahatbetahat_sd : num 0.0251 0.0361 0.051 0.0566 0.0656 ... #> $ taudothat_skew : num -0.06928 -0.03707 -0.00636 0.00513 -0.01851 ... #> $ betahat_skew : num 0.0203 0.0243 0.041 -0.0404 0.0327 ... #> $ alphahat_skew : num -0.009841 0.000512 -0.05707 0.027091 0.048331 ... #> $ alphahatbetahat_skew : num 0.0964 0.1106 0.1433 0.1398 0.1952 ... #> $ taudothat_kurt : num 0.00913 -0.04743 0.06648 -0.07831 -0.02394 ... #> $ betahat_kurt : num -0.0308 0.0118 -0.0785 -0.1702 -0.0745 ... #> $ alphahat_kurt : num -0.0616 0.0211 -0.0371 -0.0309 0.172 ... #> $ alphahatbetahat_kurt : num -0.0186 0.1404 -0.1003 0.0547 -0.0438 ... #> $ taudothat_bias : num 0.000633 0.00025 -0.000161 0.000521 -0.001518 ... #> $ betahat_bias : num -2.25e-03 -1.23e-03 -1.64e-03 -2.13e-03 -2.75e-05 ... #> $ alphahat_bias : num -2.57e-04 -4.14e-05 8.30e-04 -7.51e-05 -5.20e-04 ... #> $ alphahatbetahat_bias : num -0.001802 -0.000898 -0.00057 -0.001532 -0.000429 ... #> $ taudothat_mse : num 0.00075 0.00145 0.00303 0.0037 0.00503 ... #> $ betahat_mse : num 0.000751 0.001482 0.002979 0.003594 0.004926 ... #> $ alphahat_mse : num 0.000514 0.001051 0.002103 0.002602 0.003563 ... #> $ alphahatbetahat_mse : num 0.000635 0.001301 0.002602 0.003201 0.004301 ... #> $ taudothat_rmse : num 0.0274 0.0381 0.0551 0.0608 0.0709 ... #> $ betahat_rmse : num 0.0274 0.0385 0.0546 0.06 0.0702 ... #> $ alphahat_rmse : num 0.0227 0.0324 0.0459 0.051 0.0597 ... #> $ alphahatbetahat_rmse : num 0.0252 0.0361 0.051 0.0566 0.0656 ... #> $ missing : chr "MNAR.10" "MNAR.10" "MNAR.10" "MNAR.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)" ...