Recursive linear mixed models: Some results on shared parameter estimation
Linear mixed models have become an important tool for the analysis of longitudinal data as they allow modeling of the covariance structure of the observations and handle missing data. Recursive linear models allow interactions between the endogenous variables in multivariate regression analysis. Parameter restrictions cause difficulties in any linear model. In a recursive linear model, the analytical properties of combined estimators of regression coefficients which are shared by some variables are hard to derive. We give some insights in the simpler case of separate estimation and derive the analytical distributions of two-stage generalized-least-squares estimators for shared coefficients. These estimators are used as a benchmark in a simulation study for the maximum likelihood estimators. The setting of this study is characterized by few (uniform) random effects, many regressors and a large number of unbalanced observations. The maximum likelihood estimators compare favorably to the two-stage estimators and we suppose them to be satisfactory if the number of degrees of freedom is large.
longitudinal data missing data simulation study maximum likelihood estimation random-effects