# logLik: Log-Likelihood for Joint Models In JMbayes: Joint Modeling of Longitudinal and Time-to-Event Data under a Bayesian Approach

## Description

Computes the log-likelihood for a fitted joint model.

## Usage

 1 2 3 ## S3 method for class 'JMbayes' logLik(object, thetas, b, priors = TRUE, marginal.b = TRUE, marginal.thetas = FALSE, full.Laplace = FALSE, useModes = TRUE, ...) 

## Arguments

 object an object inheriting from class JMBayes. thetas a list with values for the joint model's parameters. This should have the same structure as the coefficients component of a fitted joint model. If missing object\$postMeans is used. b a numeric matrix with random effects value. This should have the same structure as the ranef component of a fitted joint model. If missing ranef(object) is used. priors logical, if TRUE the priors are also included in the computation. marginal.b logical, if TRUE the marginal log-likelihood over the random effects is returned. This marginalization is done using a Laplace approximation. marginal.thetas logical, if TRUE the marginal log-likelihood over the parameters is returned. This marginalization is done using a Laplace approximation. full.Laplace logical, if FALSE the posterior means and posterior variances are used in the Laplace approximation instead of the posterior modes and posterior hessian matrix of the random effects. Sacrificing a bit of accuracy, this will be much faster than calculating the posterior modes. Relevant only when marginal.b = TRUE. useModes logical, if TRUE the modes are used in the Laplace approximation otherwise the means. ... extra arguments; currently none is used.

## Details

Let y_i denote the vectors of longitudinal responses, T_i the observed event time, and δ_i the event indicator for subject i (i = 1, …, n). Let also p(y_i | b_i; θ) denote the probability density function (pdf) for the linear mixed model, p(T_i, δ_i | b_i; θ) the pdf for the survival submodel, and p(b_i; θ) the multivariate normal pdf for the random effects, where θ denotes the full parameter vector. Then, if priors = TRUE, and marginal.b = TRUE, function logLik() computes

\log \int p(y_i | b_i; θ) p(T_i, δ_i | b_i; θ) p(b_i; θ) db_i + \log p(θ),

where p(θ) denotes the prior distribution for the parameters. If priors = FALSE the prior is excluded from the computation, i.e.,

\log \int p(y_i | b_i; θ) p(T_i, δ_i | b_i; θ) p(b_i; θ) db_i,

and when marginal.b = FALSE, then the conditional on the random effects log-likelihood is computed, i.e.,

\log p(y_i | b_i; θ) + \log p(T_i, δ_i | b_i; θ) + \log p(b_i; θ) + \log p(θ),

when priors = TRUE and

\log p(y_i | b_i; θ) + \log p(T_i, δ_i | b_i; θ) + \log p(b_i; θ),

when priors = FALSE.

## Value

a numeric scalar of class logLik with the value of the log-likelihood. It also has the attributes df the number of parameter (excluding the random effects), and nobs the number of subjects.

## Author(s)

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

## References

Rizopoulos, D., Hatfield, L., Carlin, B. and Takkenberg, J. (2014). Combining dynamic predictions from joint models for longitudinal and time-to-event data using Bayesian model averaging. Journal of the American Statistical Association. to appear.

jointModelBayes
  1 2 3 4 5 6 7 8 9 10 11 12 ## Not run: lmeFit <- lme(log(serBilir) ~ ns(year, 2), data = pbc2, random = ~ ns(year, 2) | id) survFit <- coxph(Surv(years, status2) ~ 1, data = pbc2.id, x = TRUE) jointFit <- jointModelBayes(lmeFit, survFit, timeVar = "year") logLik(jointFit) logLik(jointFit, priors = FALSE) logLik(jointFit, marginal.b = FALSE) ## End(Not run)