Testing variance components in balanced linear growth curve models

Abstract

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.

Nonlinear mixed‐effects models with misspecified random‐effects distribution

“…Classical tests such as the likelihood ratio and score tests cannot be easily applied to this testing problem because it requires testing on the boundary of parameter space. Bootstrap and permutation tests have been suggested for testing random effects in linear and generalised linear mixed models; however, little is known on testing random effects in nonlinear mixed‐effects models. Developing such tests for random effects in nonlinear mixed‐effects models will be very helpful.…”

Sparse Principal Component Analysis for Natural Language Processing

“…Again, care ought to be taken when calculating the caught variance with associated or correlated loadings. Note that assessing and testing a significant variance in correlated models is a nonstandard testing problem [11][12][13][14].…”

Testing random effects in linear mixed‐effects models with serially correlated errors

“…; see, for example, Crainiceanu and Ruppert () Drikvandi et al. () Drikvandi et al. (); Fitzmaurice, Lipsitz, and Ibrahim (); Giampaoli and Singer (); Lee and Braun (); Miller (); Saville and Herring (); Sinha (); Stram and Lee (); Verbeke and Molenberghs ().…”

“…There is a large literature on testing random effects when measurement errors are assumed to be i.i.d. ; see, for example, Crainiceanu and Ruppert (2004) Drikvandi et al (2012) Drikvandi et al (2013); Fitzmaurice, Lipsitz, and Ibrahim (2007); Giampaoli and Singer (2009); Lee and Braun (2012); Miller (1977); Saville and Herring (2009); Sinha (2009); Stram and Lee (1994); Verbeke and Molenberghs (2003). It is well understood that the main challenge with testing random effects is that the null hypothesis puts the true values of variance components on the boundary of parameter space, and hence the asymptotic chi-squared distribution of the classical tests such as likelihood ratio, Wald, and score tests is incorrect.…”

“…It is important to test for the need of random effects in linear mixed‐effects models to decide which random effects should be included or excluded from the model. While several practical examples on testing random effects are given in (Drikvandi, Khodadadi, & Verbeke, ; Drikvandi et al., ), there are some theoretical and computational reasons why such a test on random effects is important. For example, if unnecessary random effects are included in the model, the parameter estimates will not be efficient.…”