[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
[1] "No variability observed in a component. Setting batch size to 1"
$m0a1

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 1:10
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
  # NA % NA
y    0    0


$m0a2

Bayesian linear model fitted with JointAI

Call:
glm_imp(formula = y ~ 1, family = gaussian(link = "identity"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 1:10
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
  # NA % NA
y    0    0


$m0a3

Bayesian linear model fitted with JointAI

Call:
glm_imp(formula = y ~ 1, family = gaussian(link = "log"), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
  # NA % NA
y    0    0


$m0a4

Bayesian linear model fitted with JointAI

Call:
glm_imp(formula = y ~ 1, family = gaussian(link = "inverse"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
  # NA % NA
y    0    0


$m0b1

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ 1, family = binomial(link = "logit"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
B1    0    0


$m0b2

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ 1, family = binomial(link = "probit"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
B1    0    0


$m0b3

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ 1, family = binomial(link = "log"), data = wideDF, 
    n.adapt = 150, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 151:160
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
B1    0    0


$m0b4

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ 1, family = binomial(link = "cloglog"), 
    data = wideDF, n.adapt = 50, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 51:60
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
B1    0    0


$m0c1

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1 ~ 1, family = Gamma(link = "inverse"), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
L1    0    0


$m0c2

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1 ~ 1, family = Gamma(link = "log"), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
L1    0    0


$m0d1

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P1 ~ 1, family = poisson(link = "log"), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
P1    0    0


$m0d2

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P1 ~ 1, family = poisson(link = "identity"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
P1    0    0


$m0e1

Bayesian log-normal model fitted with JointAI

Call:
lognorm_imp(formula = L1 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
L1    0    0


$m0f1

Bayesian beta model fitted with JointAI

Call:
betareg_imp(formula = Be1 ~ 1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN

Posterior summary of other parameters:
        Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
tau_Be1    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
    # NA % NA
Be1    0    0


$m1a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 1:10
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
y     0    0
C1    0    0


$m1b

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ C1, family = binomial(), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0


$m1c

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1 ~ C1, family = Gamma(), data = wideDF, n.adapt = 5, 
    n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
L1    0    0
C1    0    0


$m1d

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P1 ~ C1, family = poisson(), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
P1    0    0
C1    0    0


$m1e

Bayesian log-normal model fitted with JointAI

Call:
lognorm_imp(formula = L1 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
   # NA % NA
L1    0    0
C1    0    0


$m1f

Bayesian beta model fitted with JointAI

Call:
betareg_imp(formula = Be1 ~ C1, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN

Posterior summary of other parameters:
        Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
tau_Be1    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
         #   %
lvlone 100 100

Number and proportion of missing values:
    # NA % NA
Be1    0    0
C1     0    0


$m2a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 1:10
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 96 96

Number and proportion of missing values:
   # NA % NA
y     0    0
C2    4    4


$m2b

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B2 ~ C2, family = binomial(), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
C2    4    4
B2   20   20


$m2c

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1mis ~ C2, family = Gamma(), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
            Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1mis    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 76 76

Number and proportion of missing values:
      # NA % NA
C2       4    4
L1mis   20   20


$m2d

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P2 ~ C2, family = poisson(), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
C2    4    4
P2   20   20


$m2e

Bayesian log-normal model fitted with JointAI

Call:
lognorm_imp(formula = L1mis ~ C2, data = wideDF, n.adapt = 5, 
    n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
            Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1mis    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 76 76

Number and proportion of missing values:
      # NA % NA
C2       4    4
L1mis   20   20


$m2f

Bayesian beta model fitted with JointAI

Call:
betareg_imp(formula = Be2 ~ C2, data = wideDF, n.adapt = 5, n.iter = 10, 
    seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN

Posterior summary of other parameters:
        Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
tau_Be2    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
    # NA % NA
C2     4    4
Be2   20   20


$m3a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = C1 ~ C2 + B2 + P2 + L1mis + Be2, data = wideDF, 
    n.adapt = 5, n.iter = 10, models = c(P2 = "glm_poisson_log", 
        L1mis = "glm_gamma_inverse", Be2 = "beta"), seed = 2020, 
    warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
P2             0  0    0     0          0     NaN    NaN
L1mis          0  0    0     0          0     NaN    NaN
Be2            0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_C1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 36 36

Number and proportion of missing values:
      # NA % NA
C1       0    0
C2       4    4
B2      20   20
P2      20   20
L1mis   20   20
Be2     20   20


$m3b

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = C1 ~ C2 + B2 + P2 + L1mis, data = wideDF, n.adapt = 5, 
    n.iter = 10, models = c(C2 = "glm_gaussian_inverse", P2 = "glm_poisson_identity", 
        B2 = "glm_binomial_probit", L1mis = "lognorm"), seed = 2020, 
    warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
P2             0  0    0     0          0     NaN    NaN
L1mis          0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_C1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 48 48

Number and proportion of missing values:
      # NA % NA
C1       0    0
C2       4    4
B2      20   20
P2      20   20
L1mis   20   20


$m3c

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = C1 ~ C2 + B2 + P2 + L1mis, data = wideDF, n.adapt = 5, 
    n.iter = 10, models = c(C2 = "glm_gaussian_log", P2 = "glm_poisson_identity", 
        L1mis = "glm_gamma_log", B2 = "glm_binomial_log"), seed = 2020, 
    warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
P2             0  0    0     0          0     NaN    NaN
L1mis          0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_C1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 48 48

Number and proportion of missing values:
      # NA % NA
C1       0    0
C2       4    4
B2      20   20
P2      20   20
L1mis   20   20


$m3d

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = C1 ~ C2 + B2 + P2 + L1mis + Be2, data = wideDF, 
    n.adapt = 5, n.iter = 10, models = c(C2 = "glm_gaussian_log", 
        P2 = "glm_poisson_identity", L1mis = "glm_gamma_log", 
        B2 = "glm_binomial_log"), seed = 2020, warn = FALSE, 
    mess = FALSE, trunc = list(Be2 = c(0, 1)))


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
P2             0  0    0     0          0     NaN    NaN
L1mis          0  0    0     0          0     NaN    NaN
Be2            0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_C1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 36 36

Number and proportion of missing values:
      # NA % NA
C1       0    0
C2       4    4
B2      20   20
P2      20   20
L1mis   20   20
Be2     20   20


$m4a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ M2 + O2 * abs(C1 - C2) + log(C1), data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
                 Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)         0  0    0     0          0     NaN    NaN
M22                 0  0    0     0          0     NaN    NaN
M23                 0  0    0     0          0     NaN    NaN
M24                 0  0    0     0          0     NaN    NaN
O22                 0  0    0     0          0     NaN    NaN
O23                 0  0    0     0          0     NaN    NaN
O24                 0  0    0     0          0     NaN    NaN
abs(C1 - C2)        0  0    0     0          0     NaN    NaN
log(C1)             0  0    0     0          0     NaN    NaN
O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 91 91

Number and proportion of missing values:
   # NA % NA
y     0    0
C1    0    0
O2    2    2
M2    3    3
C2    4    4


$m4b

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ L1mis + abs(C1 - C2) + log(Be2), family = binomial(), 
    data = wideDF, n.adapt = 5, n.iter = 10, models = c(C2 = "glm_gaussian_log", 
        L1mis = "glm_gamma_inverse", Be2 = "beta"), seed = 2020, 
    warn = FALSE, mess = FALSE)


Posterior summary:
             Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)     0  0    0     0          0     NaN    NaN
L1mis           0  0    0     0          0     NaN    NaN
abs(C1 - C2)    0  0    0     0          0     NaN    NaN
log(Be2)        0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 60 60

Number and proportion of missing values:
      # NA % NA
B1       0    0
C1       0    0
C2       4    4
L1mis   20   20
Be2     20   20


$m5a1

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ C2 + B2 + B1 + O1, data = wideDF, n.adapt = 5, 
    n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
y     0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5a2

Bayesian linear model fitted with JointAI

Call:
glm_imp(formula = y ~ C2 + B2 + B1 + O1, family = gaussian(link = "log"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
y     0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5a3

Bayesian linear model fitted with JointAI

Call:
glm_imp(formula = y ~ C2 + B2 + B1 + O1, family = gaussian(link = "inverse"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
y     0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5b1

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ C2 + B2 + C1 + O1, family = binomial(link = "logit"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5b2

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ C2 + B2 + C1 + O1, family = binomial(link = "probit"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5b3

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ C2 + B2 + C1 + O1, family = binomial(link = "log"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5b4

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ C2 + B2 + C1 + O1, family = binomial(link = "cloglog"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
C1             0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5c1

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1 ~ C2 + B2 + B1 + O1, family = Gamma(link = "inverse"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
L1    0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5c2

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = L1 ~ C2 + B2 + B1 + O1, family = Gamma(link = "log"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
L1    0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5d1

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P1 ~ C2 + B2 + B1 + O1, family = poisson(link = "log"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
P1    0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5d2

Bayesian poisson model fitted with JointAI

Call:
glm_imp(formula = P1 ~ C2 + B2 + B1 + O1, family = poisson(link = "identity"), 
    data = wideDF, n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
P1    0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5e1

Bayesian log-normal model fitted with JointAI

Call:
lognorm_imp(formula = L1 ~ C2 + B2 + B1 + O1, data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_L1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
   # NA % NA
L1    0    0
B1    0    0
O1    0    0
C2    4    4
B2   20   20


$m5f1

Bayesian beta model fitted with JointAI

Call:
betareg_imp(formula = Be1 ~ C2 + B2 + B1 + O1, data = wideDF, 
    n.adapt = 5, n.iter = 10, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
            Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)    0  0    0     0          0     NaN    NaN
C2             0  0    0     0          0     NaN    NaN
B21            0  0    0     0          0     NaN    NaN
B11            0  0    0     0          0     NaN    NaN
O1.L           0  0    0     0          0     NaN    NaN
O1.Q           0  0    0     0          0     NaN    NaN
O1.C           0  0    0     0          0     NaN    NaN

Posterior summary of other parameters:
        Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
tau_Be1    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 77 77

Number and proportion of missing values:
    # NA % NA
Be1    0    0
B1     0    0
O1     0    0
C2     4    4
B2    20   20


$m6a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = y ~ M2 + O2 * abs(C1 - C2) + log(C1), data = wideDF, 
    n.adapt = 5, n.iter = 5, seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
                 Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)         0  0    0     0          0     NaN    NaN
M22                 0  0    0     0          0     NaN    NaN
M23                 0  0    0     0          0     NaN    NaN
M24                 0  0    0     0          0     NaN    NaN
O22                 0  0    0     0          0     NaN    NaN
O23                 0  0    0     0          0     NaN    NaN
O24                 0  0    0     0          0     NaN    NaN
abs(C1 - C2)        0  0    0     0          0     NaN    NaN
log(C1)             0  0    0     0          0     NaN    NaN
O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
        Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_y    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 91 91

Number and proportion of missing values:
   # NA % NA
y     0    0
C1    0    0
O2    2    2
M2    3    3
C2    4    4


$m6b

Bayesian binomial model fitted with JointAI

Call:
glm_imp(formula = B1 ~ M2 + O2 * abs(C1 - C2) + log(C1), family = "binomial", 
    data = wideDF, n.adapt = 5, n.iter = 5, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
                 Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)         0  0    0     0          0     NaN    NaN
M22                 0  0    0     0          0     NaN    NaN
M23                 0  0    0     0          0     NaN    NaN
M24                 0  0    0     0          0     NaN    NaN
O22                 0  0    0     0          0     NaN    NaN
O23                 0  0    0     0          0     NaN    NaN
O24                 0  0    0     0          0     NaN    NaN
abs(C1 - C2)        0  0    0     0          0     NaN    NaN
log(C1)             0  0    0     0          0     NaN    NaN
O22:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O23:abs(C1 - C2)    0  0    0     0          0     NaN    NaN
O24:abs(C1 - C2)    0  0    0     0          0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 91 91

Number and proportion of missing values:
   # NA % NA
B1    0    0
C1    0    0
O2    2    2
M2    3    3
C2    4    4


$m6c

Bayesian Gamma model fitted with JointAI

Call:
glm_imp(formula = C1 ~ M2 + O2 * abs(y - C2), family = Gamma(link = "log"), 
    data = wideDF, n.adapt = 5, n.iter = 5, seed = 2020, warn = FALSE, 
    mess = FALSE)


Posterior summary:
                Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)        0  0    0     0          0     NaN    NaN
M22                0  0    0     0          0     NaN    NaN
M23                0  0    0     0          0     NaN    NaN
M24                0  0    0     0          0     NaN    NaN
O22                0  0    0     0          0     NaN    NaN
O23                0  0    0     0          0     NaN    NaN
O24                0  0    0     0          0     NaN    NaN
abs(y - C2)        0  0    0     0          0     NaN    NaN
O22:abs(y - C2)    0  0    0     0          0     NaN    NaN
O23:abs(y - C2)    0  0    0     0          0     NaN    NaN
O24:abs(y - C2)    0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
         Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_C1    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 100 


Number and proportion of complete cases:
        #  %
lvlone 91 91

Number and proportion of missing values:
   # NA % NA
C1    0    0
y     0    0
O2    2    2
M2    3    3
C2    4    4


$m6d

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = SBP ~ age + gender + log(bili) + exp(creat), 
    data = NHANES, n.adapt = 5, n.iter = 5, seed = 2020, warn = FALSE, 
    mess = FALSE, trunc = list(bili = c(1e-05, 1e+10)))


Posterior summary:
             Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)     0  0    0     0          0     NaN    NaN
age             0  0    0     0          0     NaN    NaN
genderfemale    0  0    0     0          0     NaN    NaN
log(bili)       0  0    0     0          0     NaN    NaN
exp(creat)      0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
          Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_SBP    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 186 


Number and proportion of complete cases:
         #    %
lvlone 178 95.7

Number and proportion of missing values:
       # NA % NA
SBP       0  0.0
age       0  0.0
gender    0  0.0
bili      8  4.3
creat     8  4.3


$m6e

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = SBP ~ age + gender + log(bili) + exp(creat), 
    data = NHANES, n.adapt = 5, n.iter = 5, models = c(bili = "lognorm", 
        creat = "lm"), seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
             Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)     0  0    0     0          0     NaN    NaN
age             0  0    0     0          0     NaN    NaN
genderfemale    0  0    0     0          0     NaN    NaN
log(bili)       0  0    0     0          0     NaN    NaN
exp(creat)      0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
          Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_SBP    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 186 


Number and proportion of complete cases:
         #    %
lvlone 178 95.7

Number and proportion of missing values:
       # NA % NA
SBP       0  0.0
age       0  0.0
gender    0  0.0
bili      8  4.3
creat     8  4.3


$m6f

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = SBP ~ age + gender + log(bili) + exp(creat), 
    data = NHANES, n.adapt = 5, n.iter = 5, models = c(bili = "glm_gamma_inverse", 
        creat = "lm"), seed = 2020, warn = FALSE, mess = FALSE)


Posterior summary:
             Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)     0  0    0     0          0     NaN    NaN
age             0  0    0     0          0     NaN    NaN
genderfemale    0  0    0     0          0     NaN    NaN
log(bili)       0  0    0     0          0     NaN    NaN
exp(creat)      0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
          Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_SBP    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:10
Sample size per chain = 5 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 186 


Number and proportion of complete cases:
         #    %
lvlone 178 95.7

Number and proportion of missing values:
       # NA % NA
SBP       0  0.0
age       0  0.0
gender    0  0.0
bili      8  4.3
creat     8  4.3


$mod7a

Bayesian linear model fitted with JointAI

Call:
lm_imp(formula = SBP ~ ns(age, df = 2) + gender + I(bili^2) + 
    I(bili^3), data = NHANES, n.adapt = 5, n.iter = 10, seed = 2020, 
    warn = FALSE, mess = FALSE)


Posterior summary:
                 Mean SD 2.5% 97.5% tail-prob. GR-crit MCE/SD
(Intercept)         0  0    0     0          0     NaN    NaN
ns(age, df = 2)1    0  0    0     0          0     NaN    NaN
ns(age, df = 2)2    0  0    0     0          0     NaN    NaN
genderfemale        0  0    0     0          0     NaN    NaN
I(bili^2)           0  0    0     0          0     NaN    NaN
I(bili^3)           0  0    0     0          0     NaN    NaN

Posterior summary of residual std. deviation:
          Mean SD 2.5% 97.5% GR-crit MCE/SD
sigma_SBP    0  0    0     0     NaN    NaN


MCMC settings:
Iterations = 6:15
Sample size per chain = 10 
Thinning interval = 1 
Number of chains = 3 

Number of observations: 186 


Number and proportion of complete cases:
         #    %
lvlone 178 95.7

Number and proportion of missing values:
       # NA % NA
SBP       0  0.0
age       0  0.0
gender    0  0.0
bili      8  4.3


