logLik function

Log-Likelihood for Joint Models

Computes the log-likelihood for a fitted joint model.

## 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 $\delta_i$

the event indicator for subject $i$ ($i = 1, \ldots, n$). Let also $p(y_i | b_i; \theta)$ denote the probability density function (pdf) for the linear mixed model, $p(T_i, \delta_i | b_i; \theta)$ the pdf for the survival submodel, and $p(b_i; \theta)$ the multivariate normal pdf for the random effects, where $\theta$ denotes the full parameter vector. Then, if priors = TRUE, and marginal.b = TRUE, function logLik() computes

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

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

when priors = TRUE and

when priors = FALSE.

Returns

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.

See Also

jointModelBayes

Examples

## 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)