Reverse attenuation in interaction terms due to covariate measurement error.

Abstract

Covariate measurement error may cause biases in parameters of regression coefficients in generalized linear models. The influence of measurement error on interaction parameters has, however, only rarely been investigated in depth, and if so, attenuation effects were reported. In this paper, we show that also reverse attenuation of interaction effects may emerge, namely when heteroscedastic measurement error or sampling variances of a mismeasured covariate are present, which are not unrealistic scenarios in practice. Theoretical findings are illustrated with simulations. A Bayesian approach employing integrated nested Laplace approximations is suggested to model the heteroscedastic measurement error and covariate variances, and an application shows that the method is able to reveal approximately correct parameter estimates.