Convergence issue using a LMM with random intercepts and slopes per patient, and with a continuous AR1 correlation structure - lme4

Question

Without providing a reproducible example (because that converged, and my data did not), my data is in a long format and includes 104 patients of which 304 measurements were taken. Most only have 2 measurements (n=68), followed by 5 (n=32), 4 (n=3), 3 (n=1), and 6 measurements (n=1). Some repeated measurements are taken fairly short after each other (for example for 74 of the 304 measurements the time in between was ~0.5 years), where for some patients with only two measurements the time in between is 5 years. The average follow-up time is about 3.5 years.
So far I've modeled a random intercept and slope model:
library(nlme)
ris <-
lme(fixed=outcome~ 1 + fu_time + age*fu_time + sex*fu_time + smoking*fu_time +
obesity*fu_time + diab*fu_time + hypt*fu_time + hyperchol*fu_time +
ckd*fu_time,
random=~1 + fu_time|patid,
data=data,
na.action="na.omit",
method="ML")
To further take into account the differing time in between subsequent measurements but keeping the increasing variances over time, I've tried to specify a model with (1) a random intercept, (2) a continuous AR1 correlation structure, and (3) heterogeneous variances:
ri_cAR1_hetvar <-
update(ris,
random=~1|patid,
correlation=corCAR1(form=~1|patid),
weight=varIdent(form=~1|fu_time),
control=lmeControl(opt="optim")) # does not converge.
This model does not converge. As per advice of Ben Bolker previously here is some output from running debug(nlme:::logLik.reStruct) followed by the following commands:
### Running str(object)
List of 1
$ patid: 'pdLogChol' num 0.0752
..- attr(*, "formula")=Class 'formula' language ~1
.. .. ..- attr(*, ".Environment")=<environment: 0x000000001ec31628>
..- attr(*, "Dimnames")=List of 2
.. ..$ : chr "(Intercept)"
.. ..$ : chr "(Intercept)"
- attr(*, "settings")= int [1:4] 0 1 0 4
- attr(*, "class")= chr "reStruct"
- attr(*, "plen")= Named int 1
..- attr(*, "names")= chr "patid"
### Running str(conLin)
List of 5
$ Xy : num [1:314, 1:22] 1 0.816 0.816 0.816 0.816 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:314] "1" "2" "3" "4" ...
.. ..$ : chr [1:22] "(Intercept)" "(Intercept)" "fu_time" "age" ...
$ dims :List of 15
..$ N : int 314
..$ ZXrows : int 314
..$ ZXcols : num 22
..$ Q : int 1
..$ StrRows: num 125
..$ qvec : Named num [1:3] 1 0 0
.. ..- attr(*, "names")= chr [1:3] "patid" "" ""
..$ ngrps : Named int [1:3] 104 1 1
.. ..- attr(*, "names")= chr [1:3] "patid" "X" "y"
..$ DmOff : Named num [1:3] 0 1 401
.. ..- attr(*, "names")= chr [1:3] "" "patid" ""
..$ ncol : Named num [1:3] 1 20 1
.. ..- attr(*, "names")= chr [1:3] "patid" "" ""
..$ nrot : Named num [1:3] 21 1 0
.. ..- attr(*, "names")= chr [1:3] "" "" ""
..$ ZXoff :List of 3
.. ..$ patid: num [1:104] 0 6 8 13 15 18 23 28 30 32 ...
.. ..$ X : Named num 314
.. .. ..- attr(*, "names")= chr "patid"
.. ..$ y : Named num 6594
.. .. ..- attr(*, "names")= chr ""
..$ ZXlen :List of 3
.. ..$ patid: num [1:104] 6 2 5 2 3 5 5 2 2 2 ...
.. ..$ X : num 314
.. ..$ y : num 314
..$ SToff :List of 3
.. ..$ patid: num [1:104] 0 1 2 3 4 5 6 7 8 9 ...
.. ..$ X : Named num 229
.. .. ..- attr(*, "names")= chr "patid"
.. ..$ y : Named num 2749
.. .. ..- attr(*, "names")= chr ""
..$ DecOff :List of 3
.. ..$ PXE_nr: num [1:104] 0 1 2 3 4 5 6 7 8 9 ...
.. ..$ X : Named num 125
.. .. ..- attr(*, "names")= chr "patid"
.. ..$ y : Named num 2625
.. .. ..- attr(*, "names")= chr ""
..$ DecLen :List of 3
.. ..$ PXE_nr: num [1:104] 1 1 1 1 1 1 1 1 1 1 ...
.. ..$ X : num 125
.. ..$ y : num 125
$ logLik :Class 'logLik' : 4.3 (df=178)
$ sigma : num 0
$ auxSigma: num 0
### Running dput(object)
structure(list(patid= structure(-1.29387589179439, formula = ~1, Dimnames = list(
"(Intercept)", "(Intercept)"), class = c("pdLogChol", "pdSymm",
"pdMat"))), settings = c(0L, 1L, 0L, 4L), class = "reStruct", plen = c(patid= 1L))
I understand this question might be difficult to answer without a reproducible example, but posting anymore of my data is not really an option, and model works on the subsets of my data that I had prepared for this question.
If anyone has any ideas how I could further diagnose this problem, the help would be very much appreciated!
Update
I've noticed that the problem arises when I specify different variances per week by adding weight=varIdent(form=~1|fu_time), and nót per se by adding a continuous AR1 (that works fine). Might the problem be in how many parameters are estimated in the model with heterogenous variances? As in, I thought that that model still only just estimates phi, but now that I think of it it might estimate a parameter for every timepoint, which in my case is a continuous variable with a lot of levels...