Converting Repeated Measures mixed model formula from SAS to R

Question

There are several questions and posts about mixed models for more complex experimental designs, so I thought this more simple model would help other beginners in this proces

Answer 1

Please try below:

model1 <- lme(
  Y ~ GROUP + X1,
  random = ~ GROUP | person,
  correlation = corCompSymm(form = ~ day | person),
  na.action = na.exclude, data = df1, method = "REML"
)
summary(model1)

I think random = ~ groupvar | subjvar option with R lme provides similar result of repeated / subject = subjvar group = groupvar option with SAS/MIXED in this case.

Edit:

SAS/MIXED

R (a revised model2)

model2 <- lme(
  Y ~ GROUP + X1,
  random = list(person = pdDiag(form = ~ GROUP - 1)),
  correlation = corCompSymm(form = ~ day | person),
  weights = varIdent(form = ~ 1 | GROUP),
  na.action = na.exclude, data = df1, method = "REML"
)
summary(model2)

So, I think these covariance structures are very similar (σ_g1 = τ_g² + σ₁).

Edit 2:

Covariate estimates (SAS/MIXED):

Variance            person          GROUP TEST        8789.23
CS                  person          GROUP TEST         125.79
Variance            person          GROUP CONTROL       82775
CS                  person          GROUP CONTROL       33297

So

TEST group diagonal element
  = 125.79 + 8789.23
  = 8915.02
CONTROL group diagonal element
  = 33297 + 82775
  = 116072

where diagonal element = σ_k1 + σ_k².

Covariate estimates (R lme):

Random effects:
 Formula: ~GROUP - 1 | person
 Structure: Diagonal
        GROUP1TEST GROUP2CONTROL Residual
StdDev:   14.56864       184.692 93.28885

Correlation Structure: Compound symmetry
 Formula: ~day | person 
 Parameter estimate(s):
         Rho 
-0.009929987 
Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | GROUP 
 Parameter estimates:
   1TEST 2CONTROL 
1.000000 3.068837 

So

TEST group diagonal element
  = 14.56864^2 + (3.068837^0.5 * 93.28885 * -0.009929987) + 93.28885^2
  = 8913.432
CONTROL group diagonal element
  = 184.692^2  + (3.068837^0.5 * 93.28885 * -0.009929987) + (3.068837 * 93.28885)^2
  = 116070.5

where diagonal element = τ_g² + σ₁ + σ_g².