Maximum likelihood estimation of generalized linear models with covariate measurement error
Sophia Rabe-Hesketh
Graduate School of Education
University of California
Berkeley, CA
|
Anders Skrondal
Division of Epidemiology
Norwegian Institute of
Public Health, Oslo
|
Andrew Pickles
School of Epidemiology
and Health Science
& CCSR
The University of Manchester
|
Abstract. Generalized linear models with covariate measurement error can be estimated
by maximum likelihood using gllamm, a program that fits a large class
of multilevel latent variable models (Rabe-Hesketh, Skrondal, and Pickles
2004). The program uses adaptive quadrature to evaluate the log likelihood,
producing more reliable results than many other methods (Rabe-Hesketh,
Skrondal, and Pickles 2002). For a single covariate measured with error
(assuming a classical measurement model), we describe a
“wrapper” command, cme, that calls gllamm to estimate the
model. The wrapper makes life easy for the user by accepting a simple syntax
and data structure and producing extended and easily interpretable output.
The commands for preparing the data and running gllamm can also be
obtained from cme. We first discuss the case where several measurements are
available and subsequently consider estimation when the measurement error
variance is instead assumed known. The latter approach is useful for
sensitivity analysis assessing the impact of assuming perfectly measured
covariates in generalized linear models. An advantage of using gllamm
directly is that the classical covariate measurement error model can be
extended in various ways. For instance, we can use nonparametric maximum
likelihood estimation (NPMLE) to relax the normality assumption for the true
covariate. We can also specify a congeneric measurement model which relaxes
the assumption that the measurements for a unit are exchangeable replicates
by allowing for different measurement scales and error variances.
View all articles by these authors:
Sophia Rabe-Hesketh, Anders Skrondal, Andrew Pickles
View all articles with these keywords:
covariate measurement error, measurement model, congeneric measurement model, factor model, adaptive quadrature, nonparametric maximum likelihood, NPMLE, latent class model, empirical Bayes, simulation, wrapper, sensitivity analysis, gllamm, cme
Download citation: BibTeX RIS
Download citation and abstract: BibTeX RIS
|
