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Direction of dependence in measurement error models.
Wolfgang Wiedermann1, Edgar C Merkle2, Alexander von Eye3
1Department of Educational, School, and Counseling Psychology, University of Missouri, Columbia, Missouri, USA.
The British Journal of Mathematical and Statistical Psychology
|September 6, 2017
Summary
This study extends regression direction dependence methods to account for measurement error. It introduces remedies for biased results and assesses robustness, offering new tools for analyzing observational data.
Area of Science:
- Statistics
- Econometrics
- Psychometrics
Background:
- Direction dependence methods in regression are advancing rapidly.
- Previous methods assumed predictors were measured without error.
- Measurement error can bias the direction of regression dependence.
Purpose of the Study:
- Extend direction dependence principles to measurement error models.
- Address bias in direction dependence decisions caused by measurement error.
- Propose methods for robust analysis in the presence of measurement error.
Main Methods:
- Asymmetric reliability coefficient representations using higher moments.
- Method of moments (MOM) estimation to correct for bias.
- Sensitivity analysis for unreliably measured outcomes.
- Monte Carlo simulations to evaluate MOM performance.
Main Results:
- Measurement error attenuates skewness and excess kurtosis.
- Identified conditions where direction dependence decisions are biased.
- MOM estimation provides a remedy for biased direction dependence.
- Sensitivity analysis demonstrates robustness of decisions under certain conditions.
Conclusions:
- The study successfully extends direction dependence to measurement error models.
- MOM estimation is a viable approach for handling measurement error in direction dependence.
- The findings have implications for causal inference from observational data.
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