Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/15396
Title: | The gradient function as an exploratory goodness-of-fit assessment of the random-effects distribution in mixed models | Authors: | VERBEKE, Geert MOLENBERGHS, Geert |
Issue Date: | 2013 | Publisher: | OXFORD UNIV PRESS | Source: | BIOSTATISTICS, 14 (3), p. 477-490 | 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. | Notes: | Katholieke Univ Leuven, Interuniv Inst Biostat & Stat Bioinformat, B-3000 Louvain, Belgium. Univ Hasselt, Interuniv Inst Biostat & Stat Bioinformat, B-3590 Diepenbeek, Belgium. | Keywords: | Directional derivative; Gradient; Latent variables; Mixed models; Random effects; Random-effects distribution;directional derivative; gradient; latent variables; mixed models; random effects; random-effects distribution | Document URI: | http://hdl.handle.net/1942/15396 | ISSN: | 1465-4644 | e-ISSN: | 1468-4357 | DOI: | 10.1093/biostatistics/kxs059 | ISI #: | 000320433000006 | Rights: | (c) The Author 2013. Published by Oxford University Press. All rights reserved | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
kxs059.pdf Restricted Access | Published version | 472.77 kB | Adobe PDF | View/Open Request a copy |
SCOPUSTM
Citations
36
checked on Sep 3, 2020
WEB OF SCIENCETM
Citations
43
checked on Apr 23, 2024
Page view(s)
60
checked on Sep 7, 2022
Download(s)
78
checked on Sep 7, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.