rvalues | R Documentation |
Given data on a collection of units, this function computes r-values which are percentiles constructed to maximize the agreement between the reported percentiles and the percentiles of the effect of interest. Additional details about r-values are provided below and can also be found in the listed references.
rvalues(data, family = gaussian, hypers = "estimate", prior = "conjugate", alpha.grid = NULL, ngrid = NULL, smooth = "none", control = list())
data |
A data frame or a matrix with the number of rows equal to the number of sampling units. The first column should contain the main estimates, and the second column should contain the nuisance terms. |
family |
An argument which determines the sampling distribution; this could be either
|
hypers |
values of the hyperparameters; only meaningful when the conjugate prior is used; if set to "estimate", the hyperparameters are found through maximum likelihood; if not set to "estimate" the user should supply a vector of length two. |
prior |
the form of the prior; either |
alpha.grid |
a numeric vector of points in (0,1); this grid is used in the discrete approximation of r-values |
ngrid |
number of grid points for alpha.grid; only relevant when |
smooth |
either |
control |
a list of control parameters for estimation of the prior; only used when the prior is nonparametric |
The r-value computation assumes the following two-level sampling model
X_i|θ_i ~ p(x|θ_i,η_i)
and θ_i ~ F, for i = 1,...,n,
with parameters of interest θ_i, effect size estimates X_i,
and nuisance terms η_i. The form of p(x|θ_i,η_i) is determined
by the family
argument. When family = gaussian
, it is assumed that
X_i|θ_i,η_i ~ N(θ_i,η_i^{2}).
When family = binomial
, the (X_i,η_i) represent the number of successes
and number of trials respectively, and it is assumed that X_i|θ_i,η_i ~
Binomial(θ_i,η_i). When family = poisson
, the {X_i} should be
counts, and it is assumed that X_i|θ_i,η_i ~ Poisson(θ_i * η_i).
The distribution of the effect sizes F may be a parametric distribution
that is conjugate to the corresponding family
argument,
or it may be estimated nonparametrically. When it is desired that F be
parametric (i.e., prior = "conjugate"
), the default is to estimate the
hyperparameters (i.e., hypers = "estimate"
), but these may be supplied by the
user as a vector of length two. To estimate F nonparametrically, one
should use prior = "nonparametric"
(see npmle
for
further details about nonparametric estimation of F).
The r-value, r_i, assigned to the ith case of interest is determined by r_i = inf[ 0 < α < 1: V_α(X_i,η_i) ≥ λ(α) ] where V_α(X_i,η_i) = P( θ_i ≥ θ_α|X_i,η_i) is the posterior probability that θ_i exceeds the threshold θ_α, and λ(α) is the upper-αth quantile associated with the marginal distribution of V_α(X_i,η_i) (i.e., P(V_α(X_i,η_i) ≥ λ(α)) = α). Similarly, the threshold θ_α is the upper-αth quantile of F (i.e., P(θ_i ≥ θ_α) = α ).
An object of class "rvals" which is a list containing at least the following components:
main |
a data frame containing the r-values, the r-value rankings along with the rankings from several other common procedures |
aux |
a list containing other extraneous information |
rvalues |
a vector of r-values |
Nicholas C. Henderson and Michael A. Newton
Henderson, N.C. and Newton, M.A. (2016). Making the cut: improved ranking and selection for large-scale inference. J. Royal Statist. Soc. B., 78(4), 781-804. doi: 10.1111/rssb.12131 https://arxiv.org/abs/1312.5776
rvaluesMCMC
, PostSummaries
, Valpha
## Not run: ### Binomial example with Beta prior: data(fluEnrich) flu.rvals <- rvalues(fluEnrich, family = binomial) hist(flu.rvals$rvalues) ### look at the r-values for indices 10 and 2484 fig_indices <- c(10,2484) fluEnrich[fig_indices,] flu.rvals$rvalues[fig_indices] ### Gaussian sampling distribution with nonparametric prior ### Use a maximum of 5 iterations for the nonparam. estimate data(hiv) hiv.rvals <- rvalues(hiv, prior = "nonparametric") ## End(Not run)
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