In that particular example the value of "4" was pulled out of the air. There is no particular justification. There is a strong relationship between the "effective" degrees of freedom and the variance of the random effect, and I often find the df scale easier to interpret. See the Hodges and Sargent paper in Biometrika (2001) for a nice explanation of the connection in linear models. Terry T. ======= begin included message ======== I've been following the example in the R help page: http://stat.ethz.ch/R-manual/R-devel/library/survival/html/frailty.html library(survival); coxph(Surv(time, status) ~ age + frailty(inst, df=4), lung) Here, in this particular example they fixed the degrees of freedom for the random institution effects to be 4. But, how did they decide?