Statistical analysis of controlled calibration model with replicates

Abstract

In this work, we generalize the controlled calibration model by assuming replication on both variables. Likelihood-based methodology is used to estimate the model parameters and the Fisher information matrix is used to construct confidence intervals for the unknown value of the regressor variable. Further, we study the local influence diagnostic method which is based on the conditional expectation of the complete-data log-likelihood function related to the EM algorithm. Some useful perturbation schemes are discussed. A simulation study is carried out to assess the effect of the measurement error on the estimation of the parameter of interest. This new approach is illustrated with a real data set.

Keywords:

• local influence
• regression model
• linear calibration model
• measurement error model
• Berkson model

Acknowledgements

The authors thank the editor and two anonymous referees for helpful suggestions and comments. BGBA has been partially finantial supported by grants from Brazilian educational agencies: CNPq and FACEPE. VHL was supported in part by grants from FAPESP-Brazil (2010/012465) and CNPq-Brazil (308109/2008-2).