删除 lme 中随机效应与解释摘要输出之间相关性的术语

机器算法验证 r 混合模式 lme4-nlme
2022-04-09 17:02:17

我想拟合一个没有随机效应之间相关项的模型lmelmer这方面是相当直截了当的......

# lmer without correlation term
m1 <- lmer(distance ~ (1|Subject) + age + (0+age|Subject) + Sex, data = Orthodont)
VarCorr(m1)
# Groups    Name        Std.Dev.
# Subject   (Intercept) 1.474105
# Subject.1 age         0.099979
# Residual              1.402591

我想我可以使用lme以下规范删除相关项...

# lme without correlation term?
m2 <- lme(distance ~ age + Sex, data = Orthodont, random = list(~ 1 | Subject, ~-1+ age | Subject))
VarCorr(m2)
#             Variance            StdDev    
# Subject =   pdLogChol(1)                  
# (Intercept) 2.172946296         1.47409169
# Subject =   pdLogChol(-1 + age)           
# age         0.009996006         0.09998003
# Residual    1.967260819         1.40259075

我并不完全相信这些是相同的模型,部分原因是我找不到任何详细说明如何指定这种特定形式的资源,部分原因是输出print对我来说有点神秘......

m2 
# Linear mixed-effects model fit by REML
#   Data: Orthodont 
#   Log-restricted-likelihood: -218.3227
#   Fixed: distance ~ age + Sex 
# (Intercept)         age   SexFemale 
#  17.5806928   0.6601852  -2.0117005 
# 
# Random effects:
#  Formula: ~1 | Subject
#         (Intercept)
# StdDev:    1.474092
# 
#  Formula: ~-1 + age | Subject %in% Subject
#                age Residual
# StdDev: 0.09998003 1.402591
# 
# Number of Observations: 108
# Number of Groups: 
#                Subject Subject.1 %in% Subject 
#                     27                     27 

特别是Subject %in% Subject指的是什么?为什么残差被视为第二个随机效应项的一部分?

1个回答

虽然原则上您的方法有效,但这并不是使随机截距和斜率不相关的“标准”方法。您可以使用lmepdClasses(请参阅 参考资料help(pdClasses))为随机效应的方差-协方差矩阵提供特定结构。在这里,您要使该矩阵对角线。你可以这样做:

m3 <- lme(distance ~ age + Sex, data = Orthodont, random = list(Subject = pdDiag(~ age))
m3

Linear mixed-effects model fit by REML
  Data: Orthodont 
  Log-restricted-likelihood: -218.3227
  Fixed: distance ~ age + Sex 
(Intercept)         age   SexFemale 
 17.5806928   0.6601852  -2.0117005 

Random effects:
 Formula: ~age | Subject
 Structure: Diagonal
        (Intercept)        age Residual
StdDev:    1.474092 0.09998003 1.402591

Number of Observations: 108
Number of Groups: 27 

您会发现参数估计实际上与 model 相同m2,但结果的呈现更“合乎逻辑”。