Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The gradient function as an exploratory goodness-of-fit assessment of the random-effects distribution in mixed models

The gradient function as an exploratory goodness-of-fit assessment of the random-effects... 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 exploratory 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 calculations in addition to the computations needed to fit the model, and can be applied to a wide range of mixed models (linear, generalized linear, non-linear), with univariate as well as multivariate random effects, as long as the distribution for the outcomes conditional on the random effects is correctly specified. In case of model misspecification, the gradient function gives an important, albeit informal, indication on how the model can be improved in terms of random-effects distribution. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biostatistics Oxford University Press

The gradient function as an exploratory goodness-of-fit assessment of the random-effects distribution in mixed models

Verbeke, Geert; Molenberghs, Geert
Biostatistics , Volume 14 (3) – Jul 31, 2013
Download PDF
14 pages

Loading next page...
 
/lp/oxford-university-press/the-gradient-function-as-an-exploratory-goodness-of-fit-assessment-of-oBKOH0Blr3

References (45)

Publisher
Oxford University Press
Copyright
The Author 2013. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissionsoup.com.
Subject
Articles
ISSN
1465-4644
eISSN
1468-4357
DOI
10.1093/biostatistics/kxs059
pmid
23376427
Publisher site
See Article on Publisher Site

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 exploratory 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 calculations in addition to the computations needed to fit the model, and can be applied to a wide range of mixed models (linear, generalized linear, non-linear), with univariate as well as multivariate random effects, as long as the distribution for the outcomes conditional on the random effects is correctly specified. In case of model misspecification, the gradient function gives an important, albeit informal, indication on how the model can be improved in terms of random-effects distribution. 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.

Journal

Biostatistics – Oxford University Press

Published: Jul 31, 2013

Keywords: Directional derivative Gradient Latent variables Mixed models Random effects Random-effects distribution

There are no references for this article.