R/results_mvn_fit.ols.R
results_mvn_fit.ols.RdResults: Simple Mediation Model - Multivariate Normal Distribution - Complete Data - Fit Ordinary Least Squares
results_mvn_fit.ols
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
Mean of estimated slope of path from x to m \(\left( \hat{\alpha} \right)\).
Mean of estimated indirect effect of x on y through m \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 standardized indirect effect of x on y through m \(\left( \hat{\alpha}^{\prime} \hat{\beta}^{\prime} \right)\).
Mean of estimated variance of x \(\left( \hat{\sigma}_{x}^{2} \right)\).
Mean of estimated error variance of m \(\left( \hat{\sigma}_{\varepsilon_{m}}^{2} \right)\).
Mean of estimated error variance of y \(\left( \hat{\sigma}_{\varepsilon_{y}}^{2} \right)\).
Mean of estimated mean of x \(\left( \hat{\mu}_x \right)\).
Mean of estimated standard error of \(\hat{\delta}_{y}\).
Mean of estimated standard error of \(\hat{\dot{\tau}}\).
Mean of estimated standard error of \(\hat{\beta}\).
Mean of estimated standard error of \(\hat{\delta}_{m}\).
Mean of estimated standard error of \(\hat{\alpha}\).
Mean of estimated textbook standard error of \(\hat{\dot{\tau}}^{\prime}\).
Mean of estimated textbook standard error of \(\hat{\beta}^{\prime}\).
Mean of estimated textbook standard error of \(\hat{\alpha}^{\prime}\).
Mean of estimated delta method standard error of \(\hat{\dot{\tau}}^{\prime}\).
Mean of estimated delta method standard error of \(\hat{\beta}^{\prime}\).
Mean of estimated delta method standard error of \(\hat{\alpha}^{\prime}\).
Population parameter \(\alpha \beta\).
Variance of estimated intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 intercept of y \(\left( \hat{\delta}_y \right)\).
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 intercept of m \(\left( \hat{\delta}_{m} \right)\).
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 \(\left( \hat{\alpha} \hat{\beta} \right)\).
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 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.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_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 deltayhat taudothat #> 1 110.2721 73.3221 100 28.59258 14.45045 14.48643 0.1414002 #> 2 110.2721 73.3221 100 28.59258 14.45045 14.43182 0.1412213 #> 3 110.2721 73.3221 100 28.59258 14.45045 14.53134 0.1405349 #> 4 110.2721 73.3221 100 28.59258 14.45045 14.49848 0.1414157 #> 5 110.2721 73.3221 100 28.59258 14.45045 14.44328 0.1402906 #> 6 110.2721 73.3221 100 28.59258 14.45045 14.39262 0.1414066 #> betahat deltamhat alphahat alphahatbetahat taudothatprime betahatprime #> 1 0.7137815 28.59225 0.7141127 0.5097122 0.1414578 0.7139323 #> 2 0.7144869 28.56226 0.7143225 0.5103810 0.1411358 0.7143124 #> 3 0.7142294 28.53130 0.7148167 0.5105478 0.1404725 0.7141807 #> 4 0.7136251 28.60118 0.7140369 0.5095902 0.1414693 0.7129967 #> 5 0.7151770 28.63775 0.7136012 0.5103061 0.1402090 0.7142253 #> 6 0.7147568 28.73824 0.7126990 0.5094397 0.1412288 0.7132173 #> alphahatprime alphahatprimebetahatprime sigma2xhat sigma2hatepsilonmhat #> 1 0.7139719 0.5097527 225.0168 110.2471 #> 2 0.7135210 0.5097172 224.8010 110.3907 #> 3 0.7135072 0.5096705 224.7686 110.3063 #> 4 0.7134799 0.5088352 225.1110 110.1553 #> 5 0.7126436 0.5091470 225.4959 110.5357 #> 6 0.7112758 0.5075375 224.6785 110.3495 #> sigma2hatepsilonyhat muxhat sehatdeltayhat sehattaudothat sehatbetahat #> 1 73.26388 99.98883 1.970546 0.02581596 0.02581714 #> 2 73.26451 99.99682 2.791567 0.03656752 0.03654401 #> 3 73.33910 99.99533 3.961914 0.05192462 0.05188132 #> 4 73.46467 100.01784 4.439130 0.05815536 0.05818509 #> 5 73.49001 100.00405 5.135397 0.06723544 0.06725550 #> 6 73.21583 99.98233 6.322471 0.08267451 0.08271525 #> sehatdeltamhat sehatalphahat sehattaudothatprimetb sehatbetahatprimetb #> 1 2.240217 0.02215727 0.02582406 0.02582406 #> 2 3.174881 0.03139997 0.03653815 0.03653815 #> 3 4.497713 0.04448584 0.05188753 0.05188753 #> 4 5.026856 0.04970921 0.05814493 0.05814493 #> 5 5.818570 0.05754724 0.06719045 0.06719045 #> 6 7.155403 0.07079108 0.08256441 0.08256441 #> sehatalphahatprimetb sehattaudothatprimedelta sehatbetahatprimedelta #> 1 0.02215266 0.02577879 0.02246935 #> 2 0.03136508 0.03645267 0.03176707 #> 3 0.04440319 0.05170211 0.04507673 #> 4 0.04966992 0.05790087 0.05052366 #> 5 0.05746881 0.06684604 0.05829196 #> 6 0.07064603 0.08196752 0.07152695 #> sehatalphahatprimedelta theta deltayhat_var taudothat_var betahat_var #> 1 0.01550311 0.509902 3.809151 0.0006766288 0.0006872608 #> 2 0.02195379 0.509902 7.910203 0.0013166379 0.0013428911 #> 3 0.03104972 0.509902 15.898203 0.0027661321 0.0027626205 #> 4 0.03471668 0.509902 19.411751 0.0034041240 0.0033470956 #> 5 0.04018246 0.509902 27.309337 0.0045092302 0.0044723632 #> 6 0.04941033 0.509902 40.907599 0.0070705337 0.0068454896 #> deltamhat_var alphahat_var alphahatbetahat_var taudothatprime_var #> 1 4.915371 0.0004819305 0.0005886978 0.0006765683 #> 2 10.075260 0.0009876332 0.0011984475 0.0013108209 #> 3 20.072372 0.0019793814 0.0024342226 0.0027542678 #> 4 25.124194 0.0024631209 0.0029990743 0.0033998349 #> 5 34.022714 0.0033331922 0.0039483460 0.0044614393 #> 6 50.996017 0.0050008716 0.0061032551 0.0070212491 #> betahatprime_var alphahatprime_var alphahatprimebetahatprime_var deltayhat_sd #> 1 0.0005125293 0.0002382752 0.0004089399 1.951705 #> 2 0.0010147296 0.0004784026 0.0008046243 2.812508 #> 3 0.0021202151 0.0009553470 0.0016709913 3.987255 #> 4 0.0025756887 0.0012138294 0.0020655566 4.405877 #> 5 0.0033572898 0.0016609980 0.0027337293 5.225834 #> 6 0.0053137170 0.0024857559 0.0042524901 6.395905 #> taudothat_sd betahat_sd deltamhat_sd alphahat_sd alphahatbetahat_sd #> 1 0.02601209 0.02621566 2.217064 0.02195292 0.02426309 #> 2 0.03628551 0.03664548 3.174155 0.03142663 0.03461860 #> 3 0.05259403 0.05256064 4.480220 0.04449024 0.04933784 #> 4 0.05834487 0.05785409 5.012404 0.04962984 0.05476380 #> 5 0.06715080 0.06687573 5.832899 0.05773380 0.06283587 #> 6 0.08408647 0.08273747 7.141150 0.07071684 0.07812333 #> taudothatprime_sd betahatprime_sd alphahatprime_sd #> 1 0.02601093 0.02263911 0.01543617 #> 2 0.03620526 0.03185482 0.02187242 #> 3 0.05248112 0.04604579 0.03090869 #> 4 0.05830810 0.05075124 0.03484005 #> 5 0.06679401 0.05794212 0.04075534 #> 6 0.08379289 0.07289525 0.04985736 #> alphahatprimebetahatprime_sd deltayhat_skew taudothat_skew betahat_skew #> 1 0.02022226 6.973007e-02 -0.07881650 0.009080102 #> 2 0.02836590 3.592776e-02 -0.01040012 0.010047673 #> 3 0.04087776 -3.659058e-02 -0.04734244 0.049517177 #> 4 0.04544839 7.661420e-03 0.02098277 -0.034159405 #> 5 0.05228508 2.351047e-02 -0.03424817 0.038785585 #> 6 0.06521112 4.153125e-05 0.02548358 -0.024592445 #> deltamhat_skew alphahat_skew alphahatbetahat_skew taudothatprime_skew #> 1 0.003265346 -0.013253843 0.1091220 -0.08016861 #> 2 0.005413936 0.002196486 0.1189809 -0.02011563 #> 3 0.026963622 -0.052709729 0.1613471 -0.06340359 #> 4 -0.007357077 0.016526796 0.1209768 0.01295208 #> 5 -0.013000470 0.029762089 0.1853423 -0.06025686 #> 6 0.029425139 -0.020559340 0.1978930 0.01914671 #> betahatprime_skew alphahatprime_skew alphahatprimebetahatprime_skew #> 1 0.01821504 -0.1325748 0.08541395 #> 2 -0.06742263 -0.2405968 0.07537910 #> 3 -0.04031868 -0.2454082 0.07949305 #> 4 -0.12926390 -0.2982075 0.04872286 #> 5 -0.10885204 -0.3948730 0.08538549 #> 6 -0.17048200 -0.4276851 0.10997593 #> deltayhat_kurt taudothat_kurt betahat_kurt deltamhat_kurt alphahat_kurt #> 1 -0.002157981 -0.059229752 -0.07110298 -0.063814543 -0.063011768 #> 2 -0.010072440 -0.046067411 0.04769081 -0.004597911 0.008850368 #> 3 -0.032250203 0.032860516 -0.11791075 -0.056129020 -0.039486953 #> 4 0.098042436 0.020982976 -0.12777236 -0.014540047 -0.065638704 #> 5 0.046916897 0.008660788 -0.05971792 0.160877424 0.173845776 #> 6 0.080335027 0.131789932 0.01954482 0.081072053 0.056486157 #> alphahatbetahat_kurt taudothatprime_kurt betahatprime_kurt alphahatprime_kurt #> 1 -0.020512804 -0.065562760 -0.002103363 0.04593188 #> 2 0.127688084 -0.041339609 0.034104051 0.26807059 #> 3 -0.072165728 0.002509757 -0.079877735 0.10945659 #> 4 0.001530886 -0.012580275 -0.036065005 0.21823402 #> 5 -0.070674356 -0.014274740 -0.106420751 0.36145223 #> 6 -0.044210029 0.138175020 0.165839973 0.34622446 #> alphahatprimebetahatprime_kurt deltayhat_bias taudothat_bias betahat_bias #> 1 0.06785347 0.035987598 -2.116869e-05 -0.0002926589 #> 2 0.04669690 -0.018628999 -2.000520e-04 0.0004126741 #> 3 0.01241322 0.080891281 -8.864559e-04 0.0001552392 #> 4 -0.01095818 0.048031423 -5.699136e-06 -0.0004491207 #> 5 -0.05953858 -0.007163018 -1.130724e-03 0.0011028119 #> 6 0.01427715 -0.057822939 -1.473119e-05 0.0006825698 #> deltamhat_bias alphahat_bias alphahatbetahat_bias taudothatprime_bias #> 1 -0.000328294 3.847711e-05 -0.0001897400 3.648554e-05 #> 2 -0.030322245 2.483411e-04 0.0004790956 -2.855657e-04 #> 3 -0.061280869 7.425323e-04 0.0006458804 -9.488728e-04 #> 4 0.008594821 -3.725503e-05 -0.0003117182 4.791364e-05 #> 5 0.045169043 -4.729432e-04 0.0004041181 -1.212324e-03 #> 6 0.145658921 -1.375181e-03 -0.0004622804 -1.925299e-04 #> betahatprime_bias alphahatprime_bias alphahatprimebetahatprime_bias #> 1 -0.0001419340 -0.0001023382 -0.0001492743 #> 2 0.0002382473 -0.0005532089 -0.0001847023 #> 3 0.0001064590 -0.0005670051 -0.0002314646 #> 4 -0.0010775136 -0.0005942860 -0.0010667166 #> 5 0.0001510686 -0.0014305572 -0.0007549715 #> 6 -0.0008568636 -0.0027983925 -0.0023644555 #> deltayhat_mse taudothat_mse betahat_mse deltamhat_mse alphahat_mse #> 1 3.809684 0.000676494 0.000687209 4.914388 0.0004818356 #> 2 7.908968 0.001316415 0.001342793 10.074164 0.0009874973 #> 3 15.901567 0.002766365 0.002762092 20.072113 0.0019795369 #> 4 19.410176 0.003403443 0.003346628 25.119243 0.0024626296 #> 5 27.303926 0.004509607 0.004472685 34.017950 0.0033327492 #> 6 40.902761 0.007069120 0.006844586 51.007035 0.0050017626 #> alphahatbetahat_mse taudothatprime_mse betahatprime_mse alphahatprime_mse #> 1 0.000588616 0.0006764343 0.0005124469 0.0002382381 #> 2 0.001198437 0.0013106402 0.0010145835 0.0004786130 #> 3 0.002434153 0.0027546173 0.0021198024 0.0009554774 #> 4 0.002998572 0.0033991573 0.0025763346 0.0012139398 #> 5 0.003947720 0.0044620168 0.0033566411 0.0016627123 #> 6 0.006102248 0.0070198820 0.0053133885 0.0024930898 #> alphahatprimebetahatprime_mse deltayhat_rmse taudothat_rmse betahat_rmse #> 1 0.0004088804 1.951841 0.02600950 0.02621467 #> 2 0.0008044975 2.812289 0.03628243 0.03664414 #> 3 0.0016707106 3.987677 0.05259624 0.05255561 #> 4 0.0020662813 4.405698 0.05833904 0.05785005 #> 5 0.0027337526 5.225316 0.06715361 0.06687813 #> 6 0.0042572302 6.395527 0.08407806 0.08273202 #> deltamhat_rmse alphahat_rmse alphahatbetahat_rmse taudothatprime_rmse #> 1 2.216842 0.02195075 0.02426141 0.02600835 #> 2 3.173982 0.03142447 0.03461845 0.03620277 #> 3 4.480191 0.04449199 0.04933714 0.05248445 #> 4 5.011910 0.04962489 0.05475922 0.05830229 #> 5 5.832491 0.05772997 0.06283088 0.06679833 #> 6 7.141921 0.07072314 0.07811689 0.08378474 #> betahatprime_rmse alphahatprime_rmse alphahatprimebetahatprime_rmse missing #> 1 0.02263729 0.01543496 0.02022079 Complete #> 2 0.03185253 0.02187723 0.02836367 Complete #> 3 0.04604131 0.03091080 0.04087433 Complete #> 4 0.05075761 0.03484164 0.04545637 Complete #> 5 0.05793653 0.04077637 0.05228530 Complete #> 6 0.07289299 0.04993085 0.06524745 Complete #> std Method n_label alpha_label beta_label taudot_label #> 1 Unstandardized fit n: 1000 α: 0.71 β: 0.71 τ̇: 0.14 #> 2 Unstandardized fit n: 500 α: 0.71 β: 0.71 τ̇: 0.14 #> 3 Unstandardized fit n: 250 α: 0.71 β: 0.71 τ̇: 0.14 #> 4 Unstandardized fit n: 200 α: 0.71 β: 0.71 τ̇: 0.14 #> 5 Unstandardized fit n: 150 α: 0.71 β: 0.71 τ̇: 0.14 #> 6 Unstandardized fit n: 100 α: 0.71 β: 0.71 τ̇: 0.14 #> theta_label #> 1 0.51(0.71,0.71) #> 2 0.51(0.71,0.71) #> 3 0.51(0.71,0.71) #> 4 0.51(0.71,0.71) #> 5 0.51(0.71,0.71) #> 6 0.51(0.71,0.71)#> 'data.frame': 531 obs. of 117 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 ... #> $ deltayhat : num 14.5 14.4 14.5 14.5 14.4 ... #> $ taudothat : num 0.141 0.141 0.141 0.141 0.14 ... #> $ betahat : num 0.714 0.714 0.714 0.714 0.715 ... #> $ deltamhat : num 28.6 28.6 28.5 28.6 28.6 ... #> $ alphahat : num 0.714 0.714 0.715 0.714 0.714 ... #> $ alphahatbetahat : num 0.51 0.51 0.511 0.51 0.51 ... #> $ 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 ... #> $ alphahatprimebetahatprime : num 0.51 0.51 0.51 0.509 0.509 ... #> $ sigma2xhat : num 225 225 225 225 225 ... #> $ sigma2hatepsilonmhat : num 110 110 110 110 111 ... #> $ sigma2hatepsilonyhat : num 73.3 73.3 73.3 73.5 73.5 ... #> $ muxhat : num 100 100 100 100 100 ... #> $ sehatdeltayhat : num 1.97 2.79 3.96 4.44 5.14 ... #> $ sehattaudothat : num 0.0258 0.0366 0.0519 0.0582 0.0672 ... #> $ sehatbetahat : num 0.0258 0.0365 0.0519 0.0582 0.0673 ... #> $ sehatdeltamhat : num 2.24 3.17 4.5 5.03 5.82 ... #> $ sehatalphahat : num 0.0222 0.0314 0.0445 0.0497 0.0575 ... #> $ sehattaudothatprimetb : num 0.0258 0.0365 0.0519 0.0581 0.0672 ... #> $ sehatbetahatprimetb : num 0.0258 0.0365 0.0519 0.0581 0.0672 ... #> $ sehatalphahatprimetb : num 0.0222 0.0314 0.0444 0.0497 0.0575 ... #> $ sehattaudothatprimedelta : num 0.0258 0.0365 0.0517 0.0579 0.0668 ... #> $ sehatbetahatprimedelta : num 0.0225 0.0318 0.0451 0.0505 0.0583 ... #> $ sehatalphahatprimedelta : num 0.0155 0.022 0.031 0.0347 0.0402 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ deltayhat_var : num 3.81 7.91 15.9 19.41 27.31 ... #> $ taudothat_var : num 0.000677 0.001317 0.002766 0.003404 0.004509 ... #> $ betahat_var : num 0.000687 0.001343 0.002763 0.003347 0.004472 ... #> $ deltamhat_var : num 4.92 10.08 20.07 25.12 34.02 ... #> $ alphahat_var : num 0.000482 0.000988 0.001979 0.002463 0.003333 ... #> $ alphahatbetahat_var : num 0.000589 0.001198 0.002434 0.002999 0.003948 ... #> $ 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 ... #> $ deltayhat_sd : num 1.95 2.81 3.99 4.41 5.23 ... #> $ taudothat_sd : num 0.026 0.0363 0.0526 0.0583 0.0672 ... #> $ betahat_sd : num 0.0262 0.0366 0.0526 0.0579 0.0669 ... #> $ deltamhat_sd : num 2.22 3.17 4.48 5.01 5.83 ... #> $ alphahat_sd : num 0.022 0.0314 0.0445 0.0496 0.0577 ... #> $ alphahatbetahat_sd : num 0.0243 0.0346 0.0493 0.0548 0.0628 ... #> $ 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 ... #> $ deltayhat_skew : num 0.06973 0.03593 -0.03659 0.00766 0.02351 ... #> $ taudothat_skew : num -0.0788 -0.0104 -0.0473 0.021 -0.0342 ... #> $ betahat_skew : num 0.00908 0.01005 0.04952 -0.03416 0.03879 ... #> $ deltamhat_skew : num 0.00327 0.00541 0.02696 -0.00736 -0.013 ... #> $ alphahat_skew : num -0.0133 0.0022 -0.0527 0.0165 0.0298 ... #> $ alphahatbetahat_skew : num 0.109 0.119 0.161 0.121 0.185 ... #> $ 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 ... #> $ deltayhat_kurt : num -0.00216 -0.01007 -0.03225 0.09804 0.04692 ... #> $ taudothat_kurt : num -0.05923 -0.04607 0.03286 0.02098 0.00866 ... #> $ betahat_kurt : num -0.0711 0.0477 -0.1179 -0.1278 -0.0597 ... #> $ deltamhat_kurt : num -0.0638 -0.0046 -0.0561 -0.0145 0.1609 ... #> $ alphahat_kurt : num -0.06301 0.00885 -0.03949 -0.06564 0.17385 ... #> $ alphahatbetahat_kurt : num -0.02051 0.12769 -0.07217 0.00153 -0.07067 ... #> $ 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 ... #> $ deltayhat_bias : num 0.03599 -0.01863 0.08089 0.04803 -0.00716 ... #> $ taudothat_bias : num -2.12e-05 -2.00e-04 -8.86e-04 -5.70e-06 -1.13e-03 ... #> $ betahat_bias : num -0.000293 0.000413 0.000155 -0.000449 0.001103 ... #> $ deltamhat_bias : num -0.000328 -0.030322 -0.061281 0.008595 0.045169 ... #> $ alphahat_bias : num 3.85e-05 2.48e-04 7.43e-04 -3.73e-05 -4.73e-04 ... #> $ alphahatbetahat_bias : num -0.00019 0.000479 0.000646 -0.000312 0.000404 ... #> $ 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 ... #> $ deltayhat_mse : num 3.81 7.91 15.9 19.41 27.3 ... #> $ taudothat_mse : num 0.000676 0.001316 0.002766 0.003403 0.00451 ... #> $ betahat_mse : num 0.000687 0.001343 0.002762 0.003347 0.004473 ... #> $ deltamhat_mse : num 4.91 10.07 20.07 25.12 34.02 ... #> $ alphahat_mse : num 0.000482 0.000987 0.00198 0.002463 0.003333 ... #> $ alphahatbetahat_mse : num 0.000589 0.001198 0.002434 0.002999 0.003948 ... #> $ 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 ... #> [list output truncated]