Type:	Package
Title:	Variance Components Testing for Linear and Nonlinear Mixed Effects Models
Version:	1.3.5
URL:	https://github.com/baeyc/varTestnlme/
BugReports:	https://github.com/baeyc/varTestnlme/issues
Maintainer:	Charlotte Baey <charlotte.baey@univ-lille.fr>
Description:	An implementation of the Likelihood ratio Test (LRT) for testing that, in a (non)linear mixed effects model, the variances of a subset of the random effects are equal to zero. There is no restriction on the subset of variances that can be tested: for example, it is possible to test that all the variances are equal to zero. Note that the implemented test is asymptotic. This package should be used on model fits from packages 'nlme', 'lmer', and 'saemix'. Charlotte Baey and Estelle Kuhn (2019) <doi:10.18637/jss.v107.i06>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
Imports:	mvtnorm, lmeresampler, alabama, Matrix, merDeriv, anocva, corpcor, quadprog, lme4, nlme, saemix, msm, foreach, methods, doParallel, parallel
RoxygenNote:	7.2.3
Suggests:	knitr, rmarkdown, EnvStats
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2023-09-22 12:07:26 UTC; charlotte
Author:	Charlotte Baey [aut, cre], Estelle Kuhn [aut]
Repository:	CRAN
Date/Publication:	2023-09-22 15:20:02 UTC

alt.desc

Description

create alternative description

Usage

alt.desc(msdata)

Arguments

Monte Carlo approximation of chi-bar-square weights

Description

The chi-bar-square distribution \bar{\chi}^2(I,C) is a mixture of chi-square distributions. The function provides a method to approximate the weights of the mixture components, when the number of components is known as well as the degrees of freedom of each chi-square distribution in the mixture, and given a vector of simulated values from the target \bar{\chi}^2(I,C) distribution. Note that the estimation is based on (pseudo)-random Monte Carlo samples. For reproducible results, one should fix the seed of the (pseudo)-random number generator.

Usage

approxWeights(x, df, q)

Arguments

Details

Let us assume that there are p components in the mixture, with degrees of freedom between n_1 and n_p. By definition of a mixture distribution, we have :

P(\bar{\chi}^2(I,C) \leq c) = \sum_{i=n_1}^{n_p} w_i P(\chi^2_{i} \leq c)

Choosing p-2 values c_1, \dots, c_{p-2}, the function will generate a system of p-2 equations according to the above relationship, and add two additional relationships stating that the sum of all the weights is equal to 1, and that the sum of odd weights and of even weights is equal to 1/2, so that we end up with a system a p equations with p variables.

Value

A vector containing the estimated weights, as well as their covariance matrix.

Author(s)

Charlotte Baey <charlotte.baey@univ-lille.fr>

Approximation of the inverse of the Fisher Information Matrix via parametric bootstrap

Description

When the FIM is not available, this function provides an approximation of the FIM based on an estimate of the covariance matrix of the model's parameters obtained via parametric bootstrap.

Usage

bootinvFIM(m, B = 1000, seed = 0)

Arguments

Value

the empirical covariance matrix of the parameter estimates obtained on the bootstrap sample

Author(s)

Charlotte Baey <charlotte.baey@univ-lille.fr>

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Description

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Usage

## S3 method for class 'SaemixObject'
bootinvFIM(m, B = 1000, seed = 0)

Arguments

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Description

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Usage

## S3 method for class 'lme'
bootinvFIM(m, B = 1000, seed = 0)

Arguments

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Description

Compute the inverse of the Fisher Information Matrix using parametric bootstrap

Usage

## S3 method for class 'merMod'
bootinvFIM(m, B = 1000, seed = 0)

Arguments

Chi-bar-square degrees of freedom computation

Description

Computation of the degrees of freedom of the chi-bar-square

Usage

dfChiBarSquare(msdata)

Arguments

Value

a list containing the vector of the degrees of freedom of the chi-bar-square and the dimensions of the cone of the chi-bar-square distribution

Extract FIM

Description

Extract FIM

Usage

extractFIM.lme(m, struct)

Arguments

Extracting models' structures

Description

Functions extracting the structure of the models under both hypothesis: the number of fixed and random effects, the number of tested fixed and random effects, and the residual dimension, as well as the random effects covariance structure

Usage

extractStruct(m1, m0, randm0)

Arguments

Value

A list with the following components:

Extract model structure

Description

Extract model structure

Usage

## S3 method for class 'SaemixObject'
extractStruct(m1, m0, randm0)

Arguments

Extract model structure

Description

Extract model structure

Usage

## S3 method for class 'lme'
extractStruct(m1, m0, randm0)

Arguments

Extract model structure

Description

Extract model structure

Usage

## S3 method for class 'merMod'
extractStruct(m1, m0, randm0)

Arguments

Extract covariance matrix

Description

Extract covariance matrix of the random effects for a model fitted with lme4.

Usage

extractVarCov(m)

Arguments

Extract covariance matrix

Description

Extract covariance matrix of the random effects for a model fitted with nlme.

Usage

## S3 method for class 'lme'
extractVarCov(m)

Arguments

Extract covariance matrix

Description

Extract covariance matrix of the random effects for a model fitted with lme4.

Usage

## S3 method for class 'merMod'
extractVarCov(m)

Arguments

Extract the Fisher Information Matrix

Description

Extract the Fisher Information Matrix

Usage

fim.vctest(object)

Arguments

null.desc

Description

create null.value description

Usage

null.desc(msdata)

Arguments

Details

Useful intern functions

Internal functions for constrained minimization

Description

Groups of functions used for the constrained minimization problem arising in the computation of the likelihood ratio test statistics.

Usage

objFunction(x, cst)

gradObjFunction(x, cst)

symMatrixFromVect(x)

ineqCstr(x, cst)

jacobianIneqCstr(x, cst)

eqCstr(x, cst)

jacobianEqCstr(x, cst)

Arguments

Value

value of the objective function, its gradient, and the set of inequality and equality constraints

Functions

• objFunction(): objective function to be optimized

• gradObjFunction(): gradient of the objective function

• symMatrixFromVect(): function creating a symmetric matrix from its unique elements stored in a vector

• ineqCstr(): set of inequality constraints

• jacobianIneqCstr(): jacobian of the inequality constraints

• eqCstr(): set of equality constraints

• jacobianEqCstr(): jacobian of the inequality constraints

Extract package name from a fitted mixed-effects model

Description

Extract package name from a fitted mixed-effects model

Usage

pckName(m)

Arguments

Value

a string giving the name of the package

print.desc.message

Description

print a message to indicate the null and alternative hypotheses

Usage

## S3 method for class 'desc.message'
print(msdata)

Arguments

print.res.message

Description

print a message with the results

Usage

## S3 method for class 'res.message'
print(results)

Arguments

Print

Description

Print

Usage

## S3 method for class 'vctest'
print(x, ...)

Arguments

Summary

Description

Summary

Usage

## S3 method for class 'vctest'
summary(object, ...)

Arguments

Variance component testing

Description

Perform a likelihood ratio test to test whether a subset of the variances of the random effects are equal to zero. The test is defined by two hypotheses, H0 and H1, and the model under H0 is assumed to be nested within the model under H1. These functions can be used on objects of class lme-, nlme-, mer-, lmerMod, glmerMod, nlmerMord or SaemixObject.

It is possible to tests if any subset of the variances are equal to zero. However, the function does not currently support nested random effects, and assumes that the random effects are Gaussian.

Usage

varCompTest(
  m1,
  m0,
  control = list(M = 5000, parallel = T, nb_cores = 1, B = 1000),
  pval.comp = "bounds",
  fim = "extract",
  output = TRUE
)

## S3 method for class 'lme'
varCompTest(
  m1,
  m0,
  control = list(M = 5000, parallel = FALSE, nb_cores = 1, B = 1000),
  pval.comp = "bounds",
  fim = "extract",
  output = TRUE
)

## S3 method for class 'merMod'
varCompTest(
  m1,
  m0,
  control = list(M = 5000, parallel = FALSE, nb_cores = 1, B = 1000),
  pval.comp = "bounds",
  fim = "extract",
  output = TRUE
)

## S3 method for class 'SaemixObject'
varCompTest(
  m1,
  m0,
  control = list(M = 5000, parallel = FALSE, nb_cores = 1, B = 1000),
  pval.comp = "bounds",
  fim = "extract",
  output = TRUE
)

Arguments

Details

The asymptotic distribution of the likelihood ratio test is a chi-bar-square, with weights that need to be approximated by Monte Carlo methods, apart from some specific cases where they are available explicitly. Therefore, the p-value of the test is not exact but approximated. This computation can be time-consuming, so the default behaviour of the function is to provide bounds on the exact p-value, which can be enough in practice to decide whether to reject or not the null hypothesis. This is triggered by the option pval.comp="bounds". To compute an approximation of the exact p-value, one should use the option pval.comp="approx" or pval.comp="both".

When pval.comp="approx" or pval.comp="both", the weights of the chi-bar-square distribution are computed using Monte Carlo, which might involve a larger computing time.

The control argument controls the options for chi-bar-square weights computation. It is a list with the following elements: M the size of the Monte Carlo simulation, i.e. the number of samples generated, parallel a boolean to specify if parallel computing should be used, and nbcores the number of cores to be used in case of parallel computing. Default is M=5000, parallel=FALSE and nb_cores=1. If parallel=TRUE but the value of nb_cores is not given, then it is set to the number of detected cores minus 1

Value

An object of class htest with the following components:

• statistic the likelihood ratio test statistics

• null.value

• alternative

• parameters the parameters of the limiting chi-bar-square distribution: the degrees of freedom and the weights of the chi-bar-square components and the Fisher Information Matrix

• method a character string indicating the name of the test

• pvalue a named vector containing the different p-values computed by the function: using the (estimated) weights, using the random sample from the chi-bar-square distribution, and the two bounds on the p-value.

Author(s)

Charlotte Baey <charlotte.baey@univ-lille.fr>

References

Baey C, Cournède P-H, Kuhn E, 2019. Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models. Computational Statistics and Data Analysis 135:107-122.

Silvapulle MJ, Sen PK, 2011. Constrained statistical inference: order, inequality and shape constraints.

Examples

# load lme4 package and example dataset
library(lme4)
data(Orthodont, package = "nlme")

# fit the two models under H1 and H0
m1 <- lmer(distance ~ 1 + Sex + age + age*Sex + 
(0 + age | Subject), data = Orthodont, REML = FALSE)
m0 <- lm(distance ~ 1 + Sex + age + age*Sex, data = Orthodont)

# compare them (order is important: m1 comes first)
varCompTest(m1,m0,pval.comp="bounds")

# using nlme
library(nlme)
m1 <- lme(distance ~ 1 + Sex + age + age*Sex, 
random = pdSymm(Subject ~ 1 + age), data = Orthodont, method = "ML")
m0 <- lme(distance ~ 1 + Sex, random = ~ 1 | Subject, data = Orthodont, method = "ML")

varCompTest(m1,m0)

Monte Carlo approximation of chi-bar-square weights

Description

The function provides a method to approximate the weights of the mixture components, when the number of components is known as well as the degrees of freedom of each chi-square distribution in the mixture, and given a vector of simulated values from the target \bar{\chi}^2(V,C) distribution. Note that the estimation is based on (pseudo)-random Monte Carlo samples. For reproducible results, one should fix the seed of the (pseudo)-random number generator.

Usage

weightsChiBarSquare(df, V, dimsCone, orthan, control)

Arguments

Value

A list containing the estimated weights, the standard deviations of the estimated weights and the random sample of M realizations from the chi-bar-square distribution