# Simultaneous non-significant variance parameters but significant co-variance parameters mixed models/random effects

I specified a linear mixed model in SPSS:

TNA_HRQOL is the DV
TIME_0 is a rep measures factor (0,1,2) which I specified as a covariate
TK_Name (doctors) is LVL3 subjects, TNA_Name (individuals) is LVL 2 subjects.
The random commands specify random intercepts and slopes for doctors and random intercepts for individuals.

MIXED TNA_HRQOL BY TNA_FX_FinalGroup WITH TIME_0

/FIXED=TIME_0 TNA_FX_FinalGroup TNA_FX_FinalGroup*TIME_0

/RANDOM=INTERCEPT TIME_0 | SUBJECT(TK_Name) COVTYPE(UN) SOLUTION

/RANDOM=INTERCEPT | SUBJECT(TK_Name*TNA_Name) COVTYPE(ID)

/REPEATED=TIME_0 | SUBJECT(TK_Name*TNA_Name) COVTYPE(DIAG).

which has given me these random effect results:

The model didn't converge so these estimates are out of whack. You can see that the estimate with superscript b for row UN(2,2), meant to be the slope variance est. for the level 3 random subjects, TK_Name, is redundant and the intercept variance UN(1,1) is not significant. However, the estimate for covariance between the 2 is UN(2,1) (one-tailed test). Can someone confirm that such a scenario is possible/impossible? I am thinking no variance in interecepts at start but then the DV fans out in some way, maybe with a bunch staying straight/the same across time and a bunch decreasing/increasing.

The question, driven by these results and curiosity is: Is a mixed model with no variance in intercepts but significant variance in slopes possible?

That is, no intercept at time 1 estimated (if I make time a factor rather than continuous) but random slopes estimated.

The reason being is I have data for doctors who did the same treatment on several patients and they were tracked across time and I want to figure out whether the effect on patient(DV) varies across doctors. From what I've seen it seems that the prerequisite to random slopes is random intercepts. But everyone was randomly assigned at time 1, so I wouldn't expect there to be a difference in intercepts of the DV across doctors, but I would expect the treatment effect to differ across doctors.
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