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Convert native binegbin/bipois dpars to (M, f, delta) coordinates

Source: R/mfd.R
binegbin_dpars_to_mfd.Rd

Inverse of binegbin_mfd_to_dpars(). Reads the rate dpars mu, lambdaone, lambdatwo back into the interpretable coordinates: the midpoint M of the two expected counts, congruence f, and source bias delta, optionally converting NB2 inverse dispersions to overdispersions.

As with the forward direction, the three rates are common to bipois(), bipois_partialobs(), binegbin() and binegbin_partialobs(), so this serves all four constructors; only the dispersion arguments differ.

This direction reads a stored fit, so it accepts shapex – the single dispersion of both exclusive components, declared by every binegbin fit made before 0.10.0 – as well as the current shapexone/shapextwo. The forward direction writes only current names; see its documentation for why the two directions differ.

Usage

binegbin_dpars_to_mfd(
  mu,
  lambdaone,
  lambdatwo,
  shapes = NULL,
  shapex = NULL,
  shapexone = NULL,
  shapextwo = NULL
)

Arguments

mu

Shared-component rate.

lambdaone, lambdatwo

The rates of the two source-exclusive components.

shapes, shapex

Optional NB2 inverse dispersions. If supplied, the returned list gains kappas/kappax (= 1/sqrt(shape), so shape = Inf gives 0). shapex is the single dispersion of both exclusive components, declared by a binegbin fit made before 0.10.0; no shipping family takes it now. A fit of bipois() or bipois_partialobs() has no dispersion to pass: read its three rates alone.

shapexone, shapextwo

Optional NB2 inverse dispersions of the exclusive components, as taken by both negative-binomial constructors since 0.10.0. If supplied, the returned list gains kappaxone/kappaxtwo. Mutually exclusive with shapex, which is the same quantity under its older name.

Value

A named list of M, f, delta, plus beta (the bounded bias tanh(delta)), kappas/kappax when shapes/shapex are supplied, and kappaxone/kappaxtwo when shapexone/shapextwo are supplied.

Details

Arguments are recycled to a common length, so this vectorises over posterior draws – e.g. to convert a whole posterior into interpretable coordinates.

Boundary behaviour, which the forward direction does not have:

  • lambdaone == lambdatwo == 0 (perfect congruence, f = 1): the bias is genuinely unidentified – there are no exclusive events to be biased – and delta is returned as NA, not 0. Zero would assert an unbiased source, which the data at that point cannot support.

  • M == 0 (nothing anywhere): f is undefined and returned as NA.

  • Exactly one exclusive rate 0: delta is +/-Inf, the well-defined limit where one source never records an unshared event.

Because of the first case, round-tripping is exact everywhere except at f = 1, where delta cannot be recovered. Hold one coordinate system as the source of truth rather than repeatedly converting back and forth.

See also

binegbin_mfd_to_dpars(), bipois(), bipois_partialobs(), binegbin(), binegbin_partialobs()

Examples

binegbin_dpars_to_mfd(mu = 8.04, lambdaone = 4.75, lambdatwo = 3.17)
#> $M
#> [1] 12
#> 
#> $f
#> [1] 0.67
#> 
#> $delta
#> [1] 0.2022065
#> 
#> $beta
#> [1] 0.1994949
#> 

# Round trip
d <- binegbin_mfd_to_dpars(M = 12, f = 0.67, delta = 0.2)
binegbin_dpars_to_mfd(d$mu, d$lambdaone, d$lambdatwo)[c("M", "f", "delta")]
#> $M
#> [1] 12
#> 
#> $f
#> [1] 0.67
#> 
#> $delta
#> [1] 0.2
#> 

# Perfect congruence: bias is unidentified, reported as NA
binegbin_dpars_to_mfd(mu = 12, lambdaone = 0, lambdatwo = 0)$delta
#> [1] NA