The radial smoother implemented with the TYPE=RSMOOTH option in the RANDOM statement is an approximate low-rank thin-plate spline as described in Ruppert, Wand, and Carroll (2003, Chapter 13.4–13.5). The following sections discuss in more detail the mathematical-statistical connection between mixed models and penalized splines and the determination of the number of spline knots and their location as implemented in the GLIMMIX procedure.