ZAP random-forest prediction — Msm327 • rmorie

Formula: Y-hat = (1 - theta-hat) mu-hat / (1 - exp(-mu-hat)) (eq. 15.3): under ZAP_RF the prediction is the mean of the zero-altered Poisson model.

Usage

Msm327(theta_hat, mu_hat)

Arguments

theta_hat: Estimated probability of an altered zero.
mu_hat: Estimated Poisson rate.

Value

List with estimate, y_hat, method.

Details

Book erratum: eq. (15.3) as printed, and the E(Y) line on p.651, both give the numerator as (1 - theta) exp(-mu), dropping the mu factor. The ZAP probability mass function printed directly above E(Y), the Var(Y) expression printed on the next line, and the p.652 estimating equation for mu all carry the mu. The printed form is also not a count: it decreases towards zero as mu grows. The internally consistent formula is implemented.

References

Montesinos Lopez, Montesinos Lopez & Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, eq. (15.3) p.652. DOI 10.1007/978-3-030-89010-0.

Examples

# P(altered zero) 0.3, Poisson rate 2: (1 - 0.3) * 2 / (1 - exp(-2)), the zero-truncated mean
Msm327(theta_hat = 0.3, mu_hat = 2)$estimate
#> [1] 1.619125