scMANOVAestimation {semicontMANOVA}

Multivariate ANalysis Of VAriance Maximum Likelihood Estimation with Ridge Regularization for Semicontinuous High-Dimensional Data

Description

scMANOVAestimation computes the regularized Multivariate ANalysis Of VAriance (MANOVA) maximum likelihood estimates for semicontinuous high-dimensional data. The estimation can be performed also for low-dimensional data. The regularization parameters are provided as input and the user can decide to perform the regularization adding the identity matrix to the raw estimated covariance matrix (default, ident=TRUE) or adding the diagonal values of the raw estimated covariance matrix (ident=FALSE).

Usage

  scMANOVAestimation(x, n, lambda = NULL, lambda0 = NULL,
    ident = TRUE, posdef.check = TRUE, rm.vars = NA)

Arguments

x

data.frame or matrix of data with units on the rows and variables on the columns

n

vector. The length corresponds to the number of groups, the elements to the number of observations in each group

lambda

scalar. Ridge regularization parameter

lambda0

scalar. Ridge regularization parameter under null hypothesis

ident

logical. If TRUE, lambda times the identity matrix is added to the raw estimated covariance matrix, if FALSE the diagonal values of the raw estimated covariance matrix are used instead

posdef.check

logical. Check if the estimated covariance matrix is positive definite

rm.vars

NA, NULL or vector. If NA variables are removed from the analysis when they do not have enough observations to compute covariances. If NULL or a zero length vector all the variables are retained. If it is a vector, it indicates the position of the variables to remove, no further variables are removed

Value

An object of class scMANOVAestimation which is a list with the following components

pi

matrix. Estimated proportion of missing values for each group

mu

matrix. Estimated mean vector for each group

sigmaRidge

matrix. Estimated covariance matrix with ridge regularization

sigma

matrix. Estimated covariance matrix by maximum likelihood

pi0

vector. Estimated proportion of missing values under the null hypothesis

mu0

vector. Estimated mean vector under the null hypothesis

sigma0Ridge

matrix. Estimated covariance matrix with ridge regularization under null hypothesis

sigma0

matrix. Estimated covariance matrix by maximum likelihood under null hypothesis

removed.vars

vector or NULL. columns removed in the continuous part of the log-likelihood dues to insufficient number of observations in each group

logLikPi

scalar. Log-likelihood for the discrete part of the model

logLik

scalar. Log-likelihood

logLikPi0

scalar. Log-likelihood for the discrete part of the model under the null hypothesis

logLik0

scalar. Log-likelihood under null hypothesis

Author(s)

Elena Sabbioni, Claudio Agostinelli and Alessio Farcomeni

References

Elena Sabbioni, Claudio Agostinelli and Alessio Farcomeni (2024) A regularized MANOVA test for semicontinuous high-dimensional data. arXiv: http://arxiv.org/abs/2401.04036

See Also

scMANOVA and scMANOVApermTest

Examples

  set.seed(1234)
  n <- c(5,5)
  p <- 20
  pmiss <- 0.1
  x <- scMANOVAsimulation(n=n, p=p, pmiss=pmiss)
  res <- scMANOVAestimation(x=x, n=n, lambda=3.59, lambda0=3.13)
  res