p.mamml {harmonicmeanp}

Compute a combined p-value via the model-averaged mean maximized likelihood ratio

Description

The model averaging by mean maximum likelihood (MAMML) test combines likelihood ratio tests and corrects for multiple testing while controlling the weak-sense family-wise error rate in a way that is more powerful than common alternatives including Bonferroni and Simes procedures and possesses theoretical robustness to positive correlations between tests and unequal weights. It is a frequentist analogue to Bayesian model averaging, is theoretically grounded in generalized central limit theorem, and motivates the simpler and better-calibrated harmonic mean p-value (HMP) test. The model-averaged mean maximized likelihood (MAMML) is defined as the (possibly weighted) arithmetic mean of the maximized likelihood ratios from a series of likelihood ratio tests comparing mutually exclusive alternative hypotheses with the same nested null hypothesis based on the exact same data.

Usage

p.mamml(R, nu, w = NULL, L = NULL)

Arguments

R

A numeric vector of one or more maximized likelihood ratios. Missing values (NAs) will cause a missing value to be returned.

nu

A numeric scalar or vector for the degrees of freedom corresponding to all or each of the maximized likelihood ratios respectively.

w

An optional numeric vector of weights that can be interpreted as prior model probabilities for each of the alternative hypotheses represented by the individual p-values. The sum of the weights cannot exceed one but may be less than one, which is interpreted as meaning that some p-values have been excluded.

L

The number of constituent maximized likelihood ratios. If ignored, it defaults to the length of argument R, with a warning.

Value

The model-averaged mean maximized likelihood ratio is returned.

Author(s)

Daniel J. Wilson

References

Daniel J. Wilson (2019) The harmonic mean p-value for combining dependent tests. Proceedings of the National Academy of Sciences USA 116: 1195-1200.

See Also

mamml.stat, hmp.stat, p.hmp

Examples

# For detailed examples type vignette("harmonicmeanp")
nu = 3
R = exp(0.5*rchisq(1000,nu))
mamml.stat(R)
p.mamml(R,nu,L=1000)