R/results_vm_mod_fit.ols.R
results_vm_mod_fit.ols.RdResults: Simple Mediation Model - Vale and Maurelli (1983) - Skewness = 2, Kurtosis = 7 - Complete Data - Fit Ordinary Least Squares
results_vm_mod_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.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_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.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 14.44378 0.1419724 #> 2 110.2721 73.3221 100 28.59258 14.45045 14.34276 0.1417535 #> 3 110.2721 73.3221 100 28.59258 14.45045 14.20785 0.1411131 #> 4 110.2721 73.3221 100 28.59258 14.45045 14.20233 0.1414830 #> 5 110.2721 73.3221 100 28.59258 14.45045 14.32600 0.1407554 #> 6 110.2721 73.3221 100 28.59258 14.45045 13.77031 0.1443344 #> betahat deltamhat alphahat alphahatbetahat taudothatprime betahatprime #> 1 0.7135317 28.48748 0.7151324 0.5100761 0.1419818 0.7137418 #> 2 0.7149333 28.37867 0.7164727 0.5118519 0.1412626 0.7138683 #> 3 0.7169005 28.47801 0.7152514 0.5120330 0.1410019 0.7147817 #> 4 0.7166915 28.21061 0.7180198 0.5138135 0.1409344 0.7140528 #> 5 0.7159442 28.09537 0.7192290 0.5142247 0.1406731 0.7152602 #> 6 0.7182118 27.77399 0.7226573 0.5175581 0.1434587 0.7126113 #> alphahatprime alphahatprimebetahatprime sigma2xhat sigma2hatepsilonmhat #> 1 0.7139271 0.5096007 225.0744 110.2561 #> 2 0.7136662 0.5095736 224.9368 110.3002 #> 3 0.7133199 0.5100244 225.6240 109.5242 #> 4 0.7129374 0.5092874 223.3675 109.0693 #> 5 0.7139756 0.5109265 224.4267 108.4928 #> 6 0.7142875 0.5094330 224.4800 108.2001 #> sigma2hatepsilonyhat muxhat sehatdeltayhat sehattaudothat sehatbetahat #> 1 72.95181 100.00583 1.970009 0.02580956 0.02578860 #> 2 73.10678 100.01578 2.798893 0.03667827 0.03659727 #> 3 72.02501 100.00146 3.957533 0.05179644 0.05183562 #> 4 71.87371 99.96497 4.447794 0.05830509 0.05814369 #> 5 70.63235 99.96518 5.110207 0.06715175 0.06701924 #> 6 70.80745 100.02529 6.329336 0.08326354 0.08297711 #> sehatdeltamhat sehatalphahat sehattaudothatprimetb sehatbetahatprimetb #> 1 2.242730 0.02218049 0.02580262 0.02580262 #> 2 3.179510 0.03144598 0.03655637 0.03655637 #> 3 4.491744 0.04444040 0.05170688 0.05170688 #> 4 5.044032 0.04993377 0.05796647 0.05796647 #> 5 5.817420 0.05759916 0.06701429 0.06701429 #> 6 7.153908 0.07081603 0.08247609 0.08247609 #> sehatalphahatprimetb sehattaudothatprimedelta sehatbetahatprimedelta #> 1 0.02214305 0.02575436 0.02245674 #> 2 0.03132758 0.03646152 0.03180135 #> 3 0.04432578 0.05150151 0.04493660 #> 4 0.04959686 0.05769409 0.05037000 #> 5 0.05717106 0.06662796 0.05821481 #> 6 0.07002306 0.08180639 0.07169167 #> sehatalphahatprimedelta theta deltayhat_var taudothat_var betahat_var #> 1 0.01549760 0.509902 11.88117 0.001450647 0.001979622 #> 2 0.02192365 0.509902 22.95682 0.003008059 0.003931904 #> 3 0.03100592 0.509902 43.44672 0.005831230 0.007656005 #> 4 0.03469520 0.509902 53.55329 0.007209828 0.009448197 #> 5 0.03990358 0.509902 72.17274 0.009184364 0.012037354 #> 6 0.04877400 0.509902 108.71791 0.014349527 0.018798980 #> deltamhat_var alphahat_var alphahatbetahat_var taudothatprime_var #> 1 14.52007 0.001588460 0.001629514 0.001427243 #> 2 29.04096 0.003169325 0.003278402 0.002914653 #> 3 57.88289 0.006320279 0.006456290 0.005667776 #> 4 70.63911 0.007725923 0.008176040 0.007037819 #> 5 89.90227 0.009837431 0.010775171 0.008971593 #> 6 137.50455 0.015129464 0.016441848 0.013701399 #> betahatprime_var alphahatprime_var alphahatprimebetahatprime_var deltayhat_sd #> 1 0.001115531 0.0004762925 0.0008554514 3.446907 #> 2 0.002295539 0.0009446357 0.0017772939 4.791327 #> 3 0.004485883 0.0019137861 0.0034627502 6.591413 #> 4 0.005630105 0.0022908770 0.0043380395 7.318011 #> 5 0.007183288 0.0031651434 0.0056756510 8.495454 #> 6 0.010765379 0.0045239234 0.0084673427 10.426788 #> taudothat_sd betahat_sd deltamhat_sd alphahat_sd alphahatbetahat_sd #> 1 0.03808736 0.04449294 3.810520 0.03985549 0.04036724 #> 2 0.05484577 0.06270489 5.388967 0.05629676 0.05725733 #> 3 0.07636249 0.08749860 7.608081 0.07950018 0.08035104 #> 4 0.08491070 0.09720184 8.404708 0.08789723 0.09042146 #> 5 0.09583509 0.10971488 9.481681 0.09918382 0.10380352 #> 6 0.11978951 0.13710937 11.726233 0.12300189 0.12822577 #> taudothatprime_sd betahatprime_sd alphahatprime_sd #> 1 0.03777887 0.03339956 0.02182413 #> 2 0.05398753 0.04791178 0.03073493 #> 3 0.07528463 0.06697674 0.04374684 #> 4 0.08389171 0.07503403 0.04786311 #> 5 0.09471849 0.08475428 0.05625961 #> 6 0.11705297 0.10375634 0.06726012 #> alphahatprimebetahatprime_sd deltayhat_skew taudothat_skew betahat_skew #> 1 0.02924810 -0.11189608 0.04526033 0.08062364 #> 2 0.04215796 -0.09921983 0.06625112 0.10862226 #> 3 0.05884514 -0.22582795 0.14131299 0.19750168 #> 4 0.06586379 -0.17659536 0.10759489 0.15994334 #> 5 0.07533692 -0.23803758 0.13667266 0.18376024 #> 6 0.09201817 -0.33827248 0.06394001 0.33294036 #> deltamhat_skew alphahat_skew alphahatbetahat_skew taudothatprime_skew #> 1 -0.1244886 0.1288352 0.2285358 0.01423022 #> 2 -0.1658157 0.1693780 0.3516740 0.02890403 #> 3 -0.2159688 0.2298648 0.3960709 0.07144565 #> 4 -0.2279875 0.2383293 0.5003035 0.05682260 #> 5 -0.2536373 0.2581478 0.5610875 0.07594452 #> 6 -0.4283449 0.4335725 0.6935200 -0.01140531 #> betahatprime_skew alphahatprime_skew alphahatprimebetahatprime_skew #> 1 -0.04927868 -0.03568500 0.0977280 #> 2 -0.10114995 -0.06753966 0.1712669 #> 3 -0.20092669 -0.18613920 0.1311243 #> 4 -0.15405515 -0.25939987 0.2467286 #> 5 -0.20139500 -0.24317416 0.2550646 #> 6 -0.15320045 -0.33115197 0.2753060 #> deltayhat_kurt taudothat_kurt betahat_kurt deltamhat_kurt alphahat_kurt #> 1 -0.005223661 0.16457793 0.03800433 0.02285397 0.01345425 #> 2 0.128091123 0.05439656 0.05200623 0.17566066 0.12952776 #> 3 0.391580265 0.30535396 0.26718692 0.23385350 0.24462746 #> 4 0.125151593 0.15156126 0.25545226 0.23583238 0.21267829 #> 5 0.149360007 0.11125021 0.11922652 0.16857243 0.13855946 #> 6 0.396392801 0.30936886 0.42265206 0.56158082 0.55551049 #> alphahatbetahat_kurt taudothatprime_kurt betahatprime_kurt alphahatprime_kurt #> 1 0.008517298 0.15188677 0.05933065 -0.06144867 #> 2 0.376565987 0.03573336 0.10983178 0.05417757 #> 3 0.334225794 0.17981996 0.21266383 -0.03386579 #> 4 0.595230022 0.05407503 0.17436503 0.26808868 #> 5 0.659167445 0.10453837 0.09818848 0.05059044 #> 6 1.088106452 0.07501243 0.09609666 0.02074679 #> alphahatprimebetahatprime_kurt deltayhat_bias taudothat_bias betahat_bias #> 1 0.06721209 -0.006667485 5.510376e-04 -0.0005425155 #> 2 0.16011550 -0.107687247 3.321864e-04 0.0008590961 #> 3 0.06734811 -0.242597406 -3.082815e-04 0.0028263145 #> 4 0.19439406 -0.248114080 6.163864e-05 0.0026173415 #> 5 0.20478619 -0.124446981 -6.659869e-04 0.0018699631 #> 6 0.11258893 -0.680137032 2.913023e-03 0.0041376472 #> deltamhat_bias alphahat_bias alphahatbetahat_bias taudothatprime_bias #> 1 -0.1051054 0.001058212 0.000174185 0.0005604681 #> 2 -0.2139106 0.002398469 0.001949935 -0.0001587614 #> 3 -0.1145688 0.001177233 0.002131032 -0.0004194097 #> 4 -0.3819700 0.003945640 0.003911591 -0.0004869178 #> 5 -0.4972155 0.005154854 0.004322788 -0.0007482427 #> 6 -0.8185873 0.008583132 0.007656188 0.0020373111 #> betahatprime_bias alphahatprime_bias alphahatprimebetahatprime_bias #> 1 -0.0003323677 -1.470616e-04 -0.0003012044 #> 2 -0.0002058520 -4.080295e-04 -0.0003283148 #> 3 0.0007074980 -7.542712e-04 0.0001224912 #> 4 -0.0000214116 -1.136769e-03 -0.0006145513 #> 5 0.0011860103 -9.859369e-05 0.0010245705 #> 6 -0.0014629032 2.132911e-04 -0.0004689367 #> deltayhat_mse taudothat_mse betahat_mse deltamhat_mse alphahat_mse #> 1 11.87884 0.001450660 0.001979520 14.52821 0.001589262 #> 2 22.96382 0.003007568 0.003931855 29.08091 0.003174444 #> 3 43.49689 0.005830159 0.007662462 57.88444 0.006320401 #> 4 53.60414 0.007208390 0.009453158 70.77089 0.007739946 #> 5 72.17379 0.009182971 0.012038444 90.13151 0.009862036 #> 6 109.15876 0.014355143 0.018812340 138.14714 0.015200109 #> alphahatbetahat_mse taudothatprime_mse betahatprime_mse alphahatprime_mse #> 1 0.001629219 0.001427272 0.001115418 0.0004762189 #> 2 0.003281549 0.002914096 0.002295122 0.0009446133 #> 3 0.006459540 0.005666819 0.004485487 0.0019139723 #> 4 0.008189705 0.007036648 0.005628980 0.0022917110 #> 5 0.010791703 0.008970358 0.007183258 0.0031645201 #> 6 0.016497177 0.013702809 0.010765366 0.0045230641 #> alphahatprimebetahatprime_mse deltayhat_rmse taudothat_rmse betahat_rmse #> 1 0.000855371 3.446569 0.03808754 0.04449180 #> 2 0.001777046 4.792058 0.05484130 0.06270451 #> 3 0.003462073 6.595217 0.07635548 0.08753549 #> 4 0.004337550 7.321485 0.08490224 0.09722735 #> 5 0.005675566 8.495516 0.09582782 0.10971984 #> 6 0.008465869 10.447907 0.11981295 0.13715809 #> deltamhat_rmse alphahat_rmse alphahatbetahat_rmse taudothatprime_rmse #> 1 3.811589 0.03986555 0.04036358 0.03777925 #> 2 5.392672 0.05634220 0.05728481 0.05398236 #> 3 7.608182 0.07950095 0.08037126 0.07527827 #> 4 8.412543 0.08797696 0.09049699 0.08388473 #> 5 9.493762 0.09930778 0.10388312 0.09471198 #> 6 11.753601 0.12328872 0.12844134 0.11705900 #> betahatprime_rmse alphahatprime_rmse alphahatprimebetahatprime_rmse missing #> 1 0.03339788 0.02182244 0.02924673 Complete #> 2 0.04790743 0.03073456 0.04215503 Complete #> 3 0.06697378 0.04374897 0.05883938 Complete #> 4 0.07502653 0.04787182 0.06586008 Complete #> 5 0.08475410 0.05625407 0.07533635 Complete #> 6 0.10375628 0.06725373 0.09201016 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 14.4 14.3 14.2 14.2 14.3 ... #> $ taudothat : num 0.142 0.142 0.141 0.141 0.141 ... #> $ betahat : num 0.714 0.715 0.717 0.717 0.716 ... #> $ deltamhat : num 28.5 28.4 28.5 28.2 28.1 ... #> $ alphahat : num 0.715 0.716 0.715 0.718 0.719 ... #> $ alphahatbetahat : num 0.51 0.512 0.512 0.514 0.514 ... #> $ taudothatprime : num 0.142 0.141 0.141 0.141 0.141 ... #> $ betahatprime : num 0.714 0.714 0.715 0.714 0.715 ... #> $ alphahatprime : num 0.714 0.714 0.713 0.713 0.714 ... #> $ alphahatprimebetahatprime : num 0.51 0.51 0.51 0.509 0.511 ... #> $ sigma2xhat : num 225 225 226 223 224 ... #> $ sigma2hatepsilonmhat : num 110 110 110 109 108 ... #> $ sigma2hatepsilonyhat : num 73 73.1 72 71.9 70.6 ... #> $ muxhat : num 100 100 100 100 100 ... #> $ sehatdeltayhat : num 1.97 2.8 3.96 4.45 5.11 ... #> $ sehattaudothat : num 0.0258 0.0367 0.0518 0.0583 0.0672 ... #> $ sehatbetahat : num 0.0258 0.0366 0.0518 0.0581 0.067 ... #> $ sehatdeltamhat : num 2.24 3.18 4.49 5.04 5.82 ... #> $ sehatalphahat : num 0.0222 0.0314 0.0444 0.0499 0.0576 ... #> $ sehattaudothatprimetb : num 0.0258 0.0366 0.0517 0.058 0.067 ... #> $ sehatbetahatprimetb : num 0.0258 0.0366 0.0517 0.058 0.067 ... #> $ sehatalphahatprimetb : num 0.0221 0.0313 0.0443 0.0496 0.0572 ... #> $ sehattaudothatprimedelta : num 0.0258 0.0365 0.0515 0.0577 0.0666 ... #> $ sehatbetahatprimedelta : num 0.0225 0.0318 0.0449 0.0504 0.0582 ... #> $ sehatalphahatprimedelta : num 0.0155 0.0219 0.031 0.0347 0.0399 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ deltayhat_var : num 11.9 23 43.4 53.6 72.2 ... #> $ taudothat_var : num 0.00145 0.00301 0.00583 0.00721 0.00918 ... #> $ betahat_var : num 0.00198 0.00393 0.00766 0.00945 0.01204 ... #> $ deltamhat_var : num 14.5 29 57.9 70.6 89.9 ... #> $ alphahat_var : num 0.00159 0.00317 0.00632 0.00773 0.00984 ... #> $ alphahatbetahat_var : num 0.00163 0.00328 0.00646 0.00818 0.01078 ... #> $ taudothatprime_var : num 0.00143 0.00291 0.00567 0.00704 0.00897 ... #> $ betahatprime_var : num 0.00112 0.0023 0.00449 0.00563 0.00718 ... #> $ alphahatprime_var : num 0.000476 0.000945 0.001914 0.002291 0.003165 ... #> $ alphahatprimebetahatprime_var : num 0.000855 0.001777 0.003463 0.004338 0.005676 ... #> $ deltayhat_sd : num 3.45 4.79 6.59 7.32 8.5 ... #> $ taudothat_sd : num 0.0381 0.0548 0.0764 0.0849 0.0958 ... #> $ betahat_sd : num 0.0445 0.0627 0.0875 0.0972 0.1097 ... #> $ deltamhat_sd : num 3.81 5.39 7.61 8.4 9.48 ... #> $ alphahat_sd : num 0.0399 0.0563 0.0795 0.0879 0.0992 ... #> $ alphahatbetahat_sd : num 0.0404 0.0573 0.0804 0.0904 0.1038 ... #> $ taudothatprime_sd : num 0.0378 0.054 0.0753 0.0839 0.0947 ... #> $ betahatprime_sd : num 0.0334 0.0479 0.067 0.075 0.0848 ... #> $ alphahatprime_sd : num 0.0218 0.0307 0.0437 0.0479 0.0563 ... #> $ alphahatprimebetahatprime_sd : num 0.0292 0.0422 0.0588 0.0659 0.0753 ... #> $ deltayhat_skew : num -0.1119 -0.0992 -0.2258 -0.1766 -0.238 ... #> $ taudothat_skew : num 0.0453 0.0663 0.1413 0.1076 0.1367 ... #> $ betahat_skew : num 0.0806 0.1086 0.1975 0.1599 0.1838 ... #> $ deltamhat_skew : num -0.124 -0.166 -0.216 -0.228 -0.254 ... #> $ alphahat_skew : num 0.129 0.169 0.23 0.238 0.258 ... #> $ alphahatbetahat_skew : num 0.229 0.352 0.396 0.5 0.561 ... #> $ taudothatprime_skew : num 0.0142 0.0289 0.0714 0.0568 0.0759 ... #> $ betahatprime_skew : num -0.0493 -0.1011 -0.2009 -0.1541 -0.2014 ... #> $ alphahatprime_skew : num -0.0357 -0.0675 -0.1861 -0.2594 -0.2432 ... #> $ alphahatprimebetahatprime_skew: num 0.0977 0.1713 0.1311 0.2467 0.2551 ... #> $ deltayhat_kurt : num -0.00522 0.12809 0.39158 0.12515 0.14936 ... #> $ taudothat_kurt : num 0.1646 0.0544 0.3054 0.1516 0.1113 ... #> $ betahat_kurt : num 0.038 0.052 0.267 0.255 0.119 ... #> $ deltamhat_kurt : num 0.0229 0.1757 0.2339 0.2358 0.1686 ... #> $ alphahat_kurt : num 0.0135 0.1295 0.2446 0.2127 0.1386 ... #> $ alphahatbetahat_kurt : num 0.00852 0.37657 0.33423 0.59523 0.65917 ... #> $ taudothatprime_kurt : num 0.1519 0.0357 0.1798 0.0541 0.1045 ... #> $ betahatprime_kurt : num 0.0593 0.1098 0.2127 0.1744 0.0982 ... #> $ alphahatprime_kurt : num -0.0614 0.0542 -0.0339 0.2681 0.0506 ... #> $ alphahatprimebetahatprime_kurt: num 0.0672 0.1601 0.0673 0.1944 0.2048 ... #> $ deltayhat_bias : num -0.00667 -0.10769 -0.2426 -0.24811 -0.12445 ... #> $ taudothat_bias : num 5.51e-04 3.32e-04 -3.08e-04 6.16e-05 -6.66e-04 ... #> $ betahat_bias : num -0.000543 0.000859 0.002826 0.002617 0.00187 ... #> $ deltamhat_bias : num -0.105 -0.214 -0.115 -0.382 -0.497 ... #> $ alphahat_bias : num 0.00106 0.0024 0.00118 0.00395 0.00515 ... #> $ alphahatbetahat_bias : num 0.000174 0.00195 0.002131 0.003912 0.004323 ... #> $ taudothatprime_bias : num 0.00056 -0.000159 -0.000419 -0.000487 -0.000748 ... #> $ betahatprime_bias : num -3.32e-04 -2.06e-04 7.07e-04 -2.14e-05 1.19e-03 ... #> $ alphahatprime_bias : num -1.47e-04 -4.08e-04 -7.54e-04 -1.14e-03 -9.86e-05 ... #> $ alphahatprimebetahatprime_bias: num -0.000301 -0.000328 0.000122 -0.000615 0.001025 ... #> $ deltayhat_mse : num 11.9 23 43.5 53.6 72.2 ... #> $ taudothat_mse : num 0.00145 0.00301 0.00583 0.00721 0.00918 ... #> $ betahat_mse : num 0.00198 0.00393 0.00766 0.00945 0.01204 ... #> $ deltamhat_mse : num 14.5 29.1 57.9 70.8 90.1 ... #> $ alphahat_mse : num 0.00159 0.00317 0.00632 0.00774 0.00986 ... #> $ alphahatbetahat_mse : num 0.00163 0.00328 0.00646 0.00819 0.01079 ... #> $ taudothatprime_mse : num 0.00143 0.00291 0.00567 0.00704 0.00897 ... #> $ betahatprime_mse : num 0.00112 0.0023 0.00449 0.00563 0.00718 ... #> $ alphahatprime_mse : num 0.000476 0.000945 0.001914 0.002292 0.003165 ... #> $ alphahatprimebetahatprime_mse : num 0.000855 0.001777 0.003462 0.004338 0.005676 ... #> [list output truncated]