Likelihood Mixture Tests with Identity Cov Matrix or Only p-values {MixfMRI}

Likelihood Mixture Tests with Identity Cov Matrix or Only p-values

Description

These functions test two mixture Gaussian fMRI models with diagonal covariance matrices and different numbers of clusters. These functions are similar to the EMCluster::lmt(), but is coded for fMRI models in MixfMRI.

Usage

  lmt.I(fcobj.0, fcobj.a, X.gbd, PV.gbd, tau = 0.5, n.mc.E.delta = 1000,
        n.mc.E.chi2 = 1000, verbose = FALSE)
  lmt.pv(fcobj.0, fcobj.a, X.gbd, PV.gbd, tau = 0.5, n.mc.E.delta = 1000,
        n.mc.E.chi2 = 1000, verbose = FALSE)

Arguments

fcobj.0

a fclust object for the null hypothesis.

fcobj.a

a fclust object for the alternative hypothesis.

X.gbd

a data matrix of N voxel locations. dim(X.gbd) = N x 3 for 3D data and N x 2 for 2D data.

PV.gbd

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

tau

proportion of null and alternative hypotheses.

n.mc.E.delta

number of Monte Carlo simulations for expectation of delta (difference of logL).

n.mc.E.chi2

number of Monte Carlo simulations for expectation of chisquare statistics.

verbose

if verbose.

Details

This function calls several subroutines to compute information, likelihood ratio statistics, degrees of freedom, non-centrality of chi-squared distributions ... etc. Based on Monte Carlo methods to estimate parameters of likelihood mixture tests, this function return a p-value for testing H0: fcobj.0 v.s. Ha: fcobj.a.

lmt.pv() only uses PV.gbd.

Value

A list of class lmt.I are returned.

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

EMCluster::lmt().

Examples

library(MixfMRI, quietly = TRUE)
library(EMCluster, quietly = TRUE)
.FC.CT$model.X <- "I"
.FC.CT$check.X.unit <- FALSE
.FC.CT$CONTROL$debug <- 0
  

.rem <- function(){

  ### Fit toy1.
  set.seed(1234)
  X.gbd <- toy1$X.gbd
  PV.gbd <- toy1$PV.gbd
  ret.2 <- fclust(X.gbd, PV.gbd, K = 2)
  ret.3 <- fclust(X.gbd, PV.gbd, K = 3)
  ret.4 <- fclust(X.gbd, PV.gbd, K = 4)
  ret.5 <- fclust(X.gbd, PV.gbd, K = 5)
  
  ### ARI
  RRand(toy1$CLASS.gbd, ret.2$class)
  RRand(toy1$CLASS.gbd, ret.3$class)
  RRand(toy1$CLASS.gbd, ret.4$class)
  RRand(toy1$CLASS.gbd, ret.5$class)
  
  ### Test toy1.
  (lmt.23 <- lmt.I(ret.2, ret.3, X.gbd, PV.gbd))
  (lmt.24 <- lmt.I(ret.2, ret.4, X.gbd, PV.gbd))
  (lmt.25 <- lmt.I(ret.2, ret.5, X.gbd, PV.gbd))
  (lmt.34 <- lmt.I(ret.3, ret.4, X.gbd, PV.gbd))
  (lmt.35 <- lmt.I(ret.3, ret.5, X.gbd, PV.gbd))
  (lmt.45 <- lmt.I(ret.4, ret.5, X.gbd, PV.gbd))
  
  ### Test toy1 using p-values only.
  (lmt.pv.23 <- lmt.pv(ret.2, ret.3, X.gbd, PV.gbd))
  (lmt.pv.24 <- lmt.pv(ret.2, ret.4, X.gbd, PV.gbd))
  (lmt.pv.25 <- lmt.pv(ret.2, ret.5, X.gbd, PV.gbd))
  (lmt.pv.34 <- lmt.pv(ret.3, ret.4, X.gbd, PV.gbd))
  (lmt.pv.35 <- lmt.pv(ret.3, ret.5, X.gbd, PV.gbd))
  (lmt.pv.45 <- lmt.pv(ret.4, ret.5, X.gbd, PV.gbd))

}