Statistical Modelling 16 (2) (2016), 140–159

Generalized multiple indicators, multiple causes measurement error models

Carmen D. Tekwe
Department of Epidemiology and Biostatistics,
Texas A&M Health Science Center,
College Station, TX,

Randy L. Carter
Department of Biostatistics,
University at Buffalo,
Buffalo, NY,

Harry M. Cullings
Department of Statistics,
Radiation Effects Research Foundation,


Generalized Multiple Indicators, Multiple Causes Measurement Error Models (G-MIMIC ME) can be used to study the effects of an unobservable latent variable on a set of outcomes when the causes of the latent variables are unobserved. The errors associated with the unobserved causal variables can be due to either bias recall or day-to-day variability. Another potential source of error, the Berkson error, is due to individual variations that arise from the assignment of group data to individual subjects. In this article, we accomplish the following: (a) extend the classical linear MIMIC models to allow both Berkson and classical measurement errors where the distributions of the outcome variables belong in the exponential family, (b) develop likelihood based estimation methods using the MC-EM algorithm and (c) estimate the variance of the classical measurement error associated with the approximation of the amount of radiation dose received by atomic bomb survivors at the time of their exposure. The G-MIMIC ME model is applied to study the effect of genetic damage, a latent construct based on exposure to radiation, and the


atomic bomb survivor data; Berkson error; Generalized linear models; instrumental variables; measurement error; MIMIC models.


Example data and code in zipped archive.