An Errors-In-Variables Bias Model with an Application to Salmon Hatchery Data

Abstract

This paper presents an errors-in-variables (EV) model for assessing differences between two measurements of the same phenomenon, where each measurement is subject to error. The model, equivalent to a classical EV model, specifically includes parameters associated with the relative bias between the two measurements. We derive a complete statistical theory for this errors-in-variables bias (EVB) model, including analytical formulas for confidence intervals that are exact when the error lies in one variable alone and approximate otherwise. The model is used to compare two methods of estimating the number of salmon that return to their hatchery of origin. One method involves direct counting, while the other is based on fish marked with coded wire tags (CWTs). We conclude that, for coho (Oncorhynchus kisutch) and chinook (Oncorhynchus tshawytscha) hatcheries in British Columbia, Canada, estimates from CWTs are, on average, 22% lower than comparable counting estimates.