Effect of measurement error in testing separate linear models

Abstract

Measurement error models (or errors-in variables models) have been explored since the latter part of the 19th century. Much activity and results in estimation and statistical inference have been forthcoming in linear and non-linear measurement error models, particularly in the past 10 to 15 years. Likewise, tests of separate families of hypotheses have received much attention sice Cox (1961, 1962) introduced a method of testing separate families of hypotheses. The aim of this paper is to provide results for testing separate linear models using Cox's methodology under the assumption of the functional measurement error model for which the error structure has a normal distribution. Simulations are used to compare the results of the Cox test when using estimates adjusted for measurement error, naive estimats, and estimates derived from true values. The overall conclusions derived from the simulation results are mixed. However, if the measurement error is small and collinearity between explanatory variables from the separate hypotheses is strong, then the Cox test using the adjusted estimates and the naive estimates performed just as well as the Cox test based on the "true" model.

Keywords:

• Errors
• in
• variables
• Measurement
• error
• Separate
• families
• of
• hypotheses
• Linear
• models