Covariance Matrices of Logit ETA {MixfMRI}

Covariance Matrices of Logit ETA

Description

These functions computes covariance matrix of logit ETA.

Usage

  cov.logit.ETA(x, fcobj, cov.param = NULL)

Arguments

x

an input list of two elements X.gbd and PV.gbd.

fcobj

a fclust object.

cov.param

a covariance matrix of dim = d * d for parameters, which is also a return of cov.param(). d is total number of parameters which is dependent on data and models.

Details

These functions are required to compute covariance matrices of logit ETA.

Input the returns of cov.param() to cov.logit.ETA() to obtain the cov matrix for logit ETA by the multivariate delta method on the cov matrix for parameters.

Value

A matrix.

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(), lmt.I().

Examples

library(MixfMRI, quietly = TRUE)
.FC.CT$model.X <- "I"
.FC.CT$CONTROL$debug <- 0
K <- 3
  

.rem <- function(){

  ### Fit toy1.
  set.seed(1234)
  X.gbd <- toy1$X.gbd
  X.range <- apply(X.gbd, 2, range)
  X.gbd <- t((t(X.gbd) - X.range[1,]) / (X.range[2,] - X.range[1,]))
  PV.gbd <- toy1$PV.gbd
  fcobj <- fclust(X.gbd, PV.gbd, K = K, min.1st.prop = 0.5)
  
  ### Test cov matrix of posterior z.
  x <- list(X.gbd = X.gbd, PV.gbd = PV.gbd)
  post.z <- post.prob(x, fcobj)
  cov.param <- cov.param(x, fcobj, post.z)
  cov.logit.ETA <- cov.logit.ETA(x, fcobj, cov.param = cov.param$cov)
  
  ### Compute cov matrxi of eta_k - eta_1 for all k > 1.
  A <- cbind(rep(-1, K - 1), diag(1, K - 1))
  ETA <- fcobj$param$ETA
  log.or <- log(ETA / (1 - ETA)) %*% t(A)
  cov.log.or <- A %*% cov.logit.ETA %*% t(A)

}