The Gradient Function for Checking Goodness-of-Fit of the Random-Effects Distribution in Mixed Models

• Activity Number: 224
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Geert Verbeke*+ and Geert Molenberghs
• Companies: Katholieke Universiteit Leuven and Hasselt University/Katholieke Universiteit Leuven
• Keywords: mixed models ; random effects ; model misspecification ; longitudinal data ; goodness-of-fit ; gradient function

Abstract

Inference in mixed models is often based on the marginal distribution obtained from integrating out random-effects over a pre-specified, often parametric, distribution. In this paper, we present the so-called gradient function as a simple graphical diagnostic tool to assess whether the assumed random-effects distribution produces an adequate fit to the data, in terms of marginal likelihood. The method does not require any additional calculations in addition to the computations needed to fit the model, and can be applied to every type of mixed model (linear, generalized linear, non-linear), with univariate as well as multivariate random effects. The diagnostic value of the gradient function is extensively illustrated using some simulated examples, as well as in the analysis of a real longitudinal study with binary outcome values.