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.
p.mamml(R, nu, w = NULL, L = NULL)The model-averaged mean maximized likelihood ratio is returned.
A numeric vector of one or more maximized likelihood ratios. Missing values (NAs) will cause a missing value to be returned.
A numeric scalar or vector for the degrees of freedom corresponding to all or each of the maximized likelihood ratios respectively.
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.
The number of constituent maximized likelihood ratios. If ignored, it defaults to the length of argument R, with a warning.
Daniel J. Wilson
Daniel J. Wilson (2019) The harmonic mean p-value for combining dependent tests. Proceedings of the National Academy of Sciences USA 116: 1195-1200.
mamml.stat, hmp.stat, p.hmp
# For detailed examples type vignette("harmonicmeanp")
nu = 3
R = exp(0.5*rchisq(1000,nu))
mamml.stat(R)
p.mamml(R,nu,L=1000)
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