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Using follow-up data to avoid omitted variable bias: an application to cardiovascular epidemiology
J Rehm1, G Arminger, L Kohlmeier
1Swiss Institute for the Prevention of Alcohol and Drug Problems, Lausanne.
Statistics in Medicine
|June 30, 1992
Summary
Follow-up studies help control omitted variable bias in linear models. Two models are proposed: one assuming uncorrelated omitted variables, the other allowing correlation, with a Hausman test for misspecification.
Area of Science:
- Statistics
- Econometrics
- Biostatistics
Background:
- Omitted variable bias is a common issue in linear models, potentially leading to inaccurate parameter estimates.
- Controlling for omitted variables is crucial for reliable analysis, especially in longitudinal data.
- Previous methods often struggled to address bias when omitted variables are correlated with included predictors.
Purpose of the Study:
- To propose and evaluate methods for controlling omitted variable bias in linear models using follow-up study data.
- To develop two distinct models addressing different assumptions about omitted variables.
- To introduce a misspecification test based on the differences between the proposed models.
Main Methods:
- Development of two linear models for analyzing longitudinal data with omitted variables.
- Model 1: Assumes omitted variables are time-constant and uncorrelated with predictors.
- Model 2: Assumes omitted variables are time-constant and potentially correlated with predictors (confounders).
- Application of generalized least squares (GLS) or maximum likelihood (ML) for Model 1.
- Consistent estimation using ordinary least squares (OLS) for Model 2.
- Construction of a Hausman test for model misspecification.
Main Results:
- Demonstrated that follow-up data can effectively control for omitted variable bias.
- Showcased that Model 1 requires specialized estimation methods (GLS/ML) due to error covariance structure.
- Established that Model 2 allows consistent OLS estimation even with correlated omitted variables.
- Validated the utility of the Hausman test for detecting misspecification.
Conclusions:
- Follow-up studies offer robust strategies to mitigate omitted variable bias in linear regression.
- The choice of model and estimation technique depends on assumptions about the omitted variables.
- The proposed Hausman test provides a valuable tool for assessing model adequacy in longitudinal studies.
- The methods were illustrated using determinants of serum cholesterol in adolescents.