Package 'semicontMANOVA'

Title: Multivariate ANalysis of VAriance with Ridge Regularization for Semicontinuous High-Dimensional Data
Description: Implements Multivariate ANalysis Of VAriance (MANOVA) parameters' inference and test with regularization for semicontinuous high-dimensional data. The method can be applied also in presence of low-dimensional data. The p-value can be obtained through asymptotic distribution or using a permutation procedure. The package gives also the possibility to simulate this type of data. Method is described in Elena Sabbioni, Claudio Agostinelli and Alessio Farcomeni (2024) <arXiv:2401.04036>.
Authors: Elena Sabbioni [aut, cre] , Claudio Agostinelli [aut] , Alessio Farcomeni [aut]
Maintainer: Elena Sabbioni <[email protected]>
License: GPL-2
Version: 0.1-8
Built: 2024-12-06 06:28:27 UTC
Source: CRAN

Help Index

Multivariate ANalysis Of VAriance Inference and Test with Ridge Regularization for Semicontinuous High-Dimensional Data

Description

scMANOVA performs Multivariate ANalysis Of VAriance (MANOVA) inference and test with ridge regularization in presence of semicontinuous high-dimensional data. The test is based on a Likelihood Ratio Test statistic and the p-value can be computed using either asymptotic distribution (p.value.perm = FALSE) or via permutation procedure (p.value.perm = TRUE). There is the possibility to provide as input the regularization parameters or to choose them through an optimization procedure.

Usage

scMANOVA(x, n, lambda = NULL, lambda0 = NULL, lambda.step = 0.1,
  ident = FALSE, tol = 1e-08, penalty = function(n, p) log(n),
  B = 500, p.value.perm = FALSE, fixed.lambda = FALSE, ...)

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

NULL, a scalar or a vector of length 2. Ridge regularization parameter. The optimal value of lambda is searched in the interval [0,100] if NULL, and in the specified interval when it is a vector of length 2, otherwise it is used as the optimal value

lambda0

NULL, a scalar or a vector of length 2. Ridge regularization parameter under null hypothesis. The optimal value of lambda0 is searched in the interval [0,100] if NULL, and in the specified interval when it is a vector of length 2, otherwise it is used as the optimal value

lambda.step

scalar. Step size used in the optimization procedure to find the smallest value of lambda (and lambda0) that makes the covariance matrices, under the alternative and under the null hypotheses, non singular

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

tol

scalar. Used in the optimization procedure to find the smallest value of lambda (and lambda0) that makes the covariance matrices, under the alternative and under the null, non singular

penalty

function with two arguments: sample size (n) and number of variables (p) used as penalty function in the definition of the Information Criterion to select the optimal values for lambda and lambda0

B

scalar. Number of permutations to run in the permutation test

p.value.perm

logical. If TRUE a p-value from a permutation test is evaluated, otherwise an asymptotic value is reported

fixed.lambda

logical. If TRUE the optimal values for lambda and lambda0 are evaluated just once for the observed dataset and kept fixed during the permutation test, otherwise, optimal values are evaluated for each permuted datsets

...

further parameters passed to function scMANOVApermTest

Value

An object of class scMANOVA 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
statistic

scalar. Wilks statistics
lambda

scalar. Regularization parameter
lambda0

scalar. Regularization parameter under null hypothesis
df

scalar. Model degree of freedom
df0

scalar. Model degree of freedom under null hypothesis
aic

scalar. Information criteria
aic0

scalar. Information criteria under null hypothesis
p.value

scalar. p-value of the Wilks statistic

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

scMANOVAestimation and scMANOVApermTest

Examples

set.seed(1234)
  n <- c(5,5)
  p <- 20
  pmiss <- 0.1
  x <- scMANOVAsimulation(n=n, p=p, pmiss=pmiss)
  res.asy <- scMANOVA(x=x, n=n) # Asymptotic p.value
  res.asy
  
    res.perm <- scMANOVA(x=x, n=n, p.value.perm=TRUE) # p-value by permutation test 
    res.perm

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

Multivariate ANalysis Of VAriance log-likelihood Test with Ridge Regularization for Semicontinuous High-Dimensional Data

Description

scMANOVApermTest uses a permutation procedure to perform a test based on a Multivariate ANalysis Of VAriance(MANOVA) Likelihood Ratio test statistic with a ridge regularization. The statistic is developed for semicontinuous and high-dimensional data, but can be used also in low-dimensional scenarios.

Usage

scMANOVApermTest(x, n, lambda = NULL, lambda0 = NULL, lambda.step = 0.1,
  ident = FALSE, tol = 1e-08, penalty = function(n, p) log(n), B = 500,
  parallel = c("no", "multicore", "snow"), ncpus = 1L, cl = NULL,
  only.pvalue = 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 or a vector of length 2. Ridge regularization parameter. The optimal value of lambda is searched in the specified interval when it is a vector of length 2, otherwise it is used as the optimal value

lambda0

NULL, a scalar or a vector of length 2. Ridge regularization parameter under null hypothesis. The optimal value of lambda0 is searched in the specified interval when it is a vector of length 2, otherwise it is used as the optimal value

lambda.step

scalar. Step size used in the optimization procedure to find the smallest value of lambda (and lambda0) that makes the covariance matrices, under the alternative and under the null hypothesis, non singular

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

tol

scalar. Used in the optimization procedure to find the smallest value of lambda (and lambda0) that makes the covariance matrices, under the alternative and under the null hypothesis, non singular

penalty

function with two arguments: sample size (n) and number of variables (p) used as penalty function in the definition of the Information Criterion to select the optimal values for lambda and lambda0

B

scalar. Number of permutations to run in the permutation test

parallel

The type of parallel operation to be used (if any)

ncpus

integer. Number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs.

cl

An optional parallel or snow cluster to use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the call

only.pvalue

logical. If TRUE only the p-value is returned

rm.vars

vector. It indicates the position of the variables to remove

...

Further parameters passed to parallel::mclapply in case of parallel="multicore"

Value

If only.pvalue=TRUE (default) a scalar which is the p-value of the Wilks statistic obtain by a permutation procedure, otherwise an object of class htest

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 scMANOVAestimation

Examples

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

Simulation of datasets for a semicontinuous scenarios

Description

Simulation of dataset of semicontinuous data coming from different groups, with specific marginal probabilities of a missing value, specific mean vectors and common covariance matrix.

Usage

scMANOVAsimulation(n, p, pmiss = 0, rho = 0, mu = NULL,
  sigma = NULL, only.data = TRUE)

Arguments

n

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

p

scalar. Number of variables (columns)

pmiss

scalar or vector. Proportion of missingness in each group. If it is a scalar the same proportion is used in each group

rho

scalar. If sigma=NULL then sigma is set as a covariance matrix with covariance rho equal in every entries that is not on the main diagonal of sigma, and variance equal to 1

mu

NULL or vector or matrix. If NULL the mean of each group is set zero for all the variables, if vector the different groups have the same mean. If matrix each row corresponds to the mean vector of the corresponding group

sigma

NULL or matrix. If matrix it is a covariance matrix. If NULL the value of rho is used to build the covariance matrix

only.data

logical. If TRUE only the simulated data are reported

Value

If only.data=TRUE an object of class matrix is reported otherwise a list with the following components

x

matrix. The simulated dataset
y

matrix. A matrix with zero when the corresponding entry in x is zero and one otherwise
original

matrix. The simulated dataset without missing values
mu

matrix. Mean vectors, on for each group
sigma

matrix. Covariance matric
n

As in input
p

As in input
pmiss

vector. Proportion of missingness in each group

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

scMANOVAestimation and scMANOVApermTest

Examples

set.seed(1234)
  n <- c(5,5)
  p <- 20
  pmiss <- 0.1
  x <- scMANOVAsimulation(n=n, p=p, pmiss=pmiss)