Changing reference level of binary predictor causes glmer to explode - r

Question

Running a glmer (lme4_1.1-10) on a model with a binary DV of score (coded as 1 or 0) and a few binary predictors: Trial Type, which is within-subject (Aff and Neg), and 2 between-subject variables: cdiNo (1 or 0) and cdiNot (1 or 0). Including a random effect with random slope of Trial Type by Subject. Note that here I'm modeling random slope and intercept as uncorrelated. Using bobyqa and maxIter set at 10000. Here's the model:
analysis<-glmer(score ~ TrialType*cdiNot + TrialType*cdiNo + (1|UniqueSubject) + (0+TrialType|UniqueSubject)
By default, glmer output is dummy coded to make Aff the reference level for TrialType. In that case, the output is perfectly sensible (and theoretically predicted).
AIC BIC logLik deviance df.resid
1766.8 1819.5 -873.4 1746.8 1431
Scaled residuals:
Min 1Q Median 3Q Max
-2.3214 -0.8554 0.4693 0.6288 1.5026
Random effects:
Groups Name Variance Std.Dev. Corr
UniqueSubject (Intercept) 0.3007 0.5484
UniqueSubject.1 TrialTypeAff 0.2587 0.5087
TrialTypeNeg 0.4398 0.6631 0.13
Number of obs: 1441, groups: UniqueSubject, 183
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.3728 0.5285 2.598 0.00939 **
TrialTypeNeg -1.1677 0.6652 -1.755 0.07919 .
cdiNot 0.6915 0.2280 3.033 0.00242 **
cdiNo -0.4600 0.5394 -0.853 0.39384
TrialTypeNeg:cdiNot 0.2673 0.2915 0.917 0.35904
TrialTypeNeg:cdiNo 0.1239 0.6811 0.182 0.85560
However, I want to look at the simple effect of cdiNot and cdiNo relative to the other reference level of TrialType. So, I relevel:
data$TrialType<-relevel(data$TrialType, ref="Neg")
And run the exact same model again. Now I get convergence warnings and an insane output.
AIC BIC logLik deviance df.resid
1766.8 1819.5 -873.4 1746.8 1431
Scaled residuals:
Min 1Q Median 3Q Max
-2.3351 -0.8586 0.4714 0.6301 1.4968
Random effects:
Groups Name Variance Std.Dev. Corr
UniqueSubject (Intercept) 0.3377 0.5811
UniqueSubject.1 TrialTypeNeg 0.3917 0.6258
TrialTypeAff 0.2263 0.4757 0.02
Number of obs: 1441, groups: UniqueSubject, 183
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.207190 0.001148 180.5 <2e-16 ***
TrialTypeAff 1.149480 0.001148 1001.6 <2e-16 ***
cdiNot 0.949130 0.001147 827.1 <2e-16 ***
cdiNo -0.330437 0.001148 -287.9 <2e-16 ***
TrialTypeAff:cdiNot -0.247906 0.001147 -216.1 <2e-16 ***
TrialTypeAff:cdiNo -0.107224 0.001148 -93.4 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) TrlTyA cdiNot cdiNo TrlTypAff:cdNt
TrialTypAff 0.001
cdiNot 0.000 0.000
cdiNo 0.000 0.001 0.000
TrlTypAff:cdNt 0.000 0.000 0.000 0.000
TrilTypAff:cdN 0.001 0.001 0.000 0.001 0.000
convergence code: 0
Model failed to converge with max|grad| = 0.0624071 (tol = 0.001, component 1)
Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?
But the mystery deepens. If I just add the correlation of random slope and intercept to the model, the convergence and other warnings disappear, and the output becomes sensible again. So, using Neg as the reference level and running:
analysis<-glmer(score ~ TrialType*cdiNot + TrialType*cdiNo + (TrialType|UniqueSubject)
The output is:
AIC BIC logLik deviance df.resid
1764.8 1812.2 -873.4 1746.8 1432
Scaled residuals:
Min 1Q Median 3Q Max
-2.3215 -0.8554 0.4693 0.6288 1.5026
Random effects:
Groups Name Variance Std.Dev. Corr
UniqueSubject (Intercept) 0.7405 0.8605
TrialTypeAff 0.6125 0.7826 -0.59
Number of obs: 1441, groups: UniqueSubject, 183
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.2051 0.5009 0.410 0.6821
TrialTypeAff 1.1676 0.6654 1.755 0.0793 .
cdiNot 0.9588 0.2222 4.314 1.6e-05 ***
cdiNo -0.3360 0.5154 -0.652 0.5144
TrialTypeAff:cdiNot -0.2673 0.2915 -0.917 0.3591
TrialTypeAff:cdiNo -0.1239 0.6813 -0.182 0.8557
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) TrlTyA cdiNot cdiNo TrlTypAff:cdNt
TrialTypAff -0.621
cdiNot -0.036 0.021
cdiNo -0.966 0.600 -0.121
TrlTypAff:cdNt 0.021 -0.021 -0.636 0.078
TrilTypAff:cdN 0.603 -0.966 0.077 -0.625 -0.120
I'm very confused about what might be going on. I suppose I can imagine that if one simple effect is fine and one is unidentifiable, changing the reference level could cause a convergence error (though the astronomical numbers are still unusual). But if I understand correctly, the correlation between random slope and intercept is just an extra parameter for the model to estimate. How could including this parameter make a model that wasn't converging start to?