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

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the log-likelihood for a fitted joint model.

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

`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.

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.

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.

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

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

## 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)