On the polynomial structural relationship

In estimating a linear measurement error model, extra information is generally needed to identify the model. Here the authors show that the polynomial structural model with errors in the endogenous and exogenous variables can be identified without any extra information if the degree is greater than one. They also show that a weighted least squares approach for the estimation of the parameters in the model leads to the same estimates as the solutions of a system of estimating equations.     

Linear Regression With Nested Errors Using Probability‐Linked Data

Probabilistic matching of records is widely used to create linked data sets for use in health science, epidemiological, economic, demographic and sociological research. Clearly, this type of matching can lead to linkage errors, which in turn can lead to bias and increased variability when standard statistical estimation techniques are used with the linked data. In this paper we develop unbiased regression parameter estimates to be used when fitting a linear model with nested errors to probabilistically linked data. Since estimation of variance components is typically an important objective when fitting such a model, we also develop appropriate modifications to standard methods of variance components estimation in order to account for linkage error. In particular, we focus on three widely used methods of variance components estimation: analysis of variance, maximum likelihood and restricted maximum likelihood. Simulation results show that our estimators perform reasonably well when compared to standard estimation methods that ignore linkage errors.