R/results_exp_fit.ols.R
results_exp_fit.ols.RdResults: Simple Mediation Model - Exponential X lambda = 1 - Complete Data - Fit Ordinary Least Squares
results_exp_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_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 1 #> 2 2 500 5000 0.1414214 0.7140742 0.7140742 0.509902 1 #> 3 3 250 5000 0.1414214 0.7140742 0.7140742 0.509902 1 #> 4 4 200 5000 0.1414214 0.7140742 0.7140742 0.509902 1 #> 5 5 150 5000 0.1414214 0.7140742 0.7140742 0.509902 1 #> 6 6 100 5000 0.1414214 0.7140742 0.7140742 0.509902 1 #> sigma2epsilonm sigma2epsilony mux deltam deltay deltayhat taudothat #> 1 0.490098 0.325876 1 0.2859258 0.1445045 0.1450078 0.1415686 #> 2 0.490098 0.325876 1 0.2859258 0.1445045 0.1451758 0.1418667 #> 3 0.490098 0.325876 1 0.2859258 0.1445045 0.1445434 0.1408044 #> 4 0.490098 0.325876 1 0.2859258 0.1445045 0.1431462 0.1409378 #> 5 0.490098 0.325876 1 0.2859258 0.1445045 0.1442259 0.1418885 #> 6 0.490098 0.325876 1 0.2859258 0.1445045 0.1464650 0.1403272 #> betahat deltamhat alphahat alphahatbetahat taudothatprime betahatprime #> 1 0.7137108 0.2869607 0.7138296 0.5094746 0.1414673 0.7136377 #> 2 0.7132436 0.2859318 0.7141466 0.5093660 0.1416684 0.7130701 #> 3 0.7146170 0.2859848 0.7143917 0.5105374 0.1402169 0.7139551 #> 4 0.7153911 0.2852907 0.7146685 0.5112566 0.1402191 0.7138216 #> 5 0.7130362 0.2857807 0.7136600 0.5089419 0.1410686 0.7121289 #> 6 0.7146800 0.2865333 0.7142756 0.5104024 0.1391784 0.7131720 #> alphahatprime alphahatprimebetahatprime sigma2xhat sigma2hatepsilonmhat #> 1 0.7130206 0.5088930 0.9997733 0.4902828 #> 2 0.7129324 0.5084977 1.0015939 0.4895561 #> 3 0.7107909 0.5077094 0.9978277 0.4895739 #> 4 0.7102985 0.5072841 1.0004629 0.4902243 #> 5 0.7082469 0.5047737 0.9992111 0.4901606 #> 6 0.7076980 0.5053036 1.0108322 0.4900084 #> sigma2hatepsilonyhat muxhat sehatdeltayhat sehattaudothat sehatbetahat #> 1 0.3258615 0.9997649 0.02661980 0.02585197 0.02581918 #> 2 0.3260769 1.0006898 0.03771001 0.03667920 0.03660721 #> 3 0.3252409 0.9990497 0.05343338 0.05214067 0.05185623 #> 4 0.3261767 1.0009037 0.05992836 0.05850647 0.05811813 #> 5 0.3257194 0.9980635 0.06925537 0.06778786 0.06723273 #> 6 0.3263831 1.0044812 0.08543527 0.08369976 0.08284577 #> sehatdeltamhat sehatalphahat sehattaudothatprimetb sehatbetahatprimetb #> 1 0.03134656 0.02221575 0.02581767 0.02581767 #> 2 0.04434596 0.03146730 0.03660100 0.03660100 #> 3 0.06285854 0.04486148 0.05181943 0.05181943 #> 4 0.07042258 0.05029344 0.05800440 0.05800440 #> 5 0.08135729 0.05839325 0.06715526 0.06715526 #> 6 0.10005292 0.07192712 0.08270543 0.08270543 #> sehatalphahatprimetb sehattaudothatprimedelta sehatbetahatprimedelta #> 1 0.02217488 0.02577245 0.02245895 #> 2 0.03136793 0.03651390 0.03183749 #> 3 0.04451160 0.05163625 0.04498517 #> 4 0.04981053 0.05776534 0.05032902 #> 5 0.05769490 0.06680660 0.05823949 #> 6 0.07074661 0.08211612 0.07160101 #> sehatalphahatprimedelta theta deltayhat_var taudothat_var betahat_var #> 1 0.01554022 0.509902 0.0007047691 0.000644957 0.0006517374 #> 2 0.02197488 0.509902 0.0014216276 0.001342104 0.0013187779 #> 3 0.03124773 0.509902 0.0027850746 0.002728820 0.0026982663 #> 4 0.03497497 0.509902 0.0035795486 0.003286116 0.0033393785 #> 5 0.04059469 0.509902 0.0045852959 0.004536498 0.0044529332 #> 6 0.04973074 0.509902 0.0074800973 0.007056531 0.0067942211 #> deltamhat_var alphahat_var alphahatbetahat_var taudothatprime_var #> 1 0.0009618596 0.0004909821 0.0005890664 0.0006552748 #> 2 0.0019495348 0.0009777066 0.0011745503 0.0013441720 #> 3 0.0040090370 0.0020755309 0.0024697832 0.0027038549 #> 4 0.0049794366 0.0025814641 0.0030332373 0.0033078034 #> 5 0.0065742610 0.0035752548 0.0041690653 0.0044756480 #> 6 0.0104162764 0.0053674045 0.0061698092 0.0069059272 #> betahatprime_var alphahatprime_var alphahatprimebetahatprime_var deltayhat_sd #> 1 0.0004972387 0.0004228017 0.0005248724 0.02654749 #> 2 0.0010278723 0.0008468161 0.0010829115 0.03770448 #> 3 0.0020620082 0.0016997515 0.0021551368 0.05277381 #> 4 0.0024935885 0.0021000661 0.0026139439 0.05982933 #> 5 0.0034738284 0.0028767113 0.0036342596 0.06771481 #> 6 0.0051819531 0.0043749668 0.0054775494 0.08648756 #> taudothat_sd betahat_sd deltamhat_sd alphahat_sd alphahatbetahat_sd #> 1 0.02539600 0.02552915 0.03101386 0.02215812 0.02427069 #> 2 0.03663474 0.03631498 0.04415354 0.03126830 0.03427171 #> 3 0.05223811 0.05194484 0.06331696 0.04555800 0.04969691 #> 4 0.05732465 0.05778736 0.07056512 0.05080811 0.05507483 #> 5 0.06735353 0.06673030 0.08108182 0.05979343 0.06456830 #> 6 0.08400316 0.08242707 0.10206016 0.07326257 0.07854813 #> taudothatprime_sd betahatprime_sd alphahatprime_sd #> 1 0.02559834 0.02229885 0.02056214 #> 2 0.03666295 0.03206045 0.02910010 #> 3 0.05199860 0.04540934 0.04122804 #> 4 0.05751351 0.04993584 0.04582648 #> 5 0.06690028 0.05893919 0.05363498 #> 6 0.08310191 0.07198578 0.06614353 #> alphahatprimebetahatprime_sd deltayhat_skew taudothat_skew betahat_skew #> 1 0.02291009 -4.649989e-05 0.057401306 -0.039543084 #> 2 0.03290762 5.259699e-02 0.035036209 -0.068560593 #> 3 0.04642345 3.865016e-02 -0.011009973 0.052596195 #> 4 0.05112674 -3.795424e-02 0.008347009 -0.011815246 #> 5 0.06028482 -4.625504e-03 -0.036263120 0.009058143 #> 6 0.07401047 -1.391245e-02 -0.011513244 0.007355412 #> deltamhat_skew alphahat_skew alphahatbetahat_skew taudothatprime_skew #> 1 0.026489337 -0.005406192 0.03564941 0.05385375 #> 2 -0.078065119 0.074011948 0.04487426 0.03816758 #> 3 0.032016879 0.021712998 0.20952184 -0.03793943 #> 4 -0.004908548 0.019921287 0.19693178 0.03042881 #> 5 0.027127741 0.010088134 0.16029486 -0.05929431 #> 6 -0.046305266 0.055865469 0.25289709 -0.02165714 #> betahatprime_skew alphahatprime_skew alphahatprimebetahatprime_skew #> 1 -0.07235968 -0.1276512 0.073613423 #> 2 -0.12347473 -0.1723785 0.006458581 #> 3 -0.05265443 -0.3107598 0.061121889 #> 4 -0.07455399 -0.3206904 0.145227313 #> 5 -0.11243492 -0.3726426 0.076243837 #> 6 -0.13422267 -0.4992343 0.098711517 #> deltayhat_kurt taudothat_kurt betahat_kurt deltamhat_kurt alphahat_kurt #> 1 -0.03763664 0.06587203 -0.013346636 0.04608528 0.01198751 #> 2 0.06736518 0.01575856 0.024118225 0.18396729 0.08275047 #> 3 -0.08137897 0.19542526 0.044878869 -0.03566694 0.01100637 #> 4 -0.06415976 -0.02476623 -0.071595481 0.03884834 0.08786098 #> 5 0.04787826 0.11750275 0.004994493 0.08045303 0.21964348 #> 6 0.20880011 0.06958556 0.015128127 0.06629437 0.29678435 #> alphahatbetahat_kurt taudothatprime_kurt betahatprime_kurt alphahatprime_kurt #> 1 -0.067091838 0.032770881 0.06738897 0.03859525 #> 2 0.004955615 -0.002271283 0.06336703 0.11729396 #> 3 0.108389650 0.107121611 0.08716462 0.08513643 #> 4 0.025172779 -0.042812086 0.01254992 0.09555368 #> 5 0.023850590 0.071121805 0.13435595 0.14587351 #> 6 0.171785773 0.027256242 0.10043576 0.44074308 #> alphahatprimebetahatprime_kurt deltayhat_bias taudothat_bias betahat_bias #> 1 0.1282256890 5.033298e-04 0.0001471947 -0.0003633519 #> 2 -0.0422225330 6.713161e-04 0.0004453759 -0.0008305658 #> 3 -0.0089807132 3.894835e-05 -0.0006169177 0.0005428141 #> 4 -0.0001110411 -1.358263e-03 -0.0004835539 0.0013169316 #> 5 0.0809898560 -2.786003e-04 0.0004671776 -0.0010379630 #> 6 -0.0122702691 1.960565e-03 -0.0010941113 0.0006058012 #> deltamhat_bias alphahat_bias alphahatbetahat_bias taudothatprime_bias #> 1 1.034917e-03 -2.445640e-04 -0.0004273248 4.594278e-05 #> 2 5.990914e-06 7.241184e-05 -0.0005359284 2.470475e-04 #> 3 5.900803e-05 3.175352e-04 0.0006354986 -1.204453e-03 #> 4 -6.351228e-04 5.942673e-04 0.0013546899 -1.202306e-03 #> 5 -1.450832e-04 -4.141762e-04 -0.0009600977 -3.527248e-04 #> 6 6.074581e-04 2.013981e-04 0.0005004918 -2.242979e-03 #> betahatprime_bias alphahatprime_bias alphahatprimebetahatprime_bias #> 1 -0.0004364445 -0.001053552 -0.001008910 #> 2 -0.0010040946 -0.001141756 -0.001404217 #> 3 -0.0001190429 -0.003283264 -0.002192586 #> 4 -0.0002525800 -0.003775683 -0.002617899 #> 5 -0.0019452979 -0.005827249 -0.005128250 #> 6 -0.0009021546 -0.006376156 -0.004598373 #> deltayhat_mse taudothat_mse betahat_mse deltamhat_mse alphahat_mse #> 1 0.0007048815 0.0006448497 0.0006517391 0.0009627383 0.0004909437 #> 2 0.0014217939 0.0013420344 0.0013192040 0.0019491449 0.0009775163 #> 3 0.0027845191 0.0027286547 0.0026980213 0.0040082387 0.0020752167 #> 4 0.0035806776 0.0032856924 0.0033404449 0.0049788441 0.0025813010 #> 5 0.0045844565 0.0045358091 0.0044531199 0.0065729672 0.0035747112 #> 6 0.0074824451 0.0070563165 0.0067932292 0.0104145622 0.0053663716 #> alphahatbetahat_mse taudothatprime_mse betahatprime_mse alphahatprime_mse #> 1 0.0005891312 0.0006551459 0.0004973297 0.0004238271 #> 2 0.0011746026 0.0013439642 0.0010286749 0.0008479503 #> 3 0.0024696931 0.0027047648 0.0020616100 0.0017101913 #> 4 0.0030344659 0.0033085873 0.0024931536 0.0021139019 #> 5 0.0041691533 0.0044748772 0.0034769178 0.0029100928 #> 6 0.0061688258 0.0069095769 0.0051817306 0.0044147472 #> alphahatprimebetahatprime_mse deltayhat_rmse taudothat_rmse betahat_rmse #> 1 0.0005257853 0.02654960 0.02539389 0.02552918 #> 2 0.0010846667 0.03770668 0.03663379 0.03632085 #> 3 0.0021595132 0.05276854 0.05223653 0.05194248 #> 4 0.0026202745 0.05983876 0.05732096 0.05779658 #> 5 0.0036598317 0.06770861 0.06734842 0.06673170 #> 6 0.0054975989 0.08650113 0.08400188 0.08242105 #> deltamhat_rmse alphahat_rmse alphahatbetahat_rmse taudothatprime_rmse #> 1 0.03102802 0.02215725 0.02427202 0.02559582 #> 2 0.04414912 0.03126526 0.03427248 0.03666012 #> 3 0.06331065 0.04555455 0.04969601 0.05200735 #> 4 0.07056092 0.05080651 0.05508599 0.05752032 #> 5 0.08107384 0.05978889 0.06456898 0.06689452 #> 6 0.10205176 0.07325552 0.07854187 0.08312387 #> betahatprime_rmse alphahatprime_rmse alphahatprimebetahatprime_rmse missing #> 1 0.02230089 0.02058706 0.02293001 Complete #> 2 0.03207296 0.02911959 0.03293428 Complete #> 3 0.04540496 0.04135446 0.04647056 Complete #> 4 0.04993149 0.04597719 0.05118862 Complete #> 5 0.05896539 0.05394528 0.06049654 Complete #> 6 0.07198424 0.06644356 0.07414580 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 1 1 1 1 1 1 1 1 1 1 ... #> $ sigma2epsilonm : num 0.49 0.49 0.49 0.49 0.49 ... #> $ sigma2epsilony : num 0.326 0.326 0.326 0.326 0.326 ... #> $ mux : num 1 1 1 1 1 1 1 1 1 1 ... #> $ deltam : num 0.286 0.286 0.286 0.286 0.286 ... #> $ deltay : num 0.145 0.145 0.145 0.145 0.145 ... #> $ deltayhat : num 0.145 0.145 0.145 0.143 0.144 ... #> $ taudothat : num 0.142 0.142 0.141 0.141 0.142 ... #> $ betahat : num 0.714 0.713 0.715 0.715 0.713 ... #> $ deltamhat : num 0.287 0.286 0.286 0.285 0.286 ... #> $ alphahat : num 0.714 0.714 0.714 0.715 0.714 ... #> $ alphahatbetahat : num 0.509 0.509 0.511 0.511 0.509 ... #> $ taudothatprime : num 0.141 0.142 0.14 0.14 0.141 ... #> $ betahatprime : num 0.714 0.713 0.714 0.714 0.712 ... #> $ alphahatprime : num 0.713 0.713 0.711 0.71 0.708 ... #> $ alphahatprimebetahatprime : num 0.509 0.508 0.508 0.507 0.505 ... #> $ sigma2xhat : num 1 1.002 0.998 1 0.999 ... #> $ sigma2hatepsilonmhat : num 0.49 0.49 0.49 0.49 0.49 ... #> $ sigma2hatepsilonyhat : num 0.326 0.326 0.325 0.326 0.326 ... #> $ muxhat : num 1 1.001 0.999 1.001 0.998 ... #> $ sehatdeltayhat : num 0.0266 0.0377 0.0534 0.0599 0.0693 ... #> $ sehattaudothat : num 0.0259 0.0367 0.0521 0.0585 0.0678 ... #> $ sehatbetahat : num 0.0258 0.0366 0.0519 0.0581 0.0672 ... #> $ sehatdeltamhat : num 0.0313 0.0443 0.0629 0.0704 0.0814 ... #> $ sehatalphahat : num 0.0222 0.0315 0.0449 0.0503 0.0584 ... #> $ sehattaudothatprimetb : num 0.0258 0.0366 0.0518 0.058 0.0672 ... #> $ sehatbetahatprimetb : num 0.0258 0.0366 0.0518 0.058 0.0672 ... #> $ sehatalphahatprimetb : num 0.0222 0.0314 0.0445 0.0498 0.0577 ... #> $ sehattaudothatprimedelta : num 0.0258 0.0365 0.0516 0.0578 0.0668 ... #> $ sehatbetahatprimedelta : num 0.0225 0.0318 0.045 0.0503 0.0582 ... #> $ sehatalphahatprimedelta : num 0.0155 0.022 0.0312 0.035 0.0406 ... #> $ theta : num 0.51 0.51 0.51 0.51 0.51 ... #> $ deltayhat_var : num 0.000705 0.001422 0.002785 0.00358 0.004585 ... #> $ taudothat_var : num 0.000645 0.001342 0.002729 0.003286 0.004536 ... #> $ betahat_var : num 0.000652 0.001319 0.002698 0.003339 0.004453 ... #> $ deltamhat_var : num 0.000962 0.00195 0.004009 0.004979 0.006574 ... #> $ alphahat_var : num 0.000491 0.000978 0.002076 0.002581 0.003575 ... #> $ alphahatbetahat_var : num 0.000589 0.001175 0.00247 0.003033 0.004169 ... #> $ taudothatprime_var : num 0.000655 0.001344 0.002704 0.003308 0.004476 ... #> $ betahatprime_var : num 0.000497 0.001028 0.002062 0.002494 0.003474 ... #> $ alphahatprime_var : num 0.000423 0.000847 0.0017 0.0021 0.002877 ... #> $ alphahatprimebetahatprime_var : num 0.000525 0.001083 0.002155 0.002614 0.003634 ... #> $ deltayhat_sd : num 0.0265 0.0377 0.0528 0.0598 0.0677 ... #> $ taudothat_sd : num 0.0254 0.0366 0.0522 0.0573 0.0674 ... #> $ betahat_sd : num 0.0255 0.0363 0.0519 0.0578 0.0667 ... #> $ deltamhat_sd : num 0.031 0.0442 0.0633 0.0706 0.0811 ... #> $ alphahat_sd : num 0.0222 0.0313 0.0456 0.0508 0.0598 ... #> $ alphahatbetahat_sd : num 0.0243 0.0343 0.0497 0.0551 0.0646 ... #> $ taudothatprime_sd : num 0.0256 0.0367 0.052 0.0575 0.0669 ... #> $ betahatprime_sd : num 0.0223 0.0321 0.0454 0.0499 0.0589 ... #> $ alphahatprime_sd : num 0.0206 0.0291 0.0412 0.0458 0.0536 ... #> $ alphahatprimebetahatprime_sd : num 0.0229 0.0329 0.0464 0.0511 0.0603 ... #> $ deltayhat_skew : num -4.65e-05 5.26e-02 3.87e-02 -3.80e-02 -4.63e-03 ... #> $ taudothat_skew : num 0.0574 0.03504 -0.01101 0.00835 -0.03626 ... #> $ betahat_skew : num -0.03954 -0.06856 0.0526 -0.01182 0.00906 ... #> $ deltamhat_skew : num 0.02649 -0.07807 0.03202 -0.00491 0.02713 ... #> $ alphahat_skew : num -0.00541 0.07401 0.02171 0.01992 0.01009 ... #> $ alphahatbetahat_skew : num 0.0356 0.0449 0.2095 0.1969 0.1603 ... #> $ taudothatprime_skew : num 0.0539 0.0382 -0.0379 0.0304 -0.0593 ... #> $ betahatprime_skew : num -0.0724 -0.1235 -0.0527 -0.0746 -0.1124 ... #> $ alphahatprime_skew : num -0.128 -0.172 -0.311 -0.321 -0.373 ... #> $ alphahatprimebetahatprime_skew: num 0.07361 0.00646 0.06112 0.14523 0.07624 ... #> $ deltayhat_kurt : num -0.0376 0.0674 -0.0814 -0.0642 0.0479 ... #> $ taudothat_kurt : num 0.0659 0.0158 0.1954 -0.0248 0.1175 ... #> $ betahat_kurt : num -0.01335 0.02412 0.04488 -0.0716 0.00499 ... #> $ deltamhat_kurt : num 0.0461 0.184 -0.0357 0.0388 0.0805 ... #> $ alphahat_kurt : num 0.012 0.0828 0.011 0.0879 0.2196 ... #> $ alphahatbetahat_kurt : num -0.06709 0.00496 0.10839 0.02517 0.02385 ... #> $ taudothatprime_kurt : num 0.03277 -0.00227 0.10712 -0.04281 0.07112 ... #> $ betahatprime_kurt : num 0.0674 0.0634 0.0872 0.0125 0.1344 ... #> $ alphahatprime_kurt : num 0.0386 0.1173 0.0851 0.0956 0.1459 ... #> $ alphahatprimebetahatprime_kurt: num 0.128226 -0.042223 -0.008981 -0.000111 0.08099 ... #> $ deltayhat_bias : num 5.03e-04 6.71e-04 3.89e-05 -1.36e-03 -2.79e-04 ... #> $ taudothat_bias : num 0.000147 0.000445 -0.000617 -0.000484 0.000467 ... #> $ betahat_bias : num -0.000363 -0.000831 0.000543 0.001317 -0.001038 ... #> $ deltamhat_bias : num 1.03e-03 5.99e-06 5.90e-05 -6.35e-04 -1.45e-04 ... #> $ alphahat_bias : num -2.45e-04 7.24e-05 3.18e-04 5.94e-04 -4.14e-04 ... #> $ alphahatbetahat_bias : num -0.000427 -0.000536 0.000635 0.001355 -0.00096 ... #> $ taudothatprime_bias : num 4.59e-05 2.47e-04 -1.20e-03 -1.20e-03 -3.53e-04 ... #> $ betahatprime_bias : num -0.000436 -0.001004 -0.000119 -0.000253 -0.001945 ... #> $ alphahatprime_bias : num -0.00105 -0.00114 -0.00328 -0.00378 -0.00583 ... #> $ alphahatprimebetahatprime_bias: num -0.00101 -0.0014 -0.00219 -0.00262 -0.00513 ... #> $ deltayhat_mse : num 0.000705 0.001422 0.002785 0.003581 0.004584 ... #> $ taudothat_mse : num 0.000645 0.001342 0.002729 0.003286 0.004536 ... #> $ betahat_mse : num 0.000652 0.001319 0.002698 0.00334 0.004453 ... #> $ deltamhat_mse : num 0.000963 0.001949 0.004008 0.004979 0.006573 ... #> $ alphahat_mse : num 0.000491 0.000978 0.002075 0.002581 0.003575 ... #> $ alphahatbetahat_mse : num 0.000589 0.001175 0.00247 0.003034 0.004169 ... #> $ taudothatprime_mse : num 0.000655 0.001344 0.002705 0.003309 0.004475 ... #> $ betahatprime_mse : num 0.000497 0.001029 0.002062 0.002493 0.003477 ... #> $ alphahatprime_mse : num 0.000424 0.000848 0.00171 0.002114 0.00291 ... #> $ alphahatprimebetahatprime_mse : num 0.000526 0.001085 0.00216 0.00262 0.00366 ... #> [list output truncated]