R Under development (unstable) (2026-09-29 r90598 ucrt) -- "Unsuffered Consequences" Copyright (C) 2026 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # This file is part of the standard setup for testthat. > # It is recommended that you do not modify it. > # > # Where should you do additional test configuration? > # Learn more about the roles of various files in: > # * https://r-pkgs.org/testing-design.html#sec-tests-files-overview > # * https://testthat.r-lib.org/articles/special-files.html > > library(testthat) > library(bayesics) > > test_check("bayesics") --- Bayes factor in favor of the full vs. null model: 4.81e+55; =>Level of evidence: Decisive --- Summary of factor level means --- # A tibble: 10 x 5 Variable `Post Mean` Lower Upper `Prob Dir` 1 Mean : x1 : a -0.911 -1.11 -0.716 1.000 2 Mean : x1 : b -1.09 -1.31 -0.882 1 3 Mean : x1 : c -0.915 -1.09 -0.737 1 4 Mean : x1 : d 0.905 0.707 1.10 1.000 5 Mean : x1 : e 1.05 0.854 1.25 1 6 Var : x1 : a 0.992 0.750 1.31 NA 7 Var : x1 : b 1.17 0.884 1.54 NA 8 Var : x1 : c 0.829 0.627 1.09 NA 9 Var : x1 : d 1.03 0.776 1.36 NA 10 Var : x1 : e 1.01 0.764 1.33 NA --- Summary of pairwise differences --- # A tibble: 10 x 9 Comparison `Post Mean` Lower Upper `Prob Dir` `ROPE (0.1)` EPR 1 a-b 0.182 -0.103 0.465 0.894 0.270 0.549 2 a-c 0.00419 -0.261 0.268 0.506 0.525 0.501 3 a-d -1.82 -2.09 -1.54 1 0 0.101 4 a-e -1.96 -2.24 -1.69 1 0 0.0836 5 b-c -0.178 -0.452 0.0985 0.900 0.261 0.450 6 b-d -2.00 -2.28 -1.71 1 0 0.0893 7 b-e -2.14 -2.43 -1.85 1 0 0.0740 8 c-d -1.82 -2.09 -1.55 1 0 0.0913 9 c-e -1.97 -2.23 -1.70 1 0 0.0744 10 d-e -0.145 -0.428 0.135 0.844 0.340 0.460 # i 2 more variables: `EPR Lower` , `EPR Upper` *Note: EPR (Exceedence in Pairs Rate) for a Comparison of g-h = Pr(Y_(gi) > Y_(hi)|parameters) ---------- Bayesian model averaging for linear regression models ---------- outcome ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 ---------- # A tibble: 15 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -1.08 -1.24 -0.929 1 NA (NA,NA) 2 x1 1.02 0.926 1.12 1 0 (-0.089,0.08~ 3 x2 0.0130 -0.0373 0.105 0.283 0.947 (-0.088,0.08~ 4 x3b -0.0166 -0.239 0.156 0.231 0.996 (-0.351,0.35~ 5 x3c 0.0388 -0.0923 0.298 0.291 0.991 (-0.351,0.35~ 6 x3d 2.01 1.76 2.25 1 0 (-0.351,0.35~ 7 x3e 2.14 1.89 2.38 1 0 (-0.351,0.35~ 8 x4 -0.0000604 -0.0697 0.0696 0.177 0.973 (-0.083,0.08~ 9 x5 -0.00599 -0.0917 0.0568 0.221 0.966 (-0.088,0.08~ 10 x6 -0.000371 -0.0731 0.0703 0.176 0.974 (-0.087,0.08~ 11 x7 0.0132 -0.0350 0.107 0.282 0.948 (-0.089,0.08~ 12 x8 0.00545 -0.0581 0.0867 0.224 0.970 (-0.088,0.08~ 13 x9 0.0571 0 0.192 0.503 0.648 (-0.089,0.08~ 14 x10 -0.0121 -0.105 0.0387 0.281 0.948 (-0.083,0.08~ 15 Residual variance 1.05 0.936 1.28 NA NA (NA,NA) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Cell sizes were too small for large sample approximation. Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference. ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 8 1 Not at risk 47 26 Prior on probability of exposure given outcome is: Unif(0,1) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 5.16 95% CI: (0.64,22.6) Probability that odds ratio (at risk vs. not at risk) is between 0.889 and 1.12: 0.0515 Probability that the odds ratio is greater than 1: 0.91 ---------- Cell sizes were too small for large sample approximation. Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference. ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 8 1 Not at risk 47 26 Prior on probability of exposure given outcome is: Unif(0,1) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 5.16 95% CI: (0.64,22.6) Probability that odds ratio (at risk vs. not at risk) is between 0.889 and 1.12: 0.0515 Probability that the odds ratio is greater than 1: 0.91 ---------- Cell sizes were too small for large sample approximation. Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference. ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 8 1 Not at risk 47 26 Prior on probability of exposure given outcome is: Unif(0,1) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 5.16 95% CI: (0.64,22.6) Probability that odds ratio (at risk vs. not at risk) is between 0.889 and 1.12: 0.0515 Probability that the odds ratio is greater than 1: 0.91 ---------- ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 13 6 Not at risk 52 31 Prior on log odds is: N(0, 1.17^2) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 1.39 95% CI: (0.47,3.25) Probability that odds ratio (at risk vs. not at risk) is between 0.889 and 1.12: 0.173 Probability that the odds ratio is greater than 1: 0.666 ---------- Cell sizes were too small for large sample approximation. Instead, setting uniform prior on Pr(exposure|outcome) and making exact finite sample inference. ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 8 1 Not at risk 47 26 Prior on probability of exposure given outcome is: Unif(0,1) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 5.16 95% CI: (0.64,22.6) Probability that odds ratio (at risk vs. not at risk) is between 0.952 and 1.05: 0.0215 Probability that the odds ratio is greater than 1: 0.91 ---------- ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 13 6 Not at risk 52 31 Prior on log odds is: N(0, 1.17^2) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 1.39 95% CI: (0.47,3.25) Probability that odds ratio (at risk vs. not at risk) is between 0.952 and 1.05: 0.072 Probability that the odds ratio is greater than 1: 0.666 ---------- ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 13 6 Not at risk 52 31 Prior on log odds is: N(0, 1.17^2) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 1.39 95% CI: (0.47,3.25) Probability that odds ratio (at risk vs. not at risk) is between 0.952 and 1.05: 0.072 Probability that the odds ratio is greater than 1: 0.666 ---------- ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 13 6 Not at risk 52 31 Prior on log odds is: N(10, 1.17^2) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 8.12 95% CI: (2.73,18.9) Probability that odds ratio (at risk vs. not at risk) is between 0.952 and 1.05: 0.0000271 Probability that the odds ratio is greater than 1: 1 ---------- ---------- Case-control analysis using Bayesian techniques ---------- Data: Cases Controls At risk 13 6 Not at risk 52 31 Prior on log odds is: N(0, 0.01^2) Posterior Results: ---Odds ratio (at risk vs. not at risk) Estimate: 1 95% CI: (0.981,1.02) Probability that odds ratio (at risk vs. not at risk) is between 0.952 and 1.05: 1 Probability that the odds ratio is greater than 1: 0.503 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- 2-way table test for independence using Bayesian techniques ---------- Data: column_1 column_2 column_3 row_1 42 23 9 row_2 27 1 37 row_3 46 20 6 row_4 62 7 63 row_5 35 55 69 Prior on cell probabilities is: Dirichlet with shape parameters = column_1 column_2 column_3 row_1 0.5 0.5 0.5 row_2 0.5 0.5 0.5 row_3 0.5 0.5 0.5 row_4 0.5 0.5 0.5 row_5 0.5 0.5 0.5 Estimated probabilities P_(row,col): column_1 column_2 column_3 row_1 0.08340 0.04610 0.01860 row_2 0.05400 0.00294 0.07360 row_3 0.09130 0.04020 0.01280 row_4 0.12300 0.01470 0.12500 row_5 0.06970 0.10900 0.13600 95% credible intervals: column_1 column_2 column_3 row_1 (0.061, 0.109) (0.0297, 0.0659) (0.00879, 0.0321) row_2 (0.0361, 0.0752) (0.000212, 0.00915) (0.0526, 0.0978) row_3 (0.0678, 0.118) (0.025, 0.0589) (0.00494, 0.0242) row_4 (0.0957, 0.152) (0.00618, 0.0268) (0.0974, 0.155) row_5 (0.0492, 0.0933) (0.0834, 0.137) (0.108, 0.167) Probability the odds ratio (unrestricted vs. independence) is in the ROPE (i.e., between 0.889 and 1.12): column_1 column_2 column_3 row_1 0.03420 0.06150 0.00000 row_2 0.58100 0.00000 0.00362 row_3 0.00145 0.17000 0.00000 row_4 0.47500 0.00000 0.03160 row_5 0.00000 0.00000 0.18200 Probability that P(row,col) < P(row) x P(col): column_1 column_2 column_3 row_1 0.002650 0.018300 1.000000 row_2 0.553000 1.000000 0.000241 row_3 0.000000 0.072400 1.000000 row_4 0.096700 1.000000 0.001450 row_5 1.000000 0.000000 0.016200 Probability that all odds ratios (unrestricted vs. independence) are in the ROPE: 0 Bayes factor in favor of dependence: 478000000000000000000 =>Level of evidence: Decisive ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. ---------- Analysis of Kendall's tau using Bayesian techniques ---------- Prior on the proportion for concordance is: Beta(2, 2) Posterior Results: ---Kendall's tau Estimate: 0.0887 95% CI: (0.0329,0.144) Probability that kendall's tau is between -0.05 and 0.05: 0.0868 Probability that tau is greater than 0: 0.999 ---------- Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Beta(2,3.9) prior will be used. Prior shape parameters were not supplied. Beta(3.9,2) prior will be used. The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. ---------- Generalized linear regression fit using Bayesian techniques ---------- outcome ~ x1 + x2 + x3 ---------- Values given in terms of odds ratios ---------- # A tibble: 6 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 x1 2.22 1.26 3.93 0.997 0.00180 (0.972,1.029) 2 x2 0.838 0.473 1.49 0.727 0.0694 (0.97,1.031) 3 x3b 0.429 0.0508 3.62 0.781 0.0638 (0.889,1.125) 4 x3c 0.911 0.126 6.58 0.537 0.0925 (0.889,1.125) 5 x3d 8.49 1.54 46.8 0.993 0.00535 (0.889,1.125) 6 x3e 21.5 3.91 118. 1.000 0.000223 (0.889,1.125) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. ---------- Test for heteroscedasticity in 1-way ANOVA models. Bayes factor in favor of homoscedasticity = 592366584.582148 Level of evidence: Decisive in favor of homoscedasticity ---------- ---------- Test for heteroscedasticity in 1-way ANOVA models. Bayes factor in favor of homoscedasticity = 0.028467538606378 Level of evidence: Strong in favor of heteroscedasticity ---------- The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) ---------- Linear regression fit using Bayesian techniques ---------- outcome ~ x1 + x2 + x3 ---------- # A tibble: 8 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -0.996 -1.20 -0.790 1 NA (NA,NA) 2 x1 0.943 0.849 1.04 1 1.85e-56 (-0.085,0.08~ 3 x2 0.0897 -0.00309 0.182 0.971 4.56e- 1 (-0.084,0.08~ 4 x3b 0.0428 -0.249 0.335 0.613 9.71e- 1 (-0.337,0.33~ 5 x3c -0.0155 -0.307 0.276 0.542 9.76e- 1 (-0.337,0.33~ 6 x3d 1.90 1.61 2.19 1 8.75e-24 (-0.337,0.33~ 7 x3e 1.94 1.65 2.24 1 5.61e-25 (-0.337,0.33~ 8 Residual varia~ 1.10 0.978 1.25 NA NA (NA,NA) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) By default, the fraction of data "used" is max(ncol(X) + 1,log(n)) / n. ---------- The fractional Bayes factor equaled 1.76e+60. Interpretation: Decisive (in favor of the first model) ---------- The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) The mu hyperparameter in the normal prior is not specified. It will be set automatically to 0. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The V hyperparameter in the normal prior is not specified. It will be set automatically to 4/25Diag(s^2_{X_j}) ---------- Linear regression fit using Bayesian techniques ---------- log(e_outcome) ~ x1 + x2 + x3 ---------- # A tibble: 8 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -0.996 -1.20 -0.790 1 NA (NA,NA) 2 x1 0.943 0.849 1.04 1 1.85e-56 (-0.085,0.08~ 3 x2 0.0897 -0.00309 0.182 0.971 4.56e- 1 (-0.084,0.08~ 4 x3b 0.0428 -0.249 0.335 0.613 9.71e- 1 (-0.337,0.33~ 5 x3c -0.0155 -0.307 0.276 0.542 9.76e- 1 (-0.337,0.33~ 6 x3d 1.90 1.61 2.19 1 8.75e-24 (-0.337,0.33~ 7 x3e 1.94 1.65 2.24 1 5.61e-25 (-0.337,0.33~ 8 Residual varia~ 1.10 0.978 1.25 NA NA (NA,NA) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. Finished with 500 preliminary posterior draws. ---------- Mediation analysis using Bayesian techniques ---------- Mediator model: m ~ tr + x1 Outcome model: outcome ~ m + tr + x1 ---------- # A tibble: 8 x 5 Estimand Estimate Lower Upper `Prob Dir` 1 ACME (Control) 1.08 0.486 1.80 1 2 ACME (Treatment) 1.90 0.952 3.30 1 3 ADE (Control) 0.865 0.642 1.15 1 4 ADE (Treatment) 1.68 1.28 2.23 1 5 Total Effect 2.76 1.91 4.05 1 6 ACME (Average) 1.49 0.741 2.53 1 7 ADE (Average) 1.27 1.02 1.57 1 8 Prop. Mediated (Average) 0.529 0.373 0.633 NA ---------- The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. Finished with 500 preliminary posterior draws. control_value missing; set to be the 1st quintile of tr treat_value missing; set to be the 4th quintile of tr Finished with 500 preliminary posterior draws. Finished with 500 preliminary posterior draws. ---------- Mediation analysis using Bayesian techniques ---------- Mediator model: m ~ tr + x1 Outcome model: outcome ~ m + tr + x1 ---------- # A tibble: 8 x 5 Estimand Estimate Lower Upper `Prob Dir` 1 ACME (Control) 0.638 0.367 1.01 1 2 ACME (Treatment) 2.30 1.44 3.60 1 3 ADE (Control) 0.927 0.687 1.26 1 4 ADE (Treatment) 2.59 2.02 3.52 1 5 Total Effect 3.23 2.45 4.50 1 6 ACME (Average) 1.47 0.933 2.30 1 7 ADE (Average) 1.76 1.43 2.24 1 8 Prop. Mediated (Average) 0.450 0.359 0.527 NA ---------- The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. The g hyperparameter in Zellner's g prior is not specified. It will be set automatically to n. The hyperparameters for the residual variance were not provided. Instead, the prior will put 50% prior probability that R^2 is between 0.1^2 and 0.9^2. ---------- Mediation analysis using Bayesian techniques ---------- Mediator model: m ~ tr + x1 Outcome model: outcome ~ m + tr + x1 ---------- # A tibble: 4 x 5 Estimand Estimate Lower Upper `Prob Dir` 1 ACME 2.04 1.48 2.55 1 2 ADE 2.27 1.89 2.63 1 3 Total Effect 4.31 3.76 4.88 1 4 Prop. Mediated 0.473 0.381 0.555 NA ---------- Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 ---------- Values given in terms of odds ratios ---------- # A tibble: 6 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 x1 2.46 1.28 4.71 0.997 0.00176 (0.972,1.029) 2 x2 0.841 0.458 1.54 0.712 0.0671 (0.97,1.031) 3 x3b 0.360 0.0271 4.77 0.781 0.0528 (0.889,1.125) 4 x3c 0.840 0.135 5.22 0.574 0.0989 (0.889,1.125) 5 x3d 9.33 1.36 64.3 0.988 0.00735 (0.889,1.125) 6 x3e 23.8 3.68 153. 1.000 0.000397 (0.889,1.125) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 ---------- # A tibble: 7 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -2.33 -3.83 -0.819 0.999 NA (NA,NA) 2 x1 0.900 0.250 1.55 0.997 0.00176 (-0.029,0.029) 3 x2 -0.174 -0.781 0.434 0.712 0.0671 (-0.031,0.031) 4 x3b -1.02 -3.61 1.56 0.781 0.0528 (-0.118,0.118) 5 x3c -0.175 -2.00 1.65 0.574 0.0989 (-0.118,0.118) 6 x3d 2.23 0.304 4.16 0.988 0.00735 (-0.118,0.118) 7 x3e 3.17 1.30 5.03 1.000 0.000397 (-0.118,0.118) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. Assuming all observations correspond to Bernoulli, i.e., Binomial with one trial. ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 + offset(log(time)) ---------- Values given in terms of rate ratios ---------- # A tibble: 6 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 x1 2.56 2.17 3.01 1 3.18e-28 (0.972,1.029) 2 x2 0.997 0.766 1.30 0.510 1.79e- 1 (0.97,1.031) 3 x3b 1.79 0.279 11.5 0.730 8.20e- 2 (0.889,1.125) 4 x3c 1.38 0.204 9.35 0.629 9.10e- 2 (0.889,1.125) 5 x3d 9.14 1.60 52.3 0.994 4.85e- 3 (0.889,1.125) 6 x3e 10.2 1.78 58.5 0.995 3.59e- 3 (0.889,1.125) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 + offset(log(time)) ---------- # A tibble: 7 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -2.08 -3.80 -0.368 0.991 NA (NA,NA) 2 x1 0.939 0.776 1.10 1 3.18e-28 (-0.029,0.029) 3 x2 -0.00337 -0.267 0.260 0.510 1.79e- 1 (-0.031,0.031) 4 x3b 0.582 -1.28 2.44 0.730 8.20e- 2 (-0.118,0.118) 5 x3c 0.322 -1.59 2.24 0.629 9.10e- 2 (-0.118,0.118) 6 x3d 2.21 0.470 3.96 0.994 4.85e- 3 (-0.118,0.118) 7 x3e 2.32 0.576 4.07 0.995 3.59e- 3 (-0.118,0.118) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 + offset(log(time)) ---------- Values given in terms of rate ratios ---------- # A tibble: 7 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 x1 3.41 2.00 5.84 1.000 0.00000373 (0.972,1.029) 2 x2 0.730 0.460 1.16 0.909 0.0426 (0.97,1.031) 3 x3b 0.522 0.0802 3.40 0.752 0.0779 (0.889,1.125) 4 x3c 0.653 0.0921 4.63 0.665 0.0857 (0.889,1.125) 5 x3d 4.18 0.743 23.5 0.948 0.0287 (0.889,1.125) 6 x3e 2.56 0.441 14.9 0.853 0.0604 (0.889,1.125) 7 phi 0.893 0.458 1.74 0.630 NA (NA,NA) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) ---------- Generalized linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 + offset(log(time)) ---------- # A tibble: 8 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -1.57 -3.19 0.0365 0.972 NA (NA,NA) 2 x1 1.23 0.691 1.76 1.000 0.00000373 (-0.029,0.029) 3 x2 -0.314 -0.776 0.148 0.909 0.0426 (-0.031,0.031) 4 x3b -0.650 -2.52 1.22 0.752 0.0779 (-0.118,0.118) 5 x3c -0.426 -2.38 1.53 0.665 0.0857 (-0.118,0.118) 6 x3d 1.43 -0.297 3.16 0.948 0.0287 (-0.118,0.118) 7 x3e 0.942 -0.819 2.70 0.853 0.0604 (-0.118,0.118) 8 log(phi) -0.113 -0.781 0.556 0.630 NA (NA,NA) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. ---------- Linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 ---------- # A tibble: 7 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -0.693 -1.49 0.102 0.956 NA (NA,NA) 2 x1 0.877 0.492 1.26 1.000 0.0000231 (-0.079,0.079) 3 x2 -0.0322 -0.438 0.373 0.562 0.309 (-0.083,0.083) 4 x3b -0.742 -1.93 0.444 0.890 0.204 (-0.321,0.321) 5 x3c 0.160 -0.806 1.13 0.627 0.464 (-0.321,0.321) 6 x3d 1.48 0.351 2.61 0.995 0.0212 (-0.321,0.321) 7 x3e 1.61 0.376 2.85 0.995 0.0193 (-0.321,0.321) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) ---------- Linear regression fit using Bayesian techniques (non-parametric) ---------- outcome ~ x1 + x2 + x3 ---------- # A tibble: 7 x 7 Variable `Post Mean` Lower Upper `Prob Dir` ROPE `ROPE bounds` 1 (Intercept) -0.693 -1.49 0.102 0.956 NA (NA,NA) 2 x1 0.877 0.492 1.26 1.000 0.0000231 (-0.079,0.079) 3 x2 -0.0322 -0.438 0.373 0.562 0.309 (-0.083,0.083) 4 x3b -0.742 -1.93 0.444 0.890 0.204 (-0.321,0.321) 5 x3c 0.160 -0.806 1.13 0.627 0.464 (-0.321,0.321) 6 x3d 1.48 0.351 2.61 0.995 0.0212 (-0.321,0.321) 7 x3e 1.61 0.376 2.85 0.995 0.0193 (-0.321,0.321) ---------- (Note: Lower and upper bounds are for the 95% credible interval.) Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Missing other covariate values in 'exemplar_covariates.' Using medoid observation instead. Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population rate using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of events` `Time/area base` 1 12 1 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Rate Estimate: 12.5 95% CI: (6.56,20.3) ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population rate using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of events` `Time/area base` 1 12 2 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Rate Estimate: 6.25 95% CI: (3.28,10.2) ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population rate using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of events` `Time/area base` 1 12 2 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Rate Estimate: 6.25 95% CI: (3.28,10.2) Probability that the rate is less than 10: 0.971 ---------- Prior shape parameters were not supplied. A flat Gamma(0.001,0.001) prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population rates using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of events` `Time/area base` 1 12 1 2 20 1 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Population 1 rate Estimate: 12.5 95% CI: (6.56,20.3) ---Population 2 rate Estimate: 20.5 95% CI: (12.6,30.3) ---Rate ratio (Pop 1 vs. Pop 2) Estimate: 0.641 95% CI: (0.288,1.21) Probability that rate ratio (pop 1 vs. pop 2) is between 0.889 and 1.12: 0.098 Probability that the rate ratio (Pop 1 vs. Pop 2) is less than 1: 0.923 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population rates using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of events` `Time/area base` 1 12 10 2 20 9 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Population 1 rate Estimate: 1.25 95% CI: (0.656,2.03) ---Population 2 rate Estimate: 2.28 95% CI: (1.4,3.36) ---Rate ratio (Pop 1 vs. Pop 2) Estimate: 0.577 95% CI: (0.26,1.09) Probability that rate ratio (pop 1 vs. pop 2) is between 0.889 and 1.12: 0.0638 Probability that the rate ratio (Pop 1 vs. Pop 2) is less than 1: 0.957 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population rates using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of events` `Time/area base` 1 12 10 2 20 9 Prior on the population rate: Gamma(shape=0.5, rate=0) Posterior Results: ---Population 1 rate Estimate: 1.25 95% CI: (0.656,2.03) ---Population 2 rate Estimate: 2.28 95% CI: (1.4,3.36) ---Rate ratio (Pop 1 vs. Pop 2) Estimate: 0.577 95% CI: (0.26,1.09) Probability that rate ratio (pop 1 vs. pop 2) is between 0.889 and 1.12: 0.0638 Probability that the rate ratio (Pop 1 vs. Pop 2) is less than 1: 0.957 ---------- Prior shape parameters were not supplied. A flat Gamma(0.001,0.001) prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population proportion using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of successes` `Number of failures` 1 14 19 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population proportion Estimate: 0.426 95% CI: (0.268,0.593) ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population proportion using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of successes` `Number of failures` 1 14 19 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population proportion Estimate: 0.426 95% CI: (0.268,0.593) ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of a single population proportion using Bayesian techniques ---------- Data: # A tibble: 1 x 2 `Number of successes` `Number of failures` 1 14 19 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population proportion Estimate: 0.426 95% CI: (0.268,0.593) Probability that the population proportion is less than 0.45: 0.615 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population proportions using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of successes` `Number of failures` 1 14 19 2 22 45 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population 1 proportion Estimate: 0.426 95% CI: (0.268,0.593) ---Population 2 proportion Estimate: 0.331 95% CI: (0.225,0.446) ---Difference in proportions (Pop 1 - Pop 2) Estimate: 0.0959 95% CI: (-0.1,0.295) Probability that the odds ratio (Pop 1 vs. Pop 2) is greater than 1: 0.827 Probability that the odds ratio (Pop 1 vs. Pop 2) is between 0.889 and 1.12: 0.138 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population proportions using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of successes` `Number of failures` 1 14 19 2 22 45 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population 1 proportion Estimate: 0.426 95% CI: (0.268,0.593) ---Population 2 proportion Estimate: 0.331 95% CI: (0.225,0.446) ---Difference in proportions (Pop 1 - Pop 2) Estimate: 0.0959 95% CI: (-0.1,0.295) Probability that the odds ratio (Pop 1 vs. Pop 2) is greater than 1: 0.827 Probability that the odds ratio (Pop 1 vs. Pop 2) is between 0.889 and 1.12: 0.138 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Analysis of two population proportions using Bayesian techniques ---------- Data: # A tibble: 2 x 2 `Number of successes` `Number of failures` 1 14 19 2 22 45 Prior on the population proportion: Beta(0.5, 0.5) Posterior Results: ---Population 1 proportion Estimate: 0.426 95% CI: (0.268,0.593) ---Population 2 proportion Estimate: 0.331 95% CI: (0.225,0.446) ---Difference in proportions (Pop 1 - Pop 2) Estimate: 0.0959 95% CI: (-0.1,0.295) Probability that the odds ratio (Pop 1 vs. Pop 2) is greater than 1: 0.827 Probability that the odds ratio (Pop 1 vs. Pop 2) is between 0.889 and 1.12: 0.138 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(0.5, 0.5) Posterior Results: ---Probability x > y Estimate: 0.52 95% CI: (0.384,0.654) Probability that probability x > y is between 0.45 and 0.55: 0.506 Probability that the Probability x > y is greater than 0.5: 0.611 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(0.5, 0.5) Posterior Results: ---Probability x > y Estimate: 0.696 95% CI: (0.564,0.813) Probability that probability x > y is between 0.45 and 0.55: 0.0151 Probability that the Probability x > y is greater than 0.5: 0.998 ---------- Prior shape parameters were not supplied. A uniform prior will be used. ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(1, 1) Posterior Results: ---Probability x > y Estimate: 0.308 95% CI: (0.191,0.438) Probability that probability x > y is between 0.45 and 0.55: 0.0165 Probability that the Probability x > y is less than 0.5: 0.998 ---------- ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(1, 1) Posterior Results: ---Probability x > y Estimate: 0.308 95% CI: (0.191,0.438) Probability that probability x > y is between 0.45 and 0.55: 0.0165 Probability that the Probability x > y is less than 0.5: 0.998 ---------- ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(2, 2) Posterior Results: ---Probability x > y Estimate: 0.315 95% CI: (0.199,0.443) Probability that probability x > y is between 0.45 and 0.55: 0.0197 Probability that the Probability x > y is less than 0.5: 0.997 ---------- Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. Prior shape parameters were not supplied. Jeffrey's prior will be used. ---------- Non-parametric sign test using Bayesian techniques ---------- Prior on the probability x > y: Beta(0.5, 0.5) Posterior Results: ---Probability x > y Estimate: 0.304 95% CI: (0.187,0.436) Probability that probability x > y is between 0.65 and 0.75: 0.000000235 Probability that the Probability x > y is less than 0.7: 1 ---------- ---------- Semi-parametric survival curve fitting using Bayesian techniques ---------- Number of intervals: 60 Survival curve fitted up to: 7 # A tibble: 60 x 6 Interval `Estimated rate` `2.5%` `97.5%` Shape Rate 1 (0,0.941) 0.0179 0.00580 0.0366 5 "280.00" 2 (0.941,1.05) 0.127 0.0346 0.278 4 " 31.50" 3 (1.05,1.13) 0.166 0.0452 0.363 4 " 24.10" 4 (1.13,1.3) 0.103 0.0335 0.211 5 " 48.50" 5 (1.3,1.36) 0.258 0.0702 0.565 4 " 15.50" 6 (1.36,1.46) 0.139 0.0380 0.306 4 " 28.70" 7 (1.46,1.57) 0.140 0.0381 0.306 4 " 28.60" 8 (1.57,1.63) 0.297 0.0966 0.609 5 " 16.80" 9 (1.63,1.68) 0.287 0.0783 0.630 4 " 13.90" 10 (1.68,1.77) 0.173 0.0471 0.379 4 " 23.20" # i 50 more rows Note: The time-to-event data follow a piecewise exponential model. Each interval follows an exponential distribution, whose rate has a posterior of Gamma(,). ---------- Semi-parametric survival curve fitting using Bayesian techniques ---------- Number of intervals: 20 Survival curve fitted up to: 9 x1: a # A tibble: 20 x 6 Interval `Estimated rate` `2.5%` `97.5%` Shape Rate 1 (0,1.17) 0.0439 0.0142 0.0899 5 "114.00" 2 (1.17,1.58) 0.132 0.0430 0.271 5 " 37.80" 3 (1.58,1.96) 0.148 0.0480 0.303 5 " 33.80" 4 (1.96,2.27) 0.196 0.0636 0.401 5 " 25.60" 5 (2.27,2.55) 0.231 0.0752 0.474 5 " 21.60" 6 (2.55,2.72) 0.418 0.136 0.855 5 " 12.00" 7 (2.72,2.98) 0.287 0.0931 0.587 5 " 17.40" 8 (2.98,3.43) 0.178 0.0579 0.365 5 " 28.00" 9 (3.43,3.7) 0.320 0.104 0.656 5 " 15.60" 10 (3.7,4.05) 0.272 0.0882 0.557 5 " 18.40" 11 (4.05,4.23) 0.572 0.186 1.17 5 " 8.74" 12 (4.23,4.57) 0.348 0.113 0.712 5 " 14.40" 13 (4.57,5.03) 0.289 0.0939 0.593 5 " 17.30" 14 (5.03,5.17) 1.13 0.366 2.31 5 " 4.44" 15 (5.17,5.73) 0.324 0.105 0.663 5 " 15.40" 16 (5.73,6.36) 0.352 0.114 0.722 5 " 14.20" 17 (6.36,6.87) 0.574 0.186 1.18 5 " 8.71" 18 (6.87,7.38) 0.778 0.253 1.59 5 " 6.43" 19 (7.38,7.69) 1.97 0.640 4.03 5 " 2.54" 20 (7.69,9) 1.03 0.281 2.26 4 " 3.88" ---------- x1: b # A tibble: 20 x 6 Interval `Estimated rate` `2.5%` `97.5%` Shape Rate 1 (0,1.25) 0.0404 0.0131 0.0827 5 "124.00" 2 (1.25,1.51) 0.208 0.0675 0.425 5 " 24.10" 3 (1.51,1.64) 0.420 0.136 0.861 5 " 11.90" 4 (1.64,1.96) 0.189 0.0614 0.387 5 " 26.40" 5 (1.96,2.25) 0.178 0.0484 0.389 4 " 22.50" 6 (2.25,2.74) 0.140 0.0454 0.286 5 " 35.80" 7 (2.74,2.84) 0.735 0.239 1.51 5 " 6.80" 8 (2.84,3.08) 0.339 0.110 0.695 5 " 14.70" 9 (3.08,3.32) 0.285 0.0776 0.624 4 " 14.10" 10 (3.32,3.68) 0.253 0.0823 0.519 5 " 19.70" 11 (3.68,4.02) 0.294 0.0956 0.603 5 " 17.00" 12 (4.02,4.56) 0.209 0.0678 0.427 5 " 24.00" 13 (4.56,5.06) 0.207 0.0565 0.454 4 " 19.30" 14 (5.06,5.37) 0.450 0.146 0.922 5 " 11.10" 15 (5.37,5.97) 0.270 0.0877 0.553 5 " 18.50" 16 (5.97,6.29) 0.595 0.193 1.22 5 " 8.40" 17 (6.29,6.65) 0.538 0.147 1.18 4 " 7.43" 18 (6.65,6.99) 0.872 0.283 1.79 5 " 5.74" 19 (6.99,7.22) 1.91 0.620 3.91 5 " 2.62" 20 (7.22,9) 0.381 0.104 0.835 4 " 10.50" ---------- x1: c # A tibble: 20 x 6 Interval `Estimated rate` `2.5%` `97.5%` Shape Rate 1 (0,2.26) 0.0134 0.00276 0.0322 3 "224.00" 2 (2.26,2.55) 0.111 0.0228 0.266 3 " 27.10" 3 (2.55,2.99) 0.0738 0.0152 0.178 3 " 40.70" 4 (2.99,3.42) 0.0765 0.0158 0.184 3 " 39.20" 5 (3.42,3.6) 0.129 0.0156 0.360 2 " 15.50" 6 (3.6,4.12) 0.0682 0.0141 0.164 3 " 44.00" 7 (4.12,4.38) 0.142 0.0292 0.341 3 " 21.20" 8 (4.38,5.13) 0.0506 0.0104 0.122 3 " 59.30" 9 (5.13,5.51) 0.0680 0.00824 0.189 2 " 29.40" 10 (5.51,6.27) 0.0540 0.0111 0.130 3 " 55.60" 11 (6.27,6.75) 0.0896 0.0185 0.216 3 " 33.50" 12 (6.75,7.01) 0.166 0.0341 0.399 3 " 18.10" 13 (7.01,7.42) 0.0756 0.00917 0.211 2 " 26.50" 14 (7.42,7.84) 0.114 0.0236 0.275 3 " 26.30" 15 (7.84,8.03) 0.275 0.0567 0.662 3 " 10.90" 16 (8.03,8.44) 0.128 0.0264 0.308 3 " 23.40" 17 (8.44,8.57) 0.271 0.0328 0.754 2 " 7.39" 18 (8.57,8.68) 0.555 0.114 1.34 3 " 5.41" 19 (8.68,8.84) 0.383 0.0789 0.921 3 " 7.84" 20 (8.84,9) 0.274 0.0332 0.763 2 " 7.30" ---------- Note: The time-to-event data follow a piecewise exponential model. Each interval follows an exponential distribution, whose rate has a posterior of Gamma(,). ---------- One sample population mean analysis using Bayesian techniques ---------- Prior: mu ~ N(0, sigma^2/0.001), sigma^2 ~ IG(shape=0.001/2, rate=0.001/2) Posterior Results: ---Population mean Estimate: 0.243 95% CI: (-0.0493,0.535) ---Population variance Estimate: 1.1 95% CI: (0.741,1.64) ---------- ---------- One sample population mean analysis using Bayesian techniques ---------- Prior: mu ~ N(0, sigma^2/0.001), sigma^2 ~ IG(shape=0.001/2, rate=0.001/2) Posterior Results: ---Population mean Estimate: -0.142 95% CI: (-0.391,0.106) ---Population variance Estimate: 0.798 95% CI: (0.537,1.18) ---------- ---------- Two sample population means analysis using Bayesian techniques ---------- Prior: mu ~ N(0.346, sigma^2/0.001), sigma^2 ~ IG(shape=0.001/2, rate=0.001/2) Posterior Results: ---Population 1 mean Estimate: 0.183 95% CI: (-0.0943,0.461) ---Population 2 mean Estimate: 0.89 95% CI: (0.39,1.39) ---Population 1 variance Estimate: 0.994 95% CI: (0.668,1.47) ---Population 2 variance Estimate: 0.954 95% CI: (0.451,1.98) ---Difference in population means (Pop 1 - Pop 2) Estimate: -0.707 95% CI: (-1.28,-0.138) Probability that difference in population means (pop 1 - pop 2) is between -0.1 and 0.1: 0.0149 Probability that the difference in means (x - y) is less than 0: 0.992 Bayes factor in favor of unequal group means: 0.000102 =>Level of evidence: Decisive ---------- *Note: ROPE for the difference in means is given in terms of Cohen's D. ---------- Two sample population means analysis using Bayesian techniques ---------- Prior: mu ~ N(0.174, sigma^2/0.001), sigma^2 ~ IG(shape=0.001/2, rate=0.001/2) Posterior Results: ---Population a mean Estimate: -0.0239 95% CI: (-0.302,0.254) ---Population b mean Estimate: 0.833 95% CI: (0.152,1.51) ---Population a variance Estimate: 0.995 95% CI: (0.669,1.48) ---Population b variance Estimate: 1.76 95% CI: (0.834,3.66) ---Difference in population means (Pop a - Pop b) Estimate: -0.856 95% CI: (-1.59,-0.119) Probability that difference in population means (pop a - pop b) is between -0.1 and 0.1: 0.0175 Probability that the difference in means (a - b) is less than 0: 0.988 ---------- *Note: ROPE for the difference in means is given in terms of Cohen's D. ---------- One sample population mean analysis using Bayesian techniques ---------- Prior: mu ~ N(0, sigma^2/0.001), sigma^2 ~ IG(shape=0.001/2, rate=0.001/2) Posterior Results: ---Population mean Estimate: -0.498 95% CI: (-0.825,-0.17) ---Population variance Estimate: 1.38 95% CI: (0.929,2.05) Probability that the difference in means (x - y) is less than 0: 0.998 ---------- Prior shape parameters were not supplied. Beta(2,2) prior will be used. ---------- Wilcoxon signed-rank analysis using Bayesian techniques ---------- Prior on the probability x > y: Beta(2, 2) Posterior Results: ---Probability x > y Estimate: 0.0662 95% CI: (0.0287,0.118) Probability that probability x > y is between 0.45 and 0.55: 0 Probability that the Probability x > y is less than 0.5: 1 Bayes factor in favor of phi>0.5 vs. phi<=0.5: 0 =>Level of evidence: Decisive ---------- Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. ---------- Wilcoxon rank sum analysis using Bayesian techniques ---------- Prior on Omega_x: Beta(2, 2) Posterior Results: ---Omega_x Estimate: 0.135 95% CI: (0.0957,0.179) Probability that omega_x is between 0.45 and 0.55: 0 Probability that the Omega_x is less than 0.5: 1 Bayes factor in favor of Omega_x>0.5 vs. Omega_x<=0.5: 0 =>Level of evidence: Decisive ---------- *Note: Omega_x is defined to be the proportion of (non-tied) pairs where x is bigger than y Prior shape parameters were not supplied. A uniform prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. Prior shape parameters were not supplied. Beta(2,2) prior will be used. [ FAIL 0 | WARN 3 | SKIP 0 | PASS 604 ] [ FAIL 0 | WARN 3 | SKIP 0 | PASS 604 ] > > proc.time() user system elapsed 174.81 13.01 187.76