如何从lme4获取随机效应(BLUP/条件模式)的协方差矩阵 [英] How to get covariance matrix for random effects (BLUPs/conditional modes) from lme4

问题描述

因此，我在R中拟合了带有两个随机截距的线性混合模型:

So, I've fitted a linear mixed model with two random intercepts in R:

Y = X beta  + Z b + e_i, 

其中b ~ MVN (0, Sigma); X和Z分别是固定效应模型矩阵和随机效应模型矩阵，beta和b是固定效应参数和随机效应BLUP/条件模式.

where b ~ MVN (0, Sigma); X and Z are the fixed- and random-effects model matrices respectively, and beta and b are the fixed-effect parameters and random-effects BLUPs/conditional modes.

我想了解b的基础协方差矩阵，这在lme4包中似乎并不重要.您只能通过VarCorr获得方差，而不能获得实际的相关矩阵.

I would like to get my hands on the underlying covariance matrix of b, which doesn't seem to be a trivial thing in lme4 package. You can get only the variances by VarCorr, not the actual correlation matrix.

根据其中一个小插图(第2页)，您可以计算beta的协方差:e_i * lambda * t(lambda).您可以从lme4的输出中提取所有这些组件.

According to one of the package vignettes (page 2), you can calculate the covariance of beta: e_i * lambda * t(lambda). And all those components you can extract from the output of lme4.

我想知道这是走的路吗?或者您还有其他建议吗?

I was wondering if this is the way to go? Or do you have any other suggestions?

推荐答案

来自?ranef:

如果"condVar"为"TRUE"，则每个数据框都有一个属性 称为"postVar""，这是一个具有对称形状的三维阵列 脸每个面都包含一个方差-协方差矩阵 分组因子的特定级别. (此属性的名称 是一个历史文物，在某些情况下可能会更改为"condVar" 指向未来.)

If ‘condVar’ is ‘TRUE’ each of the data frames has an attribute called ‘"postVar"’ which is a three-dimensional array with symmetric faces; each face contains the variance-covariance matrix for a particular level of the grouping factor. (The name of this attribute is a historical artifact, and may be changed to ‘condVar’ at some point in the future.)

设置示例:

library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
rr <- ranef(fm1,condVar=TRUE)

获取截距的b个值中的方差-协方差矩阵

Get the variance-covariance matrix among the b values for the intercept

pv <- attr(rr[[1]],"postVar")
str(pv)
##num [1:2, 1:2, 1:18] 145.71 -21.44 -21.44 5.31 145.71 ...

所以这是一个2x2x18的数组；每个切片是特定主体的条件截距和斜率之间的方差-协方差矩阵(根据定义，每个主体的截距和斜率与所有其他主体的截距和斜率无关).

So this is a 2x2x18 array; each slice is the variance-covariance matrix among the conditional intercept and slope for a particular subject (by definition, the intercepts and slopes for each subject are independent of the intercepts and slopes for all other subjects).

要将其转换为方差-协方差矩阵(请参见getMethod("image",sig="dgTMatrix") ...)

To convert this to a variance-covariance matrix (see getMethod("image",sig="dgTMatrix") ...)

library(Matrix)
vc <- bdiag(  ## make a block-diagonal matrix
            lapply(
                ## split 3d array into a list of sub-matrices
                split(pv,slice.index(pv,3)),
                   ## ... put them back into 2x2 matrices
                      matrix,2)) 
image(vc,sub="",xlab="",ylab="",useRaster=TRUE)

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