This function is generic; method functions can be written to handle
specific classes of objects. Classes which have methods for this
function include: `"glm"`

, `"lm"`

, `"nls"`

and
`"Arima"`

. Packages contain methods for other classes, such as
`"fitdistr"`

, `"negbin"`

and `"polr"`

in package
MASS, `"multinom"`

in package nnet and
`"gls"`

, `"gnls"`

`"lme"`

and others in package
nlme.

1 2 3 4 |

`object` |
any object from which a log-likelihood value, or a contribution to a log-likelihood value, can be extracted. |

`...` |
some methods for this generic function require additional arguments. |

`REML` |
an optional logical value. If |

`logLik`

is most commonly used for a model fitted by maximum
likelihood, and some uses, e.g. by `AIC`

, assume
this. So care is needed where other fit criteria have been used, for
example REML (the default for `"lme"`

).

For a `"glm"`

fit the `family`

does not have to
specify how to calculate the log-likelihood, so this is based on using
the family's `aic()`

function to compute the AIC. For the
`gaussian`

, `Gamma`

and
`inverse.gaussian`

families it assumed that the dispersion
of the GLM is estimated and has been counted as a parameter in the AIC
value, and for all other families it is assumed that the dispersion is
known. Note that this procedure does not give the maximized
likelihood for `"glm"`

fits from the Gamma and inverse gaussian
families, as the estimate of dispersion used is not the MLE.

For `"lm"`

fits it is assumed that the scale has been estimated
(by maximum likelihood or REML), and all the constants in the
log-likelihood are included. That method is only applicable to
single-response fits.

Returns an object of class `logLik`

. This is a number with at
least one attribute, `"df"`

(**d**egrees of **f**reedom),
giving the number of (estimated) parameters in the model.

There is a simple `print`

method for `"logLik"`

objects.

There may be other attributes depending on the method used: see the
appropriate documentation. One that is used by several methods is
`"nobs"`

, the number of observations used in estimation (after
the restrictions if `REML = TRUE`

).

José Pinheiro and Douglas Bates

For `logLik.lm`

:

Harville, D.A. (1974).
Bayesian inference for variance components using only error contrasts.
*Biometrika*, **61**, 383–385.

`logLik.gls`

, `logLik.lme`

, in
package nlme, etc.

`AIC`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
x <- 1:5
lmx <- lm(x ~ 1)
logLik(lmx) # using print.logLik() method
utils::str(logLik(lmx))
## lm method
(fm1 <- lm(rating ~ ., data = attitude))
logLik(fm1)
logLik(fm1, REML = TRUE)
utils::data(Orthodont, package = "nlme")
fm1 <- lm(distance ~ Sex * age, Orthodont)
logLik(fm1)
logLik(fm1, REML = TRUE)
``` |

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