Lines in random effects plots from the linear mixed-effects model

After fitting a linear mixed-effects model to a set of repeated-measures or longitudinal data, it is common practice to plot the estimated random effe cts. On occasion it may be observed that in these plots a straight line may appear. How did this line arise? What influence does it have on the interp retation of the results from the model? This article demonstrates an artifa ct that can occur in the plots of random effects. If a cluster has exactly one observation, the plot of any estimated random effect against any other estimated random effect will fall on a straight line. The line in the plot of a pair of estimated random effects may even lie in the opposite directio n of the direction suggested by the correlation from the random effects cov ariance matrix. For clusters with two observations at the same design point s of the variables for the random effects, the estimated random effects wil l lie on a plane. Using an example, we demonstrate the patterns in the plot s of the estimated random effects. This illustrates that care must be taken when using plots of the estimated random effects.