Statistical Modelling 3 (2003), 215232
Correcting for covariate measurement error in logistic regression
using nonparametric maximum likelihood estimation
Sophia Rabe-Hesketh,
Department of Biostatistics and Computing,
Institute of Psychiatry, King's College,
DeCrespigny Park,
London SE5 8AF,
UK
eMail: spaksrh@iop.kcl.ac.uk
Andrew Pickles,
School of Epidemiology and Health Sciences and CCSR,
The University of Manchester,
Manchester,
UK
Anders Skrondal,
Division of Epidemiology,
Norwegian Institute of Public Health,
Oslo,
Norway
Abstract:
When covariates are measured with error, inference based on
conventional generalized linear models can yield biased estimates
of regression parameters. This problem can potentially be
rectified by using generalized linear latent and mixed models
(GLLAMM), including a measurement model for the relationship
between observed an true covariates. However, the models are
typically estimated under the assumption that both the true
covariates and the measurement errors are normally distributed,
although skewed covariate distributions are often observed in
practice. In this article we relax the normality assumption
for the true covariates by developing nonparametric maximum
likelihood estimation (NPMLE) for GLLAMMs.
The methodology is applied to estimating the effect of dietary
fibre intake on coronary heart disease. We also assess the
performance of estimation of regression parameters and
empirical Bayes prediction of the true covariate. Normal as
well as skewed covariate distributions are simulated and
inference is performed based on both maximum likelihood assuming
normality and NPMLE. Both etsimators are unbiased and have similar
root mean square errors when the true covariate is normal. With a
skewed covariate, the conventional estimator is biased but has smaller
mean square error than the NPMLE. NPMLE produces substantially
improved empirical Bayes predictions of the true covariate when its
distribution is skewed.
Keywords:
Empirical Bayes prediction; factor model; generalied linear model;
GLLAMM; logistic regression; measurement error; nonparametric maximum
likelihood estimation
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