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

Hi Maarten,

Here is an example which shows the unstructured model with gls and the 
not converging model with lmer. In this example, we have three occasions 
on which the dependent variable "test" was observed, for each of 20 
persons. In total then we have 60 observations, with the "occasion" 
variable taking values 1, 2, 3. The data also contain the person id 
variable "person" and dummy variables "occ1", "occ2", "occ3" as (0 or 1) 
indicators of the occasion.  In the syntax below, a factor variable 
"factor1" is created also, to be in line with your question.

I used two different specifications for the unstructured model with gls, 
depending on whether dummies or factor1 was used. For lmer, I used these 
three different specifications, none of which converges.

The lmer syntax was added only to show the problem which lmer has with 
estimating an unstructured correlation pattern.

#------------------------------------------------------------------------------------------------------------------------------------------------------------
mydata <- 
read.table(url("https://surfdrive.surf.nl/files/index.php/s/XfE3mtbFCTUejIz/download"), 
header=TRUE)

#-------------------  unstructured correlation matrix 
-----------------------

# Before applying a model, let's first examine the variances and 
correlations
# for the three occasions. We have a strong violation of the assumptions
# of homoscedasticity and compound symmetry.
test1 <- mydata[mydata$occasion==1,"test"]
test2 <- mydata[mydata$occasion==2,"test"]
test3 <- mydata[mydata$occasion==3,"test"]
cor(cbind(test1, test2, test3))
var(cbind(test1, test2, test3))

# Unstructured model using gls from package nlme and dummies for occasion.
# This model exactly reproduces the observed correlations between occasions.
unstruc.gls1 <- gls(test ~ 1+ occ2 + occ3,
                            method="REML", data=mydata,
                            correlation=corSymm(form = ~ 1 |person),
                            weights = varIdent(form = ~1|occasion))
summary(unstruc.gls1)

# Unstructured model using factor1 for occasion instead of dummies.
# The results are exactly the same as those above, as should be.
mydata$factor1 <- as.factor(mydata$occasion)
unstruc.gls2 <- gls(test ~ factor1,
                     method="REML", data=mydata,
                     correlation=corSymm(form = ~ 1|person),
                     weights = varIdent(form = ~1|factor1))
summary(unstruc.gls2)

# Unstructured model using lmer and dummies for occasion: does not 
converge.
unstruc.lmer <- lmer(test ~ 1+ occ2 + occ3 + (1+occ2+occ3|person),
                      data=mydata, REML=TRUE)
summary(unstruc.lmer)

# Unstructured model using lmer and factor1 for occasion: does not 
converge.
unstruc.lmer <- lmer(test ~ 1+ factor1 + (1+factor1|person),
                      data=mydata, REML=TRUE)
summary(unstruc.lmer)

# Unstructured model using lmer and factor1 for occasion, no intercept 
specified: does not converge.
unstruc.lmer <- lmer(test ~ factor1 + (factor1|person),
                      data=mydata, REML=TRUE)
summary(unstruc.lmer)

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

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