# the R package afex includes an ems function that gives expected mean squares:

library(afex)

# gives the results from Table 7.3 on page 237 of the text

ems(r ~ A*B*C, random="ABC")


# check the documentation at https://cran.r-project.org/web/packages/afex/afex.pdf
# for more features of the afex package, including the ability to 
# specify nested effects in the ems function