Assessment of random effects and their distribution in mixed models Seminar

Abstract:

Mixed models are well suited for the analysis of longitudinal, multilevel, clustered and other correlated data. They incorporate subject-specifi​c random effects into the model to account for the between-subject variability as well as the within-subject correlation. Correctly specifying the random-effects part is crucial for reliable inference, however it is difficult to assess the random effects and their distribution because random effects are latent and unobservable variables. There are two main challenges when working with random effects. The first challenge is to decide which random effects to include into the model. In statistical language, this is equivalent to testing whether or not the variance components of random effects equal zero. However, test for zero variance components is a nonstandard testing problem because the null hypothesis in on the boundary of the parameter space and consequently the standard tests (likelihood ratio, Wald, and score tests) are not easily applied. The second challenge is to check the appropriateness of the assumed distribution for random effects, which is typically a (multivariate) normal distribution. In this talk, we first introduce a permutation test for inclusion or exclusion of random effects from the model which avoids the issues with the boundary of parameter space. We then introduce a likelihood-base​d diagnostic tool based on the so-called gradient function to check the adequacy of the random-effects distribution. We establish asymptotic properties of our diagnostic tool and additionally develop a parametric bootstrap algorithm for small sample situations. Our diagnostic tool can be used to check the adequacy of any parametric distribution for random effects in a wide class of mixed models, including linear, generalized linear, and non-linear mixed models, with univariate as well as multivariate random effects. Two real data applications will be presented.

Refer​ences:
1. Drikvandi, R., Verbeke, G., Khodadadi, A., and Partovi Nia, V. (2013). Testing multiple variance components in linear mixed-effects models. Biostatistics 14, 144-159.
2. Drikvandi, R., Verbeke, G., and Molenberghs, G. (2017). Diagnosing misspecificatio​n of the random-effects distribution in mixed models. Biometrics 73, 63-71.