中的“级别”数量没有限制lme4。只要数据支持这种随机效应结构，该包将能够适应任意数量的级别。

我们可以通过以下模拟来演示类似于 OP 中描述的 4 级数据集：

> set.seed(15)
> library(lme4)
> dt1 <- data.frame(expand.grid(SchoolID = LETTERS[1:6], FacultyID = LETTERS[1:6], CourseID = LETTERS[1:10], StudentID = 1:100, Score = c(NA, NA, NA)))
> dt1$Score <- as.numeric(dt1$SchoolID) + as.numeric(dt1$FacultyID) + as.numeric(dt1$CourseID) + as.numeric(dt1$StudentID) + rnorm(nrow(dt1), 0,5)
> lmm1 <- lmer(Score ~ 1 + (1 | SchoolID/FacultyID/CourseID/StudentID), data = dt1)
> summary(lmm1)  
Random effects:
 Groups                                    Name        Variance Std.Dev.
 StudentID:(CourseID:(FacultyID:SchoolID)) (Intercept) 841.6574 29.0113 
 CourseID:(FacultyID:SchoolID)             (Intercept)   0.8581  0.9263 
 FacultyID:SchoolID                        (Intercept)   2.5579  1.5993 
 SchoolID                                  (Intercept)   2.8880  1.6994 
 Residual                                               24.9743  4.9974 
Number of obs: 108000, groups:  
StudentID:(CourseID:(FacultyID:SchoolID)), 36000; CourseID:(FacultyID:SchoolID), 360; FacultyID:SchoolID, 36; SchoolID, 6

如果我们愿意，我们也可以拟合一个 5 层模型：

> dt2 <- data.frame(expand.grid(CityID = LETTERS[1:6], SchoolID = LETTERS[1:6], FacultyID = LETTERS[1:6], CourseID = LETTERS[1:10], StudentID = 1:20, Score = c(NA, NA, NA)))
> dt2$Score <- as.numeric(dt2$CityID) + as.numeric(dt2$SchoolID) + as.numeric(dt2$FacultyID) + as.numeric(dt2$CourseID) + as.numeric(dt2$StudentID) + rnorm(nrow(dt2), 0, 5)
> lmm2 <- lmer(Score ~ 1 + (1 | CityID/SchoolID/FacultyID/CourseID/StudentID), data = dt2)
> summary(lmm2)  
Random effects:
 Groups                                             Name        Variance 
Std.Dev.
 StudentID:(CourseID:(FacultyID:(SchoolID:CityID))) (Intercept) 34.778   5.897   
 CourseID:(FacultyID:(SchoolID:CityID))             (Intercept)  7.418   2.724   
 FacultyID:(SchoolID:CityID)                        (Intercept)  2.516   1.586   
 SchoolID:CityID                                    (Intercept)  2.873   1.695   
 CityID                                             (Intercept)  2.922   1.709   
 Residual                                                       24.940   4.994   
Number of obs: 129600, groups:  
StudentID:(CourseID:(FacultyID:(SchoolID:CityID))), 43200; CourseID:(FacultyID:(SchoolID:CityID)), 2160; FacultyID:(SchoolID:CityID), 216; SchoolID:CityID, 36; CityID, 6

[请注意，第二个模型可能需要一段时间才能适应！]

部分交叉结构最好通过确保每个簇中的因子被唯一编码来表示，lme4然后应该能够通过将随机效应指定为简单地处理部分交叉/部分嵌套结构

(1 | SchoolID) + (1 | FacultyID) + (1 | CourseID) + (1 | StudentID)

这意味着，例如，如果你有 StudentID 1inFaculty A和Student 1inFaculty B并且它们是不同的（即这两个学生嵌套在各自的院系中），那么它们应该分别编码为类似StudentID 1A 和StudentID 1B。我们可以用dt1上面的数据集证明这一点，通过重新编码如下因素：

> dt1.1 <- dt1
> dt1.1$FacultyID <- paste(dt1$SchoolID, dt1$FacultyID, sep = ".")
> dt1.1$CourseID <- paste(dt1.1$FacultyID, dt1$CourseID, sep = ".")
> dt1.1$StudentID <- paste(dt1.1$CourseID, dt1$StudentID, sep = ".")
> lmm1.1 <- lmer(Score ~ 1 + (1 | SchoolID) + (1 | FacultyID) + (1 | CourseID) + (1 | StudentID), data = dt1.1)
> summary(lmm1.1)  

Random effects:
 Groups    Name        Variance Std.Dev.
 StudentID (Intercept) 841.6568 29.0113 
 CourseID  (Intercept)   0.8584  0.9265 
 FacultyID (Intercept)   2.5585  1.5995 
 SchoolID  (Intercept)   2.8893  1.6998 
 Residual               24.9743  4.9974 
Number of obs: 108000, groups:  StudentID, 36000; CourseID, 360; FacultyID, 36; SchoolID, 6

请注意，模型输出与lmm1上述相同，尽管呈现方式略有不同。

到目前为止，数据是完全嵌套的。也就是说，每个学生只注册一门课程，一门课程“属于”一门学院等。为了模拟交叉因素，例如注册两门课程的学生，我们可以简单地结合相关的学生 ID：首先我们确定要组合的学生 ID：

> dt1.1[dt1.1$StudentID == "A.A.A.31" | dt1.1$StudentID == "A.A.B.31", ]
      SchoolID FacultyID CourseID StudentID    Score
10801        A       A.A    A.A.A  A.A.A.31 33.00600
10837        A       A.A    A.A.B  A.A.B.31 33.69633
46801        A       A.A    A.A.A  A.A.A.31 33.03089
46837        A       A.A    A.A.B  A.A.B.31 33.00802
82801        A       A.A    A.A.A  A.A.A.31 41.68804
82837        A       A.A    A.A.B  A.A.B.31 31.26155

并给他们相同的（唯一的）ID：

> dt1.1[dt1.1$StudentID == "A.A.A.31" | dt1.1$StudentID == "A.A.B.31", ]$StudentID   <- "CCCC"

然后我们可以用相同的调用来拟合模型：

lmm1.1 <- lmer(Score ~ 1 + (1 | SchoolID) + (1 | FacultyID) + (1 | CourseID) + (1 | StudentID), data = dt1.1)
> summary(lmm1.1)  
Random effects:
 Groups    Name        Variance Std.Dev.
 StudentID (Intercept) 841.6867 29.0118 
 CourseID  (Intercept)   0.8312  0.9117 
 FacultyID (Intercept)   2.5570  1.5991 
 SchoolID  (Intercept)   2.8851  1.6986 
 Residual               24.9742  4.9974 
Number of obs: 108000, groups:  StudentID, 35999; CourseID, 360; FacultyID, 36; SchoolID, 6

请注意，我们现在有 35,999StudentID秒，而不是 36,000 秒。

有关编码交叉和嵌套因子的更多信息，请参见此处。