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One-Inflated Binomial Family

Source: R/family_zi.R
ratiod_oibinomial.Rd

One-inflated binomial for proportions with excess ones (100% success). Useful when perfect detection/success has a structural component.

$$P(Y = n) = \psi + (1 - \psi) \cdot p^n$$ $$P(Y = y) = (1 - \psi) \cdot \binom{n}{y} p^y (1-p)^{n-y}, \quad y < n$$

Usage

ratiod_oibinomial(link_num = "logit", link_oi = "logit")

Arguments

Link function for the success probability: "logit" (default), "probit" or "cloglog".

Link function for the one-inflation probability: "logit" (default), "probit" or "cloglog".

Value

A ratiod_family object with one-inflation

Details

Use this when excess 100% success rates occur due to:

  • Perfect detection in highly suitable habitat

  • Saturation effects

  • Structural constraints ensuring full success

Examples

# Create family object
fam <- ratiod_oibinomial()
print(fam)
#> tulpaRatio family: oibinomial 
#> [Zero-inflated model]
#> One-inflated binomial numerator, fixed trials denominator 
#> 
#> Numerator:  binomial(logit)
#> ZI prob:    bernoulli()
#> Denominator: fixed (fixed)