MAXIMUM LIKELIHOOD ESTIMATION IN MULTIVARIATE CONTINUOUS VARIABLE VARIANCE COMPONENTS PANEL MODEL

Continuous variable panel models are widely used in social and business research to assess the effects of exogenous and lagged endogenous variables on endogenous variables over time. The number of time periods is generally small, however the number of independent replications measured at each time is generally large. This dissertation considers the problem of estimating the regression parameters for a "variance components" model in which the error includes a random "individual effect." The univariate version of this model has been widely studied in econometrics. Furthermore, the model appears to be an attractive alternative to cross-lagged panel models which are widely used in the social and behavioral sciences. We relate this model to the multivariate Gaussian sampling model with a pattern covariance matrix. This relationship is used to show that the explicit closed form solutions for the maximum likelihood estimates of the parameters of the variance components model do not exist. Results in the mathematical statistics literature are used to characterize and study the maximum likelihood estimators. The results are demonstrated by analysis of a panel study of patients' attitudes and perceptions toward health maintenance organizations.