  We examine the problem of variance components testing in general mixed
effects models using the likelihood ratio test. We account for the presence of
nuisance parameters, i.e. the fact that some untested variances might also be
equal to zero. Two main issues arise in this context leading to a non regular
setting. First, under the null hypothesis the true parameter value lies on the
boundary of the parameter space. Moreover, due to the presence of nuisance
parameters the exact location of these boundary points is not known, which
prevents from using classical asymptotic theory of maximum likelihood
estimation. Then, in the specific context of nonlinear mixed-effects models,
the Fisher information matrix is singular at the true parameter value. We
address these two points by proposing a shrinked parametric bootstrap
procedure, which is straightforward to apply even for nonlinear models. We show
that the procedure is consistent, solving both the boundary and the singularity
issues, and we provide a verifiable criterion for the applicability of our
theoretical results. We show through a simulation study that, compared to the
asymptotic approach, our procedure has a better small sample performance and is
more robust to the presence of nuisance parameters. A real data application is
also provided.
