Returns information about the loss functions implemented for use with the
optimisation procedure in the MortalityLaw function.
Value
A list of class availableLF with the components:
- table
Table with loss functions and codes to be used in
MortalityLaw.- legend
Table with details about the abbreviation used.
Details
The two likelihoods ("poissonL", "binomialL") are the only
objectives that yield a log-likelihood, an AIC and a BIC; the six loss
functions ("LF1" to "LF6") leave those measures undefined
(NaN) and are compared on the deviance or the loss itself.
"LF2", the squared log-ratio, is the default: it is scale-free and
robust, and it has been observed to return reliable estimates for the
high-parameter laws such as Heligman-Pollard. There is no universally best
choice, so it is worth trying more than one.
Examples
availableLF()
#>
#> Loss functions available in the package:
#>
#> LOSS FUNCTION CODE
#> L = -[Dx * log(mu) - mu*Ex] poissonL
#> L = -[Dx * log(1 - exp(-mu)) - (Ex - Dx)*mu] binomialL
#> L = [1 - mu/ov]^2 LF1
#> L = log[mu/ov]^2 LF2
#> L = [(ov - mu)^2]/ov LF3
#> L = [ov - mu]^2 LF4
#> L = [ov - mu] * log[ov/mu] LF5
#> L = abs(ov - mu) LF6
#>
#> LEGEND:
#> Dx: Death counts
#> Ex: Population exposed to risk
#> mu: Estimated value
#> ov: Observed value
#>
#> HINT: Most loss functions work well with 'poissonL'. However, for complex mortality laws like Heligman-Pollard (HP), a better fit can be obtained using other loss functions (e.g. 'LF2'). You are strongly encouraged to test different options before deciding on the final version. The results might be slightly different.