This function prints information on all models, those explicitly specified by the user and those specified automatically by JointAI for (incomplete) covariates in a JointAI object.
list_models(object, predvars = TRUE, regcoef = TRUE, otherpars = TRUE,
priors = TRUE, refcat = TRUE)object inheriting from class 'JointAI'
logical; should information on the predictor variables be
printed? (default is TRUE)
logical; should information on the regression coefficients
be printed? (default is TRUE)
logical; should information on other parameters be printed?
(default is TRUE)
logical; should information on the priors
(and hyper-parameters) be printed? (default is TRUE)
logical; should information on the reference category be
printed? (default is TRUE)
The models listed by this function are not the actual imputation models, but the conditional models that are part of the specification of the joint distribution. Briefly, the joint distribution is specified as a sequence of conditional models
\[p(y | x_1, x_2, x_3, ..., \theta) p(x_1|x_2, x_3, ..., \theta) p(x_2|x_3, ..., \theta) ...\] The actual imputation models are the full conditional distributions \(p(x_1 | \cdot)\) derived from this joint distribution. Even though the conditional distributions do not contain the outcome and all other covariates in their linear predictor, outcome and other covariates are taken into account implicitly, since imputations are sampled from the full conditional distributions. For more details, see Erler et al. (2016) and Erler et al. (2019).
The function list_models prints information on the conditional
distributions of the covariates (since they are what is specified;
the full-conditionals are automatically derived within JAGS). The outcome
is, thus, not part of the printed linear predictor, but is still included
during imputation.
Erler, N.S., Rizopoulos, D., Rosmalen, J.V., Jaddoe, V.W., Franco, O.H., & Lesaffre, E.M.E.H. (2016). Dealing with missing covariates in epidemiologic studies: A comparison between multiple imputation and a full Bayesian approach. Statistics in Medicine, 35(17), 2955-2974.
Erler NS, Rizopoulos D, Lesaffre EMEH (2021). "JointAI: Joint Analysis and Imputation of Incomplete Data in R." Journal of Statistical Software, 100(20), 1-56. doi:10.18637/jss.v100.i20 .
# (set n.adapt = 0 and n.iter = 0 to prevent MCMC sampling to save time)
mod1 <- lm_imp(y ~ C1 + C2 + M2 + O2 + B2, data = wideDF, n.adapt = 0,
n.iter = 0, mess = FALSE)
#> Warning:
#> It is currently not possible to use “contr.poly” for incomplete
#> categorical covariates. I will use “contr.treatment” instead. You can
#> specify (globally) which types of contrasts are used by changing
#> “options('contrasts')”.
list_models(mod1)
#> Linear model for “y”
#> family: gaussian
#> link: identity
#> * Predictor variables:
#> (Intercept), C1, C2, M22, M23, M24, O22, O23, O24, B21
#> * Regression coefficients:
#> beta[1:10] (normal prior(s) with mean 0 and precision 1e-04)
#> * Precision of “y” :
#> tau_y (Gamma prior with shape parameter 0.01 and rate parameter 0.01)
#>
#>
#> Binomial model for “B2”
#> family: binomial
#> link: logit
#> * Reference category: “0”
#> * Predictor variables:
#> (Intercept), C1, C2, M22, M23, M24, O22, O23, O24
#> * Regression coefficients:
#> alpha[1:9] (normal prior(s) with mean 0 and precision 1e-04)
#>
#>
#> Linear model for “C2”
#> family: gaussian
#> link: identity
#> * Predictor variables:
#> (Intercept), C1, M22, M23, M24, O22, O23, O24
#> * Regression coefficients:
#> alpha[10:17] (normal prior(s) with mean 0 and precision 1e-04)
#> * Precision of “C2” :
#> tau_C2 (Gamma prior with shape parameter 0.01 and rate parameter 0.01)
#>
#>
#> Multinomial logit model for “M2”
#> * Reference category: “1”
#> * Predictor variables:
#> (Intercept), C1, O22, O23, O24
#> * Regression coefficients:
#> M22: alpha[18:22]
#> M23: alpha[23:27]
#> M24: alpha[28:32] (normal prior(s) with mean 0 and precision 1e-04)
#>
#>
#> Cumulative logit model for “O2”
#> * Reference category: “1”
#> * Predictor variables:
#> C1
#> * Regression coefficients:
#> alpha[33] (normal prior(s) with mean 0 and precision 1e-04)
#> * Intercepts:
#> - 1: gamma_O2[1] (normal prior with mean 0 and precision 1e-04)
#> - 2: gamma_O2[2] = gamma_O2[1] + exp(delta_O2[1])
#> - 3: gamma_O2[3] = gamma_O2[2] + exp(delta_O2[2])
#> * Increments:
#> delta_O2[1:2] (normal prior(s) with mean 0 and precision 1e-04)
#>
#>