R/results_beta_fit.ols.R
results_beta_fit.ols.RdResults: Simple Mediation Model - Beta X alpha = beta = 1.5 - Complete Data - Fit Ordinary Least Squares
results_beta_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_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.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 0.0625 #> 2 2 500 5000 0.1414214 0.7140742 0.7140742 0.509902 0.0625 #> 3 3 250 5000 0.1414214 0.7140742 0.7140742 0.509902 0.0625 #> 4 4 200 5000 0.1414214 0.7140742 0.7140742 0.509902 0.0625 #> 5 5 150 5000 0.1414214 0.7140742 0.7140742 0.509902 0.0625 #> 6 6 100 5000 0.1414214 0.7140742 0.7140742 0.509902 0.0625 #> sigma2epsilonm sigma2epsilony mux deltam deltay deltayhat taudothat #> 1 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07219676 0.1413090 #> 2 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07220273 0.1415266 #> 3 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07231892 0.1416146 #> 4 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07241849 0.1415711 #> 5 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07186064 0.1402250 #> 6 0.03063113 0.02036725 0.5 0.1429629 0.07225223 0.07211498 0.1424528 #> betahat deltamhat alphahat alphahatbetahat taudothatprime betahatprime #> 1 0.7141784 0.1427821 0.7140558 0.5099650 0.1413610 0.7140157 #> 2 0.7139825 0.1428024 0.7139783 0.5097486 0.1415948 0.7136749 #> 3 0.7135569 0.1427523 0.7141594 0.5095853 0.1416203 0.7132642 #> 4 0.7133708 0.1423918 0.7148483 0.5098832 0.1416216 0.7132756 #> 5 0.7157948 0.1428798 0.7138991 0.5110294 0.1402442 0.7145832 #> 6 0.7136548 0.1431522 0.7132494 0.5088843 0.1426544 0.7123351 #> alphahatprime alphahatprimebetahatprime sigma2xhat sigma2hatepsilonmhat #> 1 0.7142405 0.5099980 0.06252239 0.03060062 #> 2 0.7141497 0.5096986 0.06253973 0.03060757 #> 3 0.7134413 0.5089413 0.06249061 0.03069570 #> 4 0.7139469 0.5093047 0.06245731 0.03064159 #> 5 0.7136493 0.5100955 0.06253869 0.03063821 #> 6 0.7128147 0.5079326 0.06252996 0.03065388 #> sigma2hatepsilonyhat muxhat sehatdeltayhat sehattaudothat sehatbetahat #> 1 0.02036407 0.5000012 0.01075160 0.02582136 0.02583621 #> 2 0.02037148 0.4998029 0.01521900 0.03656400 0.03659709 #> 3 0.02041973 0.4998144 0.02159554 0.05188666 0.05189788 #> 4 0.02039031 0.5003326 0.02416856 0.05810471 0.05811871 #> 5 0.02038871 0.4999881 0.02794057 0.06717238 0.06728139 #> 6 0.02035298 0.5003056 0.03434097 0.08253855 0.08273614 #> sehatdeltamhat sehatalphahat sehattaudothatprimetb sehatbetahatprimetb #> 1 0.01237362 0.02213680 0.02583154 0.02583154 #> 2 0.01750151 0.03132402 0.03658481 0.03658481 #> 3 0.02481919 0.04443706 0.05188443 0.05188443 #> 4 0.02776858 0.04968519 0.05812473 0.05812473 #> 5 0.03205574 0.05739466 0.06718214 0.06718214 #> 6 0.03935716 0.07046351 0.08263599 0.08263599 #> sehatalphahatprimetb sehattaudothatprimedelta sehatbetahatprimedelta #> 1 0.02214512 0.02578648 0.02247747 #> 2 0.03134042 0.03649815 0.03182476 #> 3 0.04441475 0.05169860 0.04509271 #> 4 0.04964971 0.05788165 0.05050549 #> 5 0.05741333 0.06683621 0.05829246 #> 6 0.07051905 0.08204154 0.07166761 #> sehatalphahatprimedelta theta deltayhat_var taudothat_var betahat_var #> 1 0.01549177 0.509902 0.0001168391 0.0006430459 0.0006494112 #> 2 0.02191649 0.509902 0.0002376961 0.0013637734 0.0013617549 #> 3 0.03106088 0.509902 0.0004563299 0.0027006214 0.0026892351 #> 4 0.03467876 0.509902 0.0005700355 0.0033162813 0.0033498529 #> 5 0.04008564 0.509902 0.0007604170 0.0045857132 0.0045618744 #> 6 0.04921290 0.509902 0.0012485261 0.0066657425 0.0069609530 #> deltamhat_var alphahat_var alphahatbetahat_var taudothatprime_var #> 1 0.0001520294 0.0004918727 0.0005837418 0.0006394744 #> 2 0.0003112341 0.0010160099 0.0011956067 0.0013537117 #> 3 0.0006350150 0.0020105787 0.0023823780 0.0026939078 #> 4 0.0007860254 0.0024568123 0.0029028671 0.0032976222 #> 5 0.0010008343 0.0032295190 0.0040028365 0.0045413241 #> 6 0.0015826900 0.0051255588 0.0060138926 0.0066373798 #> betahatprime_var alphahatprime_var alphahatprimebetahatprime_var deltayhat_sd #> 1 0.0004848096 0.0002131339 0.0003758568 0.01080921 #> 2 0.0010240542 0.0004139539 0.0007628163 0.01541740 #> 3 0.0020475256 0.0008731960 0.0015646503 0.02136188 #> 4 0.0024816575 0.0010822144 0.0018910240 0.02387542 #> 5 0.0034392594 0.0014082845 0.0026216159 0.02757566 #> 6 0.0050764922 0.0022583959 0.0039325481 0.03533449 #> taudothat_sd betahat_sd deltamhat_sd alphahat_sd alphahatbetahat_sd #> 1 0.02535835 0.02548355 0.01233002 0.02217820 0.02416075 #> 2 0.03692930 0.03690196 0.01764183 0.03187491 0.03457755 #> 3 0.05196750 0.05185784 0.02519950 0.04483948 0.04880961 #> 4 0.05758716 0.05787791 0.02803614 0.04956624 0.05387826 #> 5 0.06771789 0.06754165 0.03163597 0.05682886 0.06326797 #> 6 0.08164400 0.08343233 0.03978304 0.07159301 0.07754929 #> taudothatprime_sd betahatprime_sd alphahatprime_sd #> 1 0.02528783 0.02201839 0.01459911 #> 2 0.03679282 0.03200085 0.02034586 #> 3 0.05190287 0.04524959 0.02954989 #> 4 0.05742493 0.04981624 0.03289703 #> 5 0.06738935 0.05864520 0.03752712 #> 6 0.08147012 0.07124951 0.04752258 #> alphahatprimebetahatprime_sd deltayhat_skew taudothat_skew betahat_skew #> 1 0.01938703 0.02299522 -0.002463881 -0.02353780 #> 2 0.02761913 0.03214979 0.016336007 0.05245159 #> 3 0.03955566 -0.06120237 -0.046416906 0.03248882 #> 4 0.04348591 -0.02986923 0.069565468 -0.02333646 #> 5 0.05120172 -0.07141280 -0.016995428 0.04034641 #> 6 0.06271003 -0.04913833 -0.097241966 0.02302551 #> deltamhat_skew alphahat_skew alphahatbetahat_skew taudothatprime_skew #> 1 0.03115856 -0.011217548 0.03329793 -0.0138224944 #> 2 0.04764861 -0.034436275 0.14534040 0.0002902731 #> 3 0.03439394 -0.015596671 0.09148722 -0.0637205685 #> 4 0.01279562 -0.035739284 0.14989343 0.0598792292 #> 5 0.03969889 -0.009504646 0.14800164 -0.0332963392 #> 6 0.02719404 -0.062057624 0.15105105 -0.1168119280 #> betahatprime_skew alphahatprime_skew alphahatprimebetahatprime_skew #> 1 -0.07209360 -0.1075240 0.03214489 #> 2 -0.05119566 -0.1542810 0.04982212 #> 3 -0.10347393 -0.1564074 0.09180098 #> 4 -0.18300568 -0.3380634 0.02503877 #> 5 -0.11394109 -0.3239791 0.06970095 #> 6 -0.10033480 -0.4180405 0.11404048 #> deltayhat_kurt taudothat_kurt betahat_kurt deltamhat_kurt alphahat_kurt #> 1 0.070713114 -0.01698455 -0.11527452 -0.077830628 0.005222976 #> 2 -0.082794027 -0.02305574 -0.07231720 0.010420217 0.074218174 #> 3 -0.017952618 0.11245282 0.01007362 0.200824440 0.150943168 #> 4 -0.006005591 -0.01414928 -0.07783698 0.006284955 -0.034304979 #> 5 0.139718024 -0.05124505 0.19373174 0.122937023 0.078910343 #> 6 -0.087659490 0.06550892 0.02970623 0.066784824 0.019409412 #> alphahatbetahat_kurt taudothatprime_kurt betahatprime_kurt alphahatprime_kurt #> 1 -0.10316533 -0.05390806 -0.04307499 0.00914716 #> 2 -0.02564765 -0.04875285 -0.05665908 -0.02895919 #> 3 0.13513634 0.06893840 0.10067150 0.10401693 #> 4 0.03712431 -0.01048777 0.10315099 0.17803599 #> 5 0.10676255 -0.04115546 0.05700431 0.21766121 #> 6 0.03270942 0.06180440 0.08406342 0.35213414 #> alphahatprimebetahatprime_kurt deltayhat_bias taudothat_bias betahat_bias #> 1 -0.01787360 -5.546569e-05 -0.0001123180 1.042056e-04 #> 2 0.01837595 -4.949973e-05 0.0001052425 -9.174092e-05 #> 3 0.05950888 6.669170e-05 0.0001932614 -5.172904e-04 #> 4 0.02087533 1.662661e-04 0.0001497823 -7.033711e-04 #> 5 0.01470869 -3.915904e-04 -0.0011963717 1.720598e-03 #> 6 0.10623242 -1.372506e-04 0.0010314164 -4.194408e-04 #> deltamhat_bias alphahat_bias alphahatbetahat_bias taudothatprime_bias #> 1 -1.808363e-04 -1.836486e-05 6.307143e-05 -6.033005e-05 #> 2 -1.605059e-04 -9.587248e-05 -1.533673e-04 1.734491e-04 #> 3 -2.105779e-04 8.520315e-05 -3.166124e-04 1.989063e-04 #> 4 -5.710923e-04 7.740661e-04 -1.877800e-05 2.001988e-04 #> 5 -8.308506e-05 -1.750937e-04 1.127497e-03 -1.177205e-03 #> 6 1.893168e-04 -8.248087e-04 -1.017694e-03 1.233094e-03 #> betahatprime_bias alphahatprime_bias alphahatprimebetahatprime_bias #> 1 -5.849176e-05 1.663010e-04 0.0000959988 #> 2 -3.992720e-04 7.550934e-05 -0.0002033735 #> 3 -8.100286e-04 -6.329185e-04 -0.0009606649 #> 4 -7.985620e-04 -1.273398e-04 -0.0005972457 #> 5 5.089766e-04 -4.248573e-04 0.0001935644 #> 6 -1.739118e-03 -1.259457e-03 -0.0019693376 #> deltayhat_mse taudothat_mse betahat_mse deltamhat_mse alphahat_mse #> 1 0.0001168188 0.0006429299 0.0006492922 0.0001520317 0.0004917746 #> 2 0.0002376510 0.0013635118 0.0013614910 0.0003111976 0.0010158159 #> 3 0.0004562431 0.0027001186 0.0026889649 0.0006349324 0.0020101838 #> 4 0.0005699491 0.0033156405 0.0033496777 0.0007861944 0.0024569201 #> 5 0.0007604183 0.0045862274 0.0045639225 0.0010006411 0.0032289038 #> 6 0.0012482953 0.0066654732 0.0069597368 0.0015824093 0.0051252140 #> alphahatbetahat_mse taudothatprime_mse betahatprime_mse alphahatprime_mse #> 1 0.000583629 0.0006393501 0.0004847161 0.0002131189 #> 2 0.001195391 0.0013534711 0.0010240088 0.0004138768 #> 3 0.002382002 0.0026934086 0.0020477722 0.0008734219 #> 4 0.002902287 0.0032970027 0.0024817988 0.0010820142 #> 5 0.004003307 0.0045418016 0.0034388306 0.0014081833 #> 6 0.006013726 0.0066375729 0.0050785015 0.0022595304 #> alphahatprimebetahatprime_mse deltayhat_rmse taudothat_rmse betahat_rmse #> 1 0.0003757908 0.01080828 0.02535606 0.02548121 #> 2 0.0007627051 0.01541593 0.03692576 0.03689839 #> 3 0.0015652602 0.02135985 0.05196267 0.05185523 #> 4 0.0018910025 0.02387361 0.05758160 0.05787640 #> 5 0.0026211290 0.02757568 0.06772169 0.06755681 #> 6 0.0039356399 0.03533122 0.08164235 0.08342504 #> deltamhat_rmse alphahat_rmse alphahatbetahat_rmse taudothatprime_rmse #> 1 0.01233011 0.02217599 0.02415842 0.02528537 #> 2 0.01764079 0.03187187 0.03457443 0.03678955 #> 3 0.02519786 0.04483507 0.04880576 0.05189806 #> 4 0.02803916 0.04956733 0.05387288 0.05741953 #> 5 0.03163291 0.05682344 0.06327169 0.06739289 #> 6 0.03977951 0.07159060 0.07754821 0.08147130 #> betahatprime_rmse alphahatprime_rmse alphahatprimebetahatprime_rmse missing #> 1 0.02201627 0.01459859 0.01938532 Complete #> 2 0.03200014 0.02034396 0.02761712 Complete #> 3 0.04525232 0.02955371 0.03956337 Complete #> 4 0.04981766 0.03289398 0.04348566 Complete #> 5 0.05864154 0.03752577 0.05119696 Complete #> 6 0.07126361 0.04753452 0.06273468 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 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 ... #> $ sigma2epsilonm : num 0.0306 0.0306 0.0306 0.0306 0.0306 ... #> $ sigma2epsilony : num 0.0204 0.0204 0.0204 0.0204 0.0204 ... #> $ mux : num 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ... #> $ deltam : num 0.143 0.143 0.143 0.143 0.143 ... #> $ deltay : num 0.0723 0.0723 0.0723 0.0723 0.0723 ... #> $ deltayhat : num 0.0722 0.0722 0.0723 0.0724 0.0719 ... #> $ taudothat : num 0.141 0.142 0.142 0.142 0.14 ... #> $ betahat : num 0.714 0.714 0.714 0.713 0.716 ... #> $ deltamhat : num 0.143 0.143 0.143 0.142 0.143 ... #> $ alphahat : num 0.714 0.714 0.714 0.715 0.714 ... #> $ alphahatbetahat : num 0.51 0.51 0.51 0.51 0.511 ... #> $ taudothatprime : num 0.141 0.142 0.142 0.142 0.14 ... #> $ betahatprime : num 0.714 0.714 0.713 0.713 0.715 ... #> $ alphahatprime : num 0.714 0.714 0.713 0.714 0.714 ... #> $ alphahatprimebetahatprime : num 0.51 0.51 0.509 0.509 0.51 ... #> $ sigma2xhat : num 0.0625 0.0625 0.0625 0.0625 0.0625 ... #> $ sigma2hatepsilonmhat : num 0.0306 0.0306 0.0307 0.0306 0.0306 ... #> $ sigma2hatepsilonyhat : num 0.0204 0.0204 0.0204 0.0204 0.0204 ... #> $ muxhat : num 0.5 0.5 0.5 0.5 0.5 ... #> $ sehatdeltayhat : num 0.0108 0.0152 0.0216 0.0242 0.0279 ... #> $ sehattaudothat : num 0.0258 0.0366 0.0519 0.0581 0.0672 ... #> $ sehatbetahat : num 0.0258 0.0366 0.0519 0.0581 0.0673 ... #> $ sehatdeltamhat : num 0.0124 0.0175 0.0248 0.0278 0.0321 ... #> $ sehatalphahat : num 0.0221 0.0313 0.0444 0.0497 0.0574 ... #> $ sehattaudothatprimetb : num 0.0258 0.0366 0.0519 0.0581 0.0672 ... #> $ sehatbetahatprimetb : num 0.0258 0.0366 0.0519 0.0581 0.0672 ... #> $ sehatalphahatprimetb : num 0.0221 0.0313 0.0444 0.0496 0.0574 ... #> $ 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 0.0219 0.0311 0.0347 0.0401 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ deltayhat_var : num 0.000117 0.000238 0.000456 0.00057 0.00076 ... #> $ taudothat_var : num 0.000643 0.001364 0.002701 0.003316 0.004586 ... #> $ betahat_var : num 0.000649 0.001362 0.002689 0.00335 0.004562 ... #> $ deltamhat_var : num 0.000152 0.000311 0.000635 0.000786 0.001001 ... #> $ alphahat_var : num 0.000492 0.001016 0.002011 0.002457 0.00323 ... #> $ alphahatbetahat_var : num 0.000584 0.001196 0.002382 0.002903 0.004003 ... #> $ taudothatprime_var : num 0.000639 0.001354 0.002694 0.003298 0.004541 ... #> $ betahatprime_var : num 0.000485 0.001024 0.002048 0.002482 0.003439 ... #> $ alphahatprime_var : num 0.000213 0.000414 0.000873 0.001082 0.001408 ... #> $ alphahatprimebetahatprime_var : num 0.000376 0.000763 0.001565 0.001891 0.002622 ... #> $ deltayhat_sd : num 0.0108 0.0154 0.0214 0.0239 0.0276 ... #> $ taudothat_sd : num 0.0254 0.0369 0.052 0.0576 0.0677 ... #> $ betahat_sd : num 0.0255 0.0369 0.0519 0.0579 0.0675 ... #> $ deltamhat_sd : num 0.0123 0.0176 0.0252 0.028 0.0316 ... #> $ alphahat_sd : num 0.0222 0.0319 0.0448 0.0496 0.0568 ... #> $ alphahatbetahat_sd : num 0.0242 0.0346 0.0488 0.0539 0.0633 ... #> $ taudothatprime_sd : num 0.0253 0.0368 0.0519 0.0574 0.0674 ... #> $ betahatprime_sd : num 0.022 0.032 0.0452 0.0498 0.0586 ... #> $ alphahatprime_sd : num 0.0146 0.0203 0.0295 0.0329 0.0375 ... #> $ alphahatprimebetahatprime_sd : num 0.0194 0.0276 0.0396 0.0435 0.0512 ... #> $ deltayhat_skew : num 0.023 0.0321 -0.0612 -0.0299 -0.0714 ... #> $ taudothat_skew : num -0.00246 0.01634 -0.04642 0.06957 -0.017 ... #> $ betahat_skew : num -0.0235 0.0525 0.0325 -0.0233 0.0403 ... #> $ deltamhat_skew : num 0.0312 0.0476 0.0344 0.0128 0.0397 ... #> $ alphahat_skew : num -0.0112 -0.0344 -0.0156 -0.0357 -0.0095 ... #> $ alphahatbetahat_skew : num 0.0333 0.1453 0.0915 0.1499 0.148 ... #> $ taudothatprime_skew : num -0.01382 0.00029 -0.06372 0.05988 -0.0333 ... #> $ betahatprime_skew : num -0.0721 -0.0512 -0.1035 -0.183 -0.1139 ... #> $ alphahatprime_skew : num -0.108 -0.154 -0.156 -0.338 -0.324 ... #> $ alphahatprimebetahatprime_skew: num 0.0321 0.0498 0.0918 0.025 0.0697 ... #> $ deltayhat_kurt : num 0.07071 -0.08279 -0.01795 -0.00601 0.13972 ... #> $ taudothat_kurt : num -0.017 -0.0231 0.1125 -0.0141 -0.0512 ... #> $ betahat_kurt : num -0.1153 -0.0723 0.0101 -0.0778 0.1937 ... #> $ deltamhat_kurt : num -0.07783 0.01042 0.20082 0.00628 0.12294 ... #> $ alphahat_kurt : num 0.00522 0.07422 0.15094 -0.0343 0.07891 ... #> $ alphahatbetahat_kurt : num -0.1032 -0.0256 0.1351 0.0371 0.1068 ... #> $ taudothatprime_kurt : num -0.0539 -0.0488 0.0689 -0.0105 -0.0412 ... #> $ betahatprime_kurt : num -0.0431 -0.0567 0.1007 0.1032 0.057 ... #> $ alphahatprime_kurt : num 0.00915 -0.02896 0.10402 0.17804 0.21766 ... #> $ alphahatprimebetahatprime_kurt: num -0.0179 0.0184 0.0595 0.0209 0.0147 ... #> $ deltayhat_bias : num -5.55e-05 -4.95e-05 6.67e-05 1.66e-04 -3.92e-04 ... #> $ taudothat_bias : num -0.000112 0.000105 0.000193 0.00015 -0.001196 ... #> $ betahat_bias : num 1.04e-04 -9.17e-05 -5.17e-04 -7.03e-04 1.72e-03 ... #> $ deltamhat_bias : num -1.81e-04 -1.61e-04 -2.11e-04 -5.71e-04 -8.31e-05 ... #> $ alphahat_bias : num -1.84e-05 -9.59e-05 8.52e-05 7.74e-04 -1.75e-04 ... #> $ alphahatbetahat_bias : num 6.31e-05 -1.53e-04 -3.17e-04 -1.88e-05 1.13e-03 ... #> $ taudothatprime_bias : num -6.03e-05 1.73e-04 1.99e-04 2.00e-04 -1.18e-03 ... #> $ betahatprime_bias : num -5.85e-05 -3.99e-04 -8.10e-04 -7.99e-04 5.09e-04 ... #> $ alphahatprime_bias : num 1.66e-04 7.55e-05 -6.33e-04 -1.27e-04 -4.25e-04 ... #> $ alphahatprimebetahatprime_bias: num 0.000096 -0.000203 -0.000961 -0.000597 0.000194 ... #> $ deltayhat_mse : num 0.000117 0.000238 0.000456 0.00057 0.00076 ... #> $ taudothat_mse : num 0.000643 0.001364 0.0027 0.003316 0.004586 ... #> $ betahat_mse : num 0.000649 0.001361 0.002689 0.00335 0.004564 ... #> $ deltamhat_mse : num 0.000152 0.000311 0.000635 0.000786 0.001001 ... #> $ alphahat_mse : num 0.000492 0.001016 0.00201 0.002457 0.003229 ... #> $ alphahatbetahat_mse : num 0.000584 0.001195 0.002382 0.002902 0.004003 ... #> $ taudothatprime_mse : num 0.000639 0.001353 0.002693 0.003297 0.004542 ... #> $ betahatprime_mse : num 0.000485 0.001024 0.002048 0.002482 0.003439 ... #> $ alphahatprime_mse : num 0.000213 0.000414 0.000873 0.001082 0.001408 ... #> $ alphahatprimebetahatprime_mse : num 0.000376 0.000763 0.001565 0.001891 0.002621 ... #> [list output truncated]