*Bounty: 50*

This is a follow-up question to Which model for my data? (testing the differences in slope for three groups).

The solution from there works (big thanks to Heteroskedastic Jim!), but I have a problem with a specific data set. Maybe someone can enlighten me why I get stuck.

Here is an example that works:

```
library(nlme)
library(emmeans)
Input = ("
Group Time Size
A 1 1.08152
A 2 1.10589
A 3 1.13292
B 1 1.04597
B 2 1.05763
B 3 1.07023
B 4 1.08612
B 5 1.10059
B 6 1.11589
B 7 1.13143
B 8 1.14741
B 9 1.16721
B 10 1.18288
C 1 1.04777
C 2 1.06145
C 3 1.07484
C 4 1.08908
C 5 1.10346
C 6 1.11866
C 7 1.13375
C 8 1.14931
C 9 1.16563
C 10 1.18294
")
dat = read.table(textConnection(Input),header=TRUE)
```

This constructs the model:

```
(m1 <- gls(Size ~ Time * Group, dat, correlation = corAR1(form = ~ Time | Group), weights = varIdent(form = ~ 1 | I(Group == "A"))))
```

And this provides me with the p-values for slope differences:

```
pairs(emtrends(m1, ~ Group, var = "Time", df = Inf, options = get_emm_option("emmeans")))
```

Now the data set where I get stuck:

```
Input = ("
Group Time Size
A 1 1.6210
A 2 2.1118
A 3 2.6026
A 4 3.0934
B 1 0.9162
B 2 1.2122
B 3 1.5082
B 4 1.8042
B 5 2.1002
B 6 2.3962
B 7 2.6922
B 8 2.9882
B 9 3.2842
B 10 3.5802
C 1 0.82701
C 2 1.13441
C 3 1.44181
C 4 1.74921
C 5 2.05661
C 6 2.36401
C 7 2.67141
C 8 2.97881
C 9 3.28621
C 10 3.59361
")
dat = read.table(textConnection(Input),header=TRUE)
```

When I construct the above model with this specific data

```
(m1 <- gls(Size ~ Time * Group, dat, correlation = corAR1(form = ~ Time | Group), weights = varIdent(form = ~ 1 | I(Group == "A"))))
```

I get this error message:

```
Error in glsEstimate(object, control = control) : computed "gls" fit is singular, rank 6
```

I have tried analyzing the data in SPSS, but I also got stuck there.

So my question is: where is the problem with my data and what can I do to solve it?

Get this bounty!!!