The outcome Y is a continuous measure of pulmonary function. The predictors includes: gender (boys and girls), treatments (control, nedocromil, albuterol), pollution measurement (continuous). Each participant has 3 visits per year. Suppose we only look at the data during the

first year of the study and assume all the visits are at the same time for all participants.

Q:

1.The investigators think different treatments may have different effect on a person's pulmonary function but the effects are believed not to change over time. Write out a linear mixed effects model with a random intercept for the data.

2.calculate the covariance matrix of the 3 pulmonary function measurements of a person under the model in the above question.

Not sure about the model, is Yijk= + 1(boyik)+ treatment j+bik+ijk right? Also, is the covariance equal to var(bik)?