Normal mixed models

This chapter discusses the mixed model with normally distributed errors. It defines the mixed model using a general matrix notation, which can be used for all types of mixed model. The chapter outlines the fixed effects model, and then extends this notation to encompass the mixed model. The mixed model extends the fixed effects model by including random effects, random coefficients and/or covariance terms in the residual variance matrix. The mixed models methods are described based on classical statistical techniques. The mixed model can be fitted by maximising the likelihood function for values of the data. The chapter introduces the Bayesian approach to fitting mixed models. It considers some practical issues related to the use and interpretation of mixed models and presents a worked example. A multi-centre trial of treatments for hypertension, and analyses the trial in greater detail are also discussed.