Likelihood, information criteria and coefficients of an L0glm fit
Source:R/model_methods.R
model_criteria.RdExtract the fitted log likelihood, parameter-count information criteria,
coefficient matrix or criterion sample size from L0glm.fit() and
L0nnpois() models, including the special families.
Usage
# S3 method for class 'L0glm_fit'
logLik(object, ..., mu_floor = 0)
# S3 method for class 'L0glm_fit'
nobs(object, ...)
# S3 method for class 'L0glm_fit'
coef(object, ...)
GIC(object, ...)
# S3 method for class 'L0glm_fit'
GIC(object, ..., mu_floor = 0)
EBIC(object, ...)
# S3 method for class 'L0glm_fit'
EBIC(object, ..., mu_floor = 0)
MBIC(object, ...)
# S3 method for class 'L0glm_fit'
MBIC(object, ..., mu_floor = 0)Arguments
- object
A model returned by
L0glm.fit()orL0nnpois().- ...
Further arguments.
stats::AIC()andstats::BIC()also accept several fitted models for comparison.- mu_floor
Nonnegative scoring-only floor for positive-family means. The default, zero, requests the exact score at the fitted means.
Value
logLik() returns an object of class logLik, with
df and nobs attributes. Each criterion returns a numeric
score; coef() returns a sparse matrix; nobs() returns the
criterion sample size.
Details
logLik() evaluates the unpenalized likelihood at the returned
coefficients, using the original prior observation weights and offsets.
The adaptive-ridge penalty is not part of this value. No additional
likelihood pass is performed when fitting ordinary GLMs or native Poisson
models; the score is calculated when requested.
The logLik object's df attribute is a model parameter count,
not the effective degrees of freedom of a ridge smoother. Nonzero
coefficients and all mandatory coefficient dimensions are counted, along
with one nuisance parameter for each estimated dispersion or NB theta.
Known dispersions and fixed NB theta do not add a nuisance parameter.
Gaussian estimated dispersion is profiled as weighted RSS divided by the
number of positive-weight observations in each channel. Estimated Gamma
and inverse-Gaussian dispersion use the same deviance-based
family$aic convention as the existing package metrics, which need
not equal the jointly maximized likelihood. For quasipoisson, the Poisson
log-likelihood kernel is divided by the fitted dispersion. The regular
criterion names report the corresponding quasi-information criteria;
logLik() marks the value with quasi=TRUE. Use a common dispersion when
comparing candidate models. Quasibinomial likelihood criteria are unavailable.
Multinomial grouped selection counts \(K-1\) parameters per active row for \(K\) categories. Ungrouped CLR selection counts nonzero entries minus active rows, imposing the zero-sum constraint. Mandatory rows count \(K-1\) parameters. Cox uses the Breslow partial log likelihood; its unspecified baseline hazard is not counted in these partial-likelihood criteria.
With \(d\) the parameter count, the scores are
$$\mathrm{AIC}=-2\ell+2d,\qquad
\mathrm{BIC}=-2\ell+d\log n,$$
$$\mathrm{GIC}=-2\ell+d\log p\log\log n.$$
EBIC() and MBIC() use the penalties documented in
information_criteria. Here \(p\) is the original selectable
predictor count, excluding mandatory terms and using at least one in
logarithms. Ordinary multichannel GLMs count coefficient entries, so
GIC() is distinct from a row-count grouped-selection objective.
These scores describe the returned fit; penalized or incompletely
converged fits need not maximize likelihood on their selected support.
nobs() reports the sample size used by the criteria. Existing
conventions are retained: the number of design rows for ordinary GLMs;
positive-weight rows for NB and multinomial; and weighted event count
for Cox. Special-family criterion sample sizes are bounded below by two.
Independent multichannel responses use the number of observations,
rather than observations times channels, in the complexity penalty.
The usual stats::AIC() and stats::BIC() methods obtain their values
through logLik(), including its df and nobs
attributes. coef() returns the sparse coefficient matrix on the
original scale and with the original coefficient dimensions.