Least Squares Estimation of Regression Parameters in Mixed E ects Models with Unmeasured Covariates

SUMMARY We consider mixed eeects models for longitudinal, repeated measures or clustered data. Unmeasured or omitted covariates in such models may be correlated with the included co-variates, and create model violations when not taken into account. Previous research and experience with longitudinal data sets suggest a general form of model which should be considered when omitted covariates are likely, such as in observational studies. We derive the marginal model between the response variable and included covariates, and consider model tting using the ordinary and weighted least squares methods, which require simple non-iterative computation and no assumptions on the distribution of random covariates or error terms. Asymptotic properties of the least squares estimators are also discussed. The results shed light on the structure of least squares estimators in mixed eeects models, and provide large sample procedures for statistical inference and prediction based on the marginal model. We present an example of the relationship between uid intake and output in very low birth weight infants, where the model is found to have the assumed structure.