Bias correction of partial-error in variables in a Poisson regression model

Previous studies on Poisson regression models with error-in-variables (EIV) assumed either a univariate EIV structure or multivariate EIV framework with all explanatory variables subject to error where the explanatory variable and error vectors are restricted to multivariate normal distributions. This study assumes that the explanatory variable and error vectors follow general distributions, with measurement error affecting only a subset of variables in the multivariate EIV framework. We define the partial-error naive estimator, derive its asymptotic bias and mean squared error, and propose a consistent estimator for the true parameter by correcting this bias. We also investigate a simplification of the new estimator when all components of the explanatory variable and error vectors are independent. This method is applicable even when the explanatory variable or error vectors follow a mixed distribution. Simulation studies and real data analysis are presented as illustrative examples to compare the performance of the partial-error naive estimator with that of the new estimator.