如何从 SAS 复制 lme4 中的随机效应？

Question

我希望在因变量 DV 上运行线性混合模型，该变量收集在两个不同的 Condition 和三个不同的 Timepoint 下。数据结构如下：

   ## dput(head(RawData,5))
    structure(list(Participant = structure(c(2L, 2L, 2L, 2L, 4L), 
  .Label = c("Jessie", "James", "Gus", "Hudson", "Flossy", 
 "Bobby", "Thomas", "Alfie", "Charles", "Will", "Mat", "Paul", "Tim", 
  "John", "Toby", "Blair"), class = "factor"), 
 xVarCondition = c(1, 1, 0, 0, 1), 
 Measure = structure(c(1L, 2L, 3L, 4L, 1L), 
.Label = c("1", "2", "3", "4", "5", "6", "7", "8", 
"9", "10", "11", "12"), class = "factor"), 
Sample = structure(c(1L, 2L, 1L, 2L, 1L), 
.Label = c("1", "2"), class = "factor"), 
 Condition = structure(c(2L, 2L, 1L, 1L, 2L),
 .Label = c("AM", "PM"), class = "factor"),
 Timepoint = structure(c(2L, 2L, 2L, 2L, 1L), 
.Label = c("Baseline", "Mid", "Post"), class = "factor"),
 DV = c(83.6381348645853, 86.9813802115179, 69.2691666620429, 
 71.3949807856125, 87.8931998204771)), 
.Names = c("Participant", "xVarCondition", "Measure", 
   "Sample", "Condition", "Timepoint", "DV"), 
 row.names = c(NA, 5L), class = "data.frame")

如Measure 所示，每个Participant 在三个Timepoints 中每个Condition 执行两次试验；但是，缺少数据，因此不一定每个参与者有 12 个级别。 xVarCondition 列只是一个虚拟变量，其中 Condition 中的每个 AM 条目都包含一个 1。 Sample 列是指每个 Condition 在每个 Timepoint 的 2 次试验。

我是 R 用户，但统计学家是 SAS 用户，他认为模型的代码应该是：

proc mixed data=RawData covtest cl alpha=α
class Participant Condition Timepoint Measure Sample;
model &dep=Condition Timepoint/s ddfm=sat outp=pred residual noint;
random int xVarCondition xVarCondition*TimePoint*Sample 
          TimePoint/subject=Participant s;

上面的 SAS 代码给出了合理的答案并且运行良好。我们相信上述模型的 lme4 语法是：

TestModel = lmer(DV ~ Condition + Timepoint + 
              (1 | Participant/Timepoint) +
              (0 + xVarCondition | Participant) +
              (1 | Participant:xVarCondition:Measure), data = RawData)

但是，运行此模型时出现以下错误：

Error: number of levels of each grouping factor must be < number of observations

是否正确指定了随机效应？

Answer 1

我无法从您的描述中完全看出，但很可能您的 Participant:xVarCondition:Measure 术语构造了一个分组变量，该变量在每个分类级别中不超过一个观察值，这将使 (1|Participant:xVarCondition:Measure) 术语与lmer 模型中始终包含的残差项。如果你真的想通过包含来覆盖错误，你可以覆盖

control=lmerControl(check.nobs.vs.nlev = "ignore")

在您的函数调用中，但是（如果我已正确诊断问题）这将导致剩余方差和 Participant:xVarCondition:Measure 方差共同无法识别。这种不可识别性通常不会对模型的其余部分造成任何问题，但我更喜欢可识别的模型（这种不可识别性总是有可能导致数值问题）。

有一个类似的例子here。

你可以检查我的猜想如下：

ifac <- with(RawData,
   interaction(Participant,xVarCondition,Measure,drop=TRUE))
length(levels(ifac)) == nrow(RawData)