LME 模型中 0 级反向求解的奇点，块 1

Question

输入数据，从 https://pastebin.com/1f7VuBkx 复制（太大而无法包含在此处）

data.frame':    972 obs. of  7 variables:
$ data_mTBS : num  20.3 22.7 0 47.8 58.7 ...
$ data_tooth: num  1 1 1 1 1 1 1 1 1 1 ...
$ Adhesive  : Factor w/ 4 levels "C-SE2","C-UBq",..: 2 2 2 2 2 2 2 2 2 2 ...
$ Approach  : Factor w/ 2 levels "ER","SE": 1 1 1 1 1 1 1 1 1 1 ...
$ Aging     : Factor w/ 2 levels "1w","6m": 1 1 1 1 1 1 2 2 2 2 ...
$ data_name : Factor w/ 40 levels "C-SE2-1","C-SE2-10",..: 11 11 11 11 11 11 11 11 11 11 ...
$ wait      : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
head(Data)


   data_mTBS data_tooth Adhesive Approach Aging data_name wait
1     20.27          1    C-UBq       ER    1w   C-UBq-1   no
2     22.73          1    C-UBq       ER    1w   C-UBq-1   no
3      0.00          1    C-UBq       ER    1w   C-UBq-1   no
4     47.79          1    C-UBq       ER    1w   C-UBq-1   no
5     58.73          1    C-UBq       ER    1w   C-UBq-1   no
6     57.02          1    C-UBq       ER    1w   C-UBq-1   no

当我运行下面的代码没有 "wait" 时，它工作得很好，但是当我尝试运行它并且模型中包含 "wait" 它给出了奇点问题。

LME_01<-lme(data_mTBS ~ Adhesive*Approach*Aging*wait, na.action=na.exclude,data = Data, random = ~ 1|data_name);

Error in MEEM(object, conLin, control$niterEM) : Singularity in backsolve at level 0, block 1

contrast_Aging<-contrast(LME_01,a = list(Aging =c("1w"),Adhesive = levels(Data$Adhesive),Approach = levels(Data$Approach) ),b = list(Aging =c("6m"), Adhesive = levels(Data$Adhesive),Approach = levels(Data$Approach)))

c1<-as.matrix(contrast$X)
Contrastsi2<-summary(glht(LME_01, c1))

&

contrast_Approach<-contrast(LME_01,
                                    a = list(Approach = c("SE"), Aging =levels(Data$Aging)   ,Adhesive = levels(Data$Adhesive)),
                                    b = list(Approach = c("ER"), Aging =levels(Data$Aging)   ,Adhesive = levels(Data$Adhesive)))

c2<-as.matrix(contrast$X)
Contrastsi3<-summary(glht(LME_01, c2))

提前致谢。

Answer 1

tl;dr 正如@HongOoi 告诉您的那样，wait 和 Adhesive 在您的模型中混淆了。 lme 比 R 中的许多其他建模函数有点 stupider/more 固执，它会明确警告您混淆了固定效应或自动为您删除其中一些。

如果绘制数据，就更容易看出这一点：

## source("SO50505290_data.txt")

library(ggplot2)
ggplot(dd,aes(Adhesive,data_mTBS,
              fill=Aging,
              alpha=Approach))+
  facet_grid(.~wait,scale="free_x",space="free",
             labeller=label_both)+
  guides(alpha = guide_legend(override.aes = list(fill = "darkgray")))+
  geom_boxplot()
ggsave("SO50505290.png")

这表明知道 wait=="no" 等同于知道 Adhesive=="C-UBq"。

备份并思考您提出的问题可能更有意义，但如果您使用 lme4::lmer 这样做，它会告诉您

fixed-effect model matrix is rank deficient so dropping 16 columns / coefficients

library(lme4)
LME_02<-lmer(data_mTBS ~ Adhesive*Approach*Aging*wait+
               (1|data_name), 
            na.action=na.exclude,data = dd)

LME 模型中 0 级反向求解的奇点，块 1

Singularity in backsolve at level 0, block 1 in LME model

r

mixed-models