Nested random effects in `lme {nlme}` - r

Question

I have to fit an LMM with an interaction random effect but without the marginal random effect, using the lme command. That is, I want to fit the model in oats.lmer (see below) but using the function lme from the nlme package.
The code is
require("nlme")
require("lme4")
oats.lmer <- lmer(yield~nitro + (1|Block:Variety), data = Oats)
summary(oats.lmer)
#Linear mixed model fit by REML ['lmerMod']
#Formula: yield ~ nitro + (1 | Block:Variety)
# Data: Oats
#
#REML criterion at convergence: 598.1
#
#Scaled residuals:
# Min 1Q Median 3Q Max
#-1.66482 -0.72807 -0.00079 0.56416 1.85467
#
#Random effects:
# Groups Name Variance Std.Dev.
# Block:Variety (Intercept) 306.8 17.51
# Residual 165.6 12.87
#Number of obs: 72, groups: Block:Variety, 18
#
#Fixed effects:
# Estimate Std. Error t value
#(Intercept) 81.872 4.846 16.90
#nitro 73.667 6.781 10.86
#
#Correlation of Fixed Effects:
# (Intr)
#nitro -0.420
I started playing with this
oats.lme <- lme(yield~nitro, data = Oats, random = (~1|Block/Variety))
summary(oats.lme)
#Linear mixed-effects model fit by REML
# Data: Oats
# AIC BIC logLik
# 603.0418 614.2842 -296.5209
#
#Random effects:
# Formula: ~1 | Block
# (Intercept)
#StdDev: 14.50596
#
# Formula: ~1 | Variety %in% Block
# (Intercept) Residual
#StdDev: 11.00468 12.86696
#
#Fixed effects: yield ~ nitro
# Value Std.Error DF t-value p-value
#(Intercept) 81.87222 6.945273 53 11.78819 0
#nitro 73.66667 6.781483 53 10.86291 0
# Correlation:
# (Intr)
#nitro -0.293
#
#Standardized Within-Group Residuals:
# Min Q1 Med Q3 Max
#-1.74380770 -0.66475227 0.01710423 0.54298809 1.80298890
#
#Number of Observations: 72
#Number of Groups:
# Block Variety %in% Block
# 6 18
but the problem is that it puts also a marginal random effect for Variety which I want to omit.
The question is: how to specify the random effects in oats.lme such that oats.lme is identical (at least structurally) to oats.lmer ?

Answer 1

It can be as simple as following:
library(nlme)
data(Oats)
## construct an auxiliary factor `f` for interaction / nesting effect
Oats$f <- with(Oats, Block:Variety)
## use `random = ~ 1 | f`
lme(yield ~ nitro, data = Oats, random = ~ 1 | f)
#Linear mixed-effects model fit by REML
# Data: Oats
# Log-restricted-likelihood: -299.0328
# Fixed: yield ~ nitro
#(Intercept) nitro
# 81.87222 73.66667
#
#Random effects:
# Formula: ~1 | f
# (Intercept) Residual
#StdDev: 17.51489 12.86695
#
#Number of Observations: 72
#Number of Groups: 18