如何在nlme与lme4中指定不同的随机效果？

Question

我想在模型中使用nlme::lme(底部的数据)指定不同的随机效果.随机效应是:1)intercept并且position变化subject; 2) intercept变化comparison.这很简单lme4::lmer:

lmer(rating ~ 1 + position + 
     (1 + position | subject) + 
     (1 | comparison), data=d)

> ...
Random effects:
 Groups     Name        Std.Dev. Corr 
 comparison (Intercept) 0.31877       
 subject    (Intercept) 0.63289       
            position    0.06254  -1.00
 Residual               0.91458      
 ...

但是,我想坚持,lme因为我也想模拟自相关结构(position是一个时间变量).我怎么能像上面那样使用lme？我在下面的尝试会影响效果,这不是我想要的.

lme(rating ~ 1 + position,
random = list( ~ 1 + position | subject,
               ~ 1 | comparison), data=d)

> ...
Random effects:
 Formula: ~1 + position | subject
 Structure: General positive-definite, Log-Cholesky parametrization
            StdDev     Corr  
(Intercept) 0.53817955 (Intr)
position    0.04847635 -1    

 Formula: ~1 | comparison %in% subject    # NESTED :(
        (Intercept)     Residual
StdDev:   0.9707665 0.0002465237
...

注:上有SO和CV一些类似的问题在这里,在这里,并在这里,但我既没有理解答案或建议是使用lmer其在这里不计;)

示例中使用的数据

d <- structure(list(rating = c(2, 3, 4, 3, 2, 4, 4, 3, 2, 1, 3, 2, 
2, 2, 4, 2, 4, 3, 2, 2, 3, 5, 3, 4, 4, 4, 3, 2, 3, 5, 4, 5, 2, 
3, 4, 2, 4, 4, 1, 2, 4, 5, 4, 2, 3, 4, 3, 2, 2, 2, 4, 5, 4, 4, 
5, 2, 3, 4, 3, 2), subject = structure(c(1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L), .Label = c("1", "2", "3", "4", "5", 
"6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", 
"17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", 
"28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", 
"39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", 
"50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", 
"61", "62", "63"), class = "factor"), position = c(1, 2, 3, 4, 
5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 
5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 
5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), comparison = structure(c(1L, 
7L, 9L, 8L, 3L, 4L, 10L, 2L, 5L, 6L, 2L, 6L, 4L, 5L, 8L, 10L, 
7L, 3L, 1L, 9L, 3L, 9L, 10L, 1L, 5L, 7L, 6L, 8L, 2L, 4L, 4L, 
2L, 8L, 6L, 7L, 5L, 1L, 10L, 9L, 3L, 5L, 10L, 6L, 3L, 2L, 9L, 
4L, 1L, 8L, 7L, 6L, 5L, 2L, 10L, 4L, 3L, 8L, 9L, 7L, 1L), contrasts = structure(c(1, 
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 
0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 
0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 
0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 
0, 0, 0, 0, 0, 0, 0, 1, -1), .Dim = c(10L, 9L), .Dimnames = list(
    c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10"), NULL)), .Label = c("1", 
"2", "3", "4", "5", "6", "7", "8", "9", "10"), class = "factor")), .Names = c("rating", 
"subject", "position", "comparison"), row.names = c(1L, 2L, 3L, 
4L, 5L, 6L, 7L, 8L, 9L, 10L, 111L, 112L, 113L, 114L, 115L, 116L, 
117L, 118L, 119L, 120L, 221L, 222L, 223L, 224L, 225L, 226L, 227L, 
228L, 229L, 230L, 331L, 332L, 333L, 334L, 335L, 336L, 337L, 338L, 
339L, 340L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L, 449L, 
450L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L, 559L, 560L
), class = "data.frame")

Answer 1

我一直想尝试解决这个问题.没有更多的工作我不认为我可以得到完全相同的模型lme4,但我可以接近.

## source("SO36643713.dat")
library(nlme)
library(lme4)

这是您想要的模型,具有完整的随机斜率项subject(相关斜率和截距)和随机截距comparison:

m1 <- lmer(rating ~ 1 + position + 
               (1 + position | subject) + 
               (1 | comparison), data=d)

这是我可以弄清楚如何复制的lme:独立拦截和斜坡.(我不特别喜欢这些模型,但它们作为人们简化过于复杂的随机效应模型的方式而被广泛使用.)

m2 <- lmer(rating ~ 1 + position + 
               (1 + position || subject) + 
               (1 | comparison), data=d)

结果:

VarCorr(m2)
##  Groups     Name        Std.Dev.
##  comparison (Intercept) 0.28115 
##  subject    position    0.00000 
##  subject.1  (Intercept) 0.28015 
##  Residual               0.93905 

对于该特定数据集,无论如何估计随机斜率具有零方差.

现在让我们为它设置lme.关键(???)洞察力是pdBlocked()矩阵内的所有项必须嵌套在同一个分组变量中.例如,Pinheiro和Bates的pp.163ff的交叉随机效应示例具有块,块内的行和块内的列作为随机效应.由于没有分组因子,comparison并且subject它们都是嵌套的,我只是要构成一个dummy"因子",其中包括整个数据集在一个块中:

d$dummy <- factor(1)

现在我们可以适应模型了.

m3 <- lme(rating~1+position,
          random=list(dummy =
                pdBlocked(list(pdIdent(~subject-1),
                               pdIdent(~position:subject),
                               pdIdent(~comparison-1)))),
          data=d)

我们在随机效应方差 - 协方差矩阵中有三个块:一个用于subject,一个用于position- subject交互,一个用于comparison.pdMat如果没有定义一个全新的类,我无法找到一种简单的方法来允许每个slope(position:subjectXX)与其相应的intercept(subjectXX)相关联.(您可能认为可以使用pdBlocked结构进行设置,但我没有看到任何方法将方差估计值限制在pdBlocked对象中的多个块之间.)

结果几乎完全相同,尽管它们的报道不同.

vv <- VarCorr(m3)
vv2 <- vv[c("subject1","position:subject1","comparison1","Residual"),]
storage.mode(vv2) <- "numeric"
print(vv2,digits=4)
                   Variance    StdDev
subject1          7.849e-02 2.802e-01
position:subject1 4.681e-11 6.842e-06
comparison1       7.905e-02 2.812e-01
Residual          8.818e-01 9.390e-01