logLik.joint | R Documentation |

Calculate joint log-likelihood, degrees of freedom, AIC and BIC of joint model fit.

```
## S3 method for class 'joint'
logLik(object, conditional = FALSE, ...)
```

`object` |
a |

`conditional` |
Logical. Should the conditional or observed data log-likelihood
be returned? See |

`...` |
additional arguments (none used). |

Calculate the log-likelihood of a joint model of survival and multivariate longitudinal
data (i.e. a `joint`

object). The argument `conditional`

manages whether
or not the log-likelihood *conditional* on the random effects, or simply
the observed data log-likelihood is returned (the default, `conditional = FALSE`

).

If `conditional = TRUE`

, then the log-likelihood conditional on the random
effects is returned. That is

```
\log f(T_i, \Delta_i, Y_i|b_i;\Omega) =
\log f(Y_i|b_i; \Omega) + \log f(T_i, \Delta_i|b_i; \Omega) + \log f(b_i|\Omega)
```

If `conditional = FALSE`

, then the observed data log-likelihood is returned i.e.

`\log\int f(Y_i|b_i; \Omega)f(T_i, \Delta_i|b_i; \Omega)f(b_i|\Omega)db_i.`

Additionally, the degrees of freedom, `\nu`

is given by

`\nu = \code{length(vech(D))} + \sum_{k=1}^K\{P_k + P_{\sigma_k}\} + P_s,`

where `P_k`

denotes the number of coefficients estimated for the `k`

th response,
and `P_{\sigma_k}`

the number of dispersion parameters estimated. `P_s`

denotes
the number of survival coefficients, i.e. the length of `c(zeta, gamma)`

. Finally,
all covariance parameters are captured in `length(vech(D))`

.

With the degrees of freedom, we can additionally compute AIC and BIC, which are defined in no special way; and are calculated using the observed data log-likelihood.

Returns an object of class `logLik`

, a number which is the log-likelihood
of the fitted model `object`

. This has multiple attributes: `df`

which is the
degrees of freedom, `df.residual`

; the number of residual degrees of freedom;
`AIC`

and `BIC`

which are the Akaike or Bayes information criterion evaluated at
either the conditional or observed log-likelihood (as requested by argument
`conditional`

).

James Murray (j.murray7@ncl.ac.uk)

Henderson R, Diggle P, Dobson A. Joint modelling of longitudinal measurements and event time
data. *Biostatistics* 2000; **1(4)**; 465-480.

Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error.
*Biometrics* 1997; **53(1)**; 330-339.

`extractAIC.joint`

and `anova.joint`

```
# Bivariate simulated data (2x Gaussian)
data <- simData(n = 100,
D = diag(c(.25, .04, .2, .02)),
gamma = c(0.4, -0.2), theta = c(-2, .2))$data
fit <- joint(list(
Y.1 ~ time + cont + bin + (1 + time|id),
Y.2 ~ time + cont + bin + (1 + time|id)
), Surv(survtime, status) ~ cont + bin,
data = data,
family = list('gaussian', 'gaussian'))
logLik(fit)
```

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