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Transform values from the link scale to the natural scale

Source: R/links.R
inverse_link.Rd

Cognitive measurement models are estimated on a link scale that keeps parameters unconstrained — a memory precision is sampled as log(kappa), a mixture weight as logit(theta) — while readers interpret them on the natural scale. inverse_link() is the back-transform, applied by recover() to estimates, interval bounds and generating values alike so that both sides of a recovery comparison are on the same scale.

Usage

inverse_link(x, link)

Arguments

x

A numeric vector of values on the link scale. NA is passed through at its own position.

A single string naming the link: one of "identity", "log", "softplus", "log1p", "logm1", "inverse", "sqrt", "logit", "probit", "tan_half", "loglog" or "cloglog". NULL is a synonym for "identity".

Value

A double vector the same length as x, on the natural scale.

Details

The vocabulary and the closed forms are taken from bmm's internal link_transform() (bmm/R/helpers-parameters.R), so the two cannot disagree about what a link name means. bmmtools ships its own copy because link_transform() is not exported.

Values outside a link's natural domain are transformed as R computes them rather than being replaced by NA: inverse_link(0, "inverse") is Inf and inverse_link(-2, "sqrt") is 4. In a scoring pipeline a visible Inf is safer than a silent NA, which would be absorbed by a metric's missing-data guard and reported as a smaller sample rather than as a problem.

Examples

inverse_link(c(-1, 0, 1), "log")
#> [1] 0.3678794 1.0000000 2.7182818
inverse_link(0, "logit")
#> [1] 0.5

# a precision sampled on the log scale, back on its own scale
inverse_link(c(1.6, 2.3), "log")
#> [1] 4.953032 9.974182