Estimated Estimating Equations: Semiparametric Inference for Clustered and Longitudinal Data
Journal
Journal of the Royal Statistical Society Series B: Statistical Methodology
Journal Volume
67
Journal Issue
4
Start Page
531-553
ISSN
1369-7412
1467-9868
Date Issued
2005-08-17
Author(s)
Hans-Georg Müller
Abstract
We introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions. This estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi-likelihood regression, where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link, and variance-covariance is an unknown smooth function of the marginal means. We propose to estimate the nonparametric link and variance-covariance functions via smoothing methods, whereas the regression parameters are obtained via the estimated estimating equations. These are score equations that contain nonparametric function estimates. The proposed estimated estimating equations approach is motivated by its flexibility and easy implementation. Moreover, if data follow a generalized linear mixed model, with either a specified or an unspecified distribution of random effects and link function, the model proposed emerges as the corresponding marginal (population-average) version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model, without the need to specify any other components of this generalized linear mixed model. Among marginal models, the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations. Applications of estimated estimating equations include diagnostics and link selection. The asymptotic distribution of the proposed estimators for the model parameters is derived, enabling statistical inference. Practical illustrations include Poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses. © 2005 Royal Statistical Society.
Subjects
Diagnostics
Generalized estimating equations
Generalized linear mixed model
Link selection
Marginal model
Quasi-likelihood
Repeated measurements
Semiparametric regression
Smoothing
Variance-covariance function
Publisher
Oxford University Press (OUP)
Type
journal article