在具有二进制DV得分（编码为1或0）和一些二元预测变量的模型上运行glmer（lme4_1.1-10）：试验类型，在主体内（Aff和Neg），以及2个主题间变量：cdiNo（1或0）和cdiNot（1或0）。包括随机试验类型随机斜率的随机效应。请注意，这里我将随机斜率和截距建模为不相关。使用bobyqa和maxIter设置为10000.这是模型：
analysis<-glmer(score ~ TrialType*cdiNot + TrialType*cdiNo + (1|UniqueSubject) + (0+TrialType|UniqueSubject)
默认情况下，glmer输出是虚拟编码，以使Aff成为TrialType的参考级别。在这种情况下，输出是完全合理的（并且在理论上预测）。
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
但是，我想看一下cdiNot和cdiNo相对于TrialType的其他参考级别的简单效果。所以，我重温：
data$TrialType<-relevel(data$TrialType, ref="Neg")
再次运行完全相同的模型。现在我收到了收敛警告和疯狂的输出。
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?
但神秘感加深了。如果我只是将随机斜率和截距的相关性添加到模型中，则收敛和其他警告消失，输出再次变得合理。因此，使用Neg作为参考级别并运行：
analysis<-glmer(score ~ TrialType*cdiNot + TrialType*cdiNo + (TrialType|UniqueSubject)
输出结果为：
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
我对可能发生的事情感到非常困惑。我想我可以想象，如果一个简单的效果很好并且一个是无法识别的，那么改变参考水平可能会导致收敛误差（尽管天文数字仍然不常见）。但如果我理解正确，随机斜率和截距之间的相关性只是模型估计的额外参数。怎么能包含这个参数使一个没有收敛的模型开始？