What is the lmer/nlme equivalent of the REPEATED subcommand in SPSS's MIXED procedure?

Hi Maarten,

In gls there are no (three) random intercepts for the occasions, there 
are only "residuals" which are allowed to correlate. Singer and Willett 
call these residuals "composite" residuals. For the observations on 
occasion 1 the model equations are:

lmer model: test1 = b0 + b1*occ1 + uj + eij
gls model: test1 = b0 + b1*occ1 + residual

This shows that uj+eij in lmer is replaced by just one term "residual" 
in gls. Hence  the term "composite residuals".

Returning to ignoring the nobs.vs.nRE rule, we could also specify this 
model with three dummies and no intercept:

# Unstructured model using lmer and dummies for occasion: does not 
converge.
unstruc.lmer <- lmer(test ~ -1+occ1+ occ2 + occ3 + 
(-1+occ1+occ2+occ3|person),
                      data=mydata, REML=TRUE,
                      control = lmerControl(check.nobs.vs.nRE = "ignore"),
                      )
summary(unstruc.lmer)

You will see in the results that the sum of each random occasion 
variance PLUS the residual variance exactly equals the observed 
variance. This implies that the unidentifiability of this model with 
lmer is caused by the fact that the 3 observed variances must be 
estimated with 4 parameters. Increasing the estimated value of the 
residual variance with a constant, A, means that for the 3 occasion 
random effect variances, the estimated values must be decreased by A to 
end up with the same estimates of the variances in the dependent 
variable at all three timepoints. And the fit in terms of loglikelihood 
would be equal.

Regards, Ben.

, relates to the also probably may have noticed that in the "solution" 
you obtained by ignoring the nobs.vs.nRE rule, the sum of the random 
occasion effect for time=1

What is the lmer/nlme equivalent of the REPEATED subcommand in SPSS's MIXED procedure?

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