Title: | Variance Components Testing for Linear and Nonlinear Mixed Effects Models |
---|---|
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>. |
Authors: | Charlotte Baey [aut, cre] , Estelle Kuhn [aut] |
Maintainer: | Charlotte Baey <[email protected]> |
License: | GPL (>= 2) |
Version: | 1.3.5 |
Built: | 2024-11-14 03:29:52 UTC |
Source: | https://github.com/baeyc/vartestnlme |
create alternative description
alt.desc(msdata)
alt.desc(msdata)
msdata |
a list containing the structure of the model and data, as an output from
|
The chi-bar-square distribution 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
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.
approxWeights(x, df, q)
approxWeights(x, df, q)
x |
a vector of i.i.d. random realizations of the target chi-bar-square distribution |
df |
a vector containing the degrees of freedom of the chi-squared components |
q |
the empirical quantile of |
Let us assume that there are components in the mixture, with degrees of
freedom between
and
. By definition of a mixture distribution, we have :
Choosing values
, the function will generate a system of
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
equations with
variables.
A vector containing the estimated weights, as well as their covariance matrix.
Charlotte Baey <[email protected]>
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.
bootinvFIM(m, B = 1000)
bootinvFIM(m, B = 1000)
m |
a fitted model that will be used as the basis of the parametric bootstrap (providing the initial maximum likelihood estimate of the parameters and the modelling framework) |
B |
the size of the bootstrap sample |
the empirical covariance matrix of the parameter estimates obtained on the bootstrap sample
Charlotte Baey <[email protected]>
Compute the inverse of the Fisher Information Matrix using parametric bootstrap
## S3 method for class 'lme' bootinvFIM(m, B = 1000)
## S3 method for class 'lme' bootinvFIM(m, B = 1000)
m |
the model under H1 |
B |
the bootstrap sample size |
Compute the inverse of the Fisher Information Matrix using parametric bootstrap
## S3 method for class 'merMod' bootinvFIM(m, B = 1000)
## S3 method for class 'merMod' bootinvFIM(m, B = 1000)
m |
the model under H1 |
B |
the bootstrap sample size |
Compute the inverse of the Fisher Information Matrix using parametric bootstrap
## S3 method for class 'SaemixObject' bootinvFIM(m, B = 1000)
## S3 method for class 'SaemixObject' bootinvFIM(m, B = 1000)
m |
the model under H1 |
B |
the bootstrap sample size |
Computation of the degrees of freedom of the chi-bar-square
dfChiBarSquare(msdata)
dfChiBarSquare(msdata)
msdata |
a list containing the structure of the model and data, as an output from
|
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
extractFIM.lme(m, struct)
extractFIM.lme(m, struct)
m |
the model to extract the FIM from |
struct |
the structure of the covariance matrix (either 'full', 'diag', or 'blockdiag) |
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
extractStruct(m1, m0, randm0)
extractStruct(m1, m0, randm0)
m1 |
the model under H1 |
m0 |
the model under H0 |
randm0 |
a boolean stating whether the model under H0 contains any random effect |
A list with the following components:
detailStruct |
a data frame containing the list of the parameters and whether they are tested or not |
nameVarTested |
the name of the variance components being tested |
nameFixedTested |
the name of the fixed effects being tested |
dims |
a list with the dimensions of fixed and random effects, tested or not tested |
structGamma |
the structure of the covariance matrix of the random effects |
Extract model structure
## S3 method for class 'lme' extractStruct(m1, m0, randm0)
## S3 method for class 'lme' extractStruct(m1, m0, randm0)
m1 |
the fit under H1 |
m0 |
the fit under H0 |
randm0 |
a boolean indicating whether random effects are present in m0 |
Extract model structure
## S3 method for class 'merMod' extractStruct(m1, m0, randm0)
## S3 method for class 'merMod' extractStruct(m1, m0, randm0)
m1 |
the fit under H1 |
m0 |
the fit under H0 |
randm0 |
a boolean indicating whether random effects are present in m0 |
Extract model structure
## S3 method for class 'SaemixObject' extractStruct(m1, m0, randm0)
## S3 method for class 'SaemixObject' extractStruct(m1, m0, randm0)
m1 |
the fit under H1 |
m0 |
the fit under H0 |
randm0 |
a boolean indicating whether random effects are present in m0 |
Extract covariance matrix of the random effects for a model fitted with lme4.
extractVarCov(m)
extractVarCov(m)
m |
a fit from lme4 package (either linear or nonlinear) |
Extract covariance matrix of the random effects for a model fitted with nlme.
## S3 method for class 'lme' extractVarCov(m)
## S3 method for class 'lme' extractVarCov(m)
m |
a fit from nlme package (either linear or nonlinear) |
Extract covariance matrix of the random effects for a model fitted with lme4.
## S3 method for class 'merMod' extractVarCov(m)
## S3 method for class 'merMod' extractVarCov(m)
m |
a fit from lme4 package (either linear or nonlinear) |
Extract the Fisher Information Matrix
fim.vctest(object)
fim.vctest(object)
object |
an object of class vctest |
create null.value description
null.desc(msdata)
null.desc(msdata)
msdata |
a list containing the structure of the model and data, as an output from
|
Useful intern functions
Groups of functions used for the constrained minimization problem arising in the computation of the likelihood ratio test statistics.
objFunction(x, cst) gradObjFunction(x, cst) symMatrixFromVect(x) ineqCstr(x, cst) jacobianIneqCstr(x, cst) eqCstr(x, cst) jacobianEqCstr(x, cst)
objFunction(x, cst) gradObjFunction(x, cst) symMatrixFromVect(x) ineqCstr(x, cst) jacobianIneqCstr(x, cst) eqCstr(x, cst) jacobianEqCstr(x, cst)
x |
A vector |
cst |
A list of constants to be passed to the optimisation function |
value of the objective function, its gradient, and the set of inequality and equality constraints
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
pckName(m)
pckName(m)
m |
a model with random effects fitted with |
a string giving the name of the package
print a message to indicate the null and alternative hypotheses
## S3 method for class 'desc.message' print(msdata)
## S3 method for class 'desc.message' print(msdata)
msdata |
a list containing the structure of the model and data, as an output from
|
print a message with the results
## S3 method for class 'res.message' print(results)
## S3 method for class 'res.message' print(results)
results |
an object of class vctest |
## S3 method for class 'vctest' print(x, ...)
## S3 method for class 'vctest' print(x, ...)
x |
an object of class vctest |
... |
additional arguments |
Summary
## S3 method for class 'vctest' summary(object, ...)
## S3 method for class 'vctest' summary(object, ...)
object |
an object of class vctest |
... |
additional arguments |
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.
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 )
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 )
m1 |
a fit of the model under H1, obtained from |
m0 |
a fit of the model under H0, obtained from the same package as |
control |
(optional) a list of control options for the computation of the chi-bar-weights (see Details section) |
pval.comp |
(optional) the method to be used to compute the p-value, one of: |
fim |
(optional) the method to compute the Fisher Information Matrix. Options are: |
output |
a boolean specifying if any output should be printed in the console (default to TRUE) |
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
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.
Charlotte Baey <[email protected]>
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.
# 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)
# 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)
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
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.
weightsChiBarSquare(df, V, dimsCone, orthan, control)
weightsChiBarSquare(df, V, dimsCone, orthan, control)
df |
a vector with the degrees of freedom of the chi-square components of the chi-bar-square distribution |
V |
a positive semi-definite matrix |
dimsCone |
a list with the dimensions of the cone C, expressed on the parameter space scale |
orthan |
a boolean specifying whether the cone is an orthan |
control |
(optional) a list of control options for the computation of the chi-bar-weights, containing
two elements: |
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