Calculate a coefficient of determination based on the likelihood-ratio test (R_LR<U+00B2>).

`r.squaredLR(x, null = NULL, null.RE = FALSE)`null.fit(x, evaluate = FALSE, RE.keep = FALSE, envir = NULL)

x

a fitted model object.

null

a fitted *null* model. If not provided, `null.fit`

will
be used to construct it. `null.fit`

's capabilities are limited to only
a few model classes, for others the *null* model has to be specified
manually.

null.RE

logical, should the null model contain random factors? Only
used if no *null* model is given, otherwise omitted, with a warning.

evaluate

if `TRUE`

evaluate the fitted model object else return
the call.

RE.keep

if `TRUE`

, the random effects of the original model are
included.

envir

the environment in which the *null* model is to be
evaluated, defaults to the environment of the original model's formula.

`r.squaredLR`

returns a value of R_LR<U+00B2>, and the
attribute `"adj.r.squared"`

gives the Nagelkerke's modified statistic.
Note that this is not the same as nor equivalent to the classical
‘adjusted R squared’.

`null.fit`

returns the fitted *null* model object (if
`evaluate = TRUE`

) or an unevaluated call to fit a *null* model.

This statistic is is one of the several proposed pseudo-R<U+00B2>'s for
nonlinear regression models. It is based on an improvement from *null*
(intercept only) model to the fitted model, and calculated as

$$R<U+00B2> = 1 - exp(-2/n * <U+33D2><U+2113>(x) - <U+33D2><U+2113>(0)) $$

where \(<U+33D2><U+2113>(x)\) and \(<U+33D2><U+2113>(0)\) are the log-likelihoods of the
fitted and the *null* model respectively.
ML estimates are used if models have been
fitted by REstricted ML (by calling `logLik`

with argument
`REML = FALSE`

). Note that the *null* model can include the random
factors of the original model, in which case the statistic represents the
‘variance explained’ by fixed effects.

For OLS models the value is consistent with classical R<U+00B2>. In some cases (e.g. in logistic regression), the maximum R_LR<U+00B2> is less than one. The modification proposed by Nagelkerke (1991) adjusts the R_LR<U+00B2> to achieve 1 at its maximum: \(R<U+0305><U+00B2> = R<U+00B2> / max(R<U+00B2>) \) where \(max(R<U+00B2>) = 1 - exp(2 / n * <U+33D2><U+2113>(0)) \).

`null.fit`

tries to guess the *null* model call, given the provided
fitted model object. This would be usually a `glm`

. The function will give
an error for an unrecognized class.

Cox, D. R. and Snell, E. J. (1989) *The analysis of binary data*, 2nd ed.
London, Chapman and Hall

Magee, L. (1990) R<U+00B2> measures based on Wald and likelihood ratio joint
significance tests. *Amer. Stat.* 44: 250-253

Nagelkerke, N. J. D. (1991) A note on a general definition of the coefficient of
determination. *Biometrika* 78: 691-692