Extract the Log-Likelihood for gips class

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.

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.

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.

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.

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
#> 'log Lik.' -32.67048 (df=10)
# 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 = ""))`
#> 'log Lik.' -32.6722 (df=3)

g_n_too_small <- gips(S, number_of_observations = 4)
logLik(g_n_too_small) # NULL # the likelihood does not exists
#> Warning: The likelihood is not defined for this `gips`.
#> ✖ The n = 4 is smaller than the minimum required n0 = 5. For more information, see section **Existence of likelihood** in documentation `?logLik.gips` or its [pkgdown page](https://przechoj.github.io/gips/reference/logLik.gips.html).
#> NULL
summary(g_n_too_small)$n0 # 5, but we set number_of_observations = 4, which is smaller
#> [1] 5

g_MAP <- find_MAP(g_n_too_small)
#> You used the default value of the 'optimizer' argument in `find_MAP()`.
#> ℹ The 'optimizer = NA' was automatically changed to 'optimizer = "BF"'.
#> ================================================================================
logLik(g_MAP) # -24.94048, this is no longer NULL
#> 'log Lik.' -24.94048 (df=3)
summary(g_MAP)$n0 # 2
#> [1] 2

Extract the Log-Likelihood for `gips` class