logLik.gips: Extract the Log-Likelihood for 'gips' class

In PrzeChoj/gips: Gaussian Model Invariant by Permutation Symmetry

Extract the Log-Likelihood for gips class

Description

Calculates Log-Likelihood of the sample based on the gips object.

Usage

## S3 method for class 'gips'
logLik(object, ...)

Arguments

object	An object of class gips. Usually, a result of a find_MAP().
...	Further arguments will be ignored.

Details

This will always be the biggest for perm = "()" (provided that p <= n).

If the found permutation still requires more parameters than n, the likelihood does not exist; thus the function returns NULL.

If the projected_cov (output of project_matrix()) is close to singular, the NA is returned.

Value

Log-Likelihood of the sample. Object of class logLik.

Possible failure situations:

• When the multivariate normal model does not exist (number_of_observations < n0), it returns NULL.

• When the multivariate normal model cannot be reasonably approximated (output of project_matrix() is singular), it returns -Inf.

In both failure situations, it shows a warning. More information can be found in the Existence of likelihood section below.

Existence of likelihood

We only consider the non-degenerate multivariate normal model. In the gips context, such a model exists only when the number of observations is bigger or equal to n0. To get n0 for the gips object g, call summary(g)$n0.

See examples where the g_n_too_small had too small number_of_observations to have likelihood. After the optimization, the likelihood did exist.

For more information, refer to C_\sigma and n0 section in vignette("Theory", package = "gips") or its pkgdown page.

Calculation details

For more details and used formulas, see the Information Criterion - AIC and BIC section in vignette("Theory", package = "gips") or its pkgdown page.

See Also

• logLik() - Generic function this logLik.gips() extends.

• find_MAP() - Usually, the logLik.gips() is called on the output of find_MAP().

• AIC.gips(), BIC.gips() - Often, one is more interested in an Information Criterion AIC or BIC.

• summary.gips() - One can get n0 by calling summary(g)$n0. To see why one may be interested in n0, see the Existence of likelihood section above.

• project_matrix() - Project the known matrix onto the found permutations space. It is mentioned in the Calculation details section above.

Examples

S <- matrix(c(
  5.15, 2.05, 3.60, 1.99,
  2.05, 5.09, 2.03, 3.57,
  3.60, 2.03, 5.21, 1.97,
  1.99, 3.57, 1.97, 5.13
), nrow = 4)
g <- gips(S, 5)
logLik(g) # -32.67048
# For perm = "()", which is default, there is p + choose(p, 2) degrees of freedom

g_map <- find_MAP(g, optimizer = "brute_force")
logLik(g_map) # -32.6722 # this will always be smaller than `logLik(gips(S, n, perm = ""))`

g_n_too_small <- gips(S, number_of_observations = 4)
logLik(g_n_too_small) # NULL # the likelihood does not exists
summary(g_n_too_small)$n0 # 5, but we set number_of_observations = 4, which is smaller

g_MAP <- find_MAP(g_n_too_small)
logLik(g_MAP) # -24.94048, this is no longer NULL
summary(g_MAP)$n0 # 2

PrzeChoj/gips documentation built on June 12, 2025, 12:23 a.m.