Zero-inflated binomial family

Zero-inflated binomial for the numerator when modeling proportions with excess zeros (e.g., species detection/non-detection).

$$P(Y = 0) = \pi + (1 - \pi) \cdot (1-p)^n$$ $$P(Y = y) = (1 - \pi) \cdot \binom{n}{y} p^y (1-p)^{n-y}, \quad y > 0$$

Usage

ratiod_zibinomial(link_num = "logit", link_zi = "logit")

Arguments

link_num

Link function for success probability (default: "logit")

link_zi

Link function for zero-inflation probability (default: "logit")

Value

A ratiod_family object with zero-inflation

Details

Use this family when modeling proportions (successes/trials) where excess zeros occur beyond what binomial predicts. Common applications:

• Species occupancy with false negatives

• Survey data with non-response

• Epidemiological data with under-reporting

See also

ratiod_binomial(), ratiod_zinegbin()

Examples

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