Variance component testing — varCompTest • varTestnlme

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

Arguments

m1: a fit of the model under H1, obtained from nlme, lme4 or saemix
m0: a fit of the model under H0, obtained from the same package as m0
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: "bounds" (the default), "approx" or "both" (see Details section)
fim: (optional) the method to compute the Fisher Information Matrix. Options are: fim="extract" to extract the FIM computed by the package which was used to fit the models, fim="compute" to evaluate the FIM using parametric bootstrap, and fim=I with I a positive semidefinite matrix, for a FIM provided by the user.
output: a boolean specifying if any output should be printed in the console (default to TRUE)

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.

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

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.

Author

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

Examples

# load lme4 package and example dataset
library(lme4)
#> Loading required package: Matrix
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")
#> Variance components testing in mixed effects models
#> Testing that the variance of the random effect associated to age is equal to 0
#> Likelihood ratio test statistic:
#> 	LRT = 46.58827
#> 
#> p-value from exact weights: 4.379151e-12
#> 

# using nlme
library(nlme)
#> 
#> Attaching package: ‘nlme’
#> The following object is masked from ‘package:lme4’:
#> 
#>     lmList
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)
#> Variance components testing in mixed effects models
#> Testing that the means of the random effects associated to age and SexFemale:age are equal to 0 and that
#>  the variance of the random effect associated to age is equal to 0
#> Likelihood ratio test statistic:
#> 	LRT = 79.15214
#> 
#> p-value from exact weights: 1.550226e-16
#>