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B1403
Title: Assessing the random effects part of mixed models Authors:  Reza Drikvandi - Durham University (United Kingdom) [presenting]
Abstract: Correctly specifying the random effects part of mixed models is crucial for both the design and the power considerations. Since random effects are latent and unobservable quantities, it is challenging to decide which random effects should be included into the model. Inclusion or exclusion of random effects from the model is equivalent to test whether or not their variance components equal zero. However, test for zero variance components is a nonstandard problem since the null hypothesis in on the boundary of the parameter space. We propose a permutation test for variance components of random effects which avoids issues with the boundary of the parameter space. Another challenging task regarding the random effects part is to make sure the assumed distribution for random effects is correctly specified. An inappropriate random-effects distribution would result in model misspecification which could lead to biased parameter estimates as well as a poor power. We introduce a likelihood-based diagnostic test based on the so-called gradient function to assess the random-effects distribution. We establish asymptotic properties of our diagnostic test and also develop a parametric bootstrap algorithm for small sample situations. Our strategy can be used to check the adequacy of any distribution for random effects in a wide class of mixed models, particularly non-linear mixed models, with univariate as well as multivariate random effects.