LRT {MixfMRI}

Likelihood ratio tests

Description

Likelihood ratio tests for merging clusters.

Usage

  lrt(PV.gbd, CLASS.gbd, K, H0.alpha = .FC.CT$LRT$H0.alpha,
      H0.beta = .FC.CT$LRT$H0.beta)

  lrt2(PV.gbd, CLASS.gbd, K, H0.mean = .FC.CT$LRT$H0.mean,
    upper.beta = .FC.CT$INIT$BETA.beta.max, proc = c("1", "2", "weight"))

  lrt.betamean(PV.gbd, CLASS.gbd, K, proc = c("1", "2"))

  lrt.betaab(PV.gbd, CLASS.gbd, K, proc = c("1", "2"))

Arguments

PV.gbd

a p-value vector of signals associated with voxels. length(PV.gbd) = N.

CLASS.gbd

a classification vector of signals associated with voxels. length(CLASS.gbd) = N.

K

number of clusters.

H0.alpha

null hypothesis for the alpha parameter of Beta distribution.

H0.beta

null hypothesis for the beta parameter of Beta distribution.

H0.mean

null hypothesis for the mean of Beta distribution.

upper.beta

BETA.beta.max, maximum value of beta parameter of Beta distribution.

proc

q-value procedure for adjusting p-values.

Details

These functions perform likelihood ratio tests for merging clusters. Only p-values coordinates (Beta density) are tested, while voxel location coordinates (multivariate Normal density) are not involved in testing.

lrt.betamean tests if means of any two pairs of mixture (p-value) component were the same. The chi-square distribution with 1 degree of freedom is used.

lrt.betaab tests if alpha and beta of any two pairs of mixture (p-value) components were the same. The chi-square distribution with 2 degrees of freedom is used.

Procedure to adjust/select plausible p-values, proc = "1" uses q-value qvalue(), proc = "2" uses fdr.bh.p2(), and proc = "weight" uses a weighted version of fdr.bh.p2().

Value

A matrix contains MLEs of parameters of Beta distribution under the null hypothesis and the union of null and alternative hypotheses. The matrix also contains testing statistics and p-values.

Author(s)

Wei-Chen Chen and Ranjan Maitra.

References

Chen, W.-C. and Maitra, R. (2021) “A Practical Model-based Segmentation Approach for Accurate Activation Detection in Single-Subject functional Magnetic Resonance Imaging Studies”, arXiv:2102.03639.

See Also

PARAM.

Examples

library(MixfMRI, quietly = TRUE)
set.seed(1234)

### Test 2d data.
da <- pval.2d.mag
id <- !is.na(da)
PV.gbd <- da[id]
id.loc <- which(id, arr.ind = TRUE)
X.gbd <- t(t(id.loc) / dim(da))
ret <- fclust(X.gbd, PV.gbd, K = 2, min.1st.prop = 0.95)
# print(ret)

### p-values of rest clusters.
ret.lrt <- lrt(PV.gbd, ret$class, K = 2)
print(ret.lrt)

.rem <- function(){

  ret.lrt2 <- lrt2(PV.gbd, ret$class, K = 3)
  print(ret.lrt2)

}