lmer线性对比: Kenward Rogers或Satterthwaite DF和SE

Question

在R中，我正在寻找一种方法来估计使用kenward-rogers或satterthwaite自由度和SE的lmer模型线性对比的置信区间。

例如，我可以使用t值(使用来自KR的df )和SE为混合模型中的固定效应参数计算CI，比如SAS和R。

mod<-lmerTest::lmer(y~time1+treatment+time1:treatment+(1|PersonID),data=data)
lmerTest::summary(mod,ddf = "Kenward-Roger")

这一产出：

Fixed effects:
                Estimate Std. Error      df t value Pr(>|t|)    
(Intercept)      49.0768     1.0435 56.4700  47.029  < 2e-16 ***
time1             5.8224     0.5963 48.0000   9.764 5.51e-13 ***
treatment         1.6819     1.4758 56.4700   1.140   0.2592    
time1:treatment   2.0425     0.8433 48.0000   2.422   0.0193 * 

允许用于time1的CI，如：

5.8224+abs(qt(0.05/2, 48))*0.5963 #7.021342
5.8224-abs(qt(0.05/2, 48))*0.5963 #4.623458

对于固定系数的线性对比，我想做同样的事情。这是p值，但没有SE输出.

pbkrtest::KRmodcomp(mod,matrix(c(0,0,1,0),nrow = 1)) 

         stat     ndf     ddf F.scaling p.value
Ftest  1.2989  1.0000 56.4670         1  0.2592

是否可以从使用这种df?的线性对比中获得SE或CI？

Answer 1

为此，您至少有两个选项:使用lsmeans包，或者手动执行它(使用函数vcovAdj.lmerMod和pbkrtest::get_Lb_ddf)。就我个人而言，如果要测试的对比不是很“简单”的话，我会选择后者，因为我发现lsmeans中的语法有点复杂。

为了举例说明，请采用以下模型：

library(pbkrtest)
library(lme4)
library(nlme) # for the 'Orthodont' data

# 'age' is a numeric variable, while 'Sex' and 'Subject' are factors
model <- lmer(distance ~ age : Sex + (1 | Subject), data = Orthodont)

Linear mixed model fit by REML ['lmerMod']
Formula: distance ~ age:Sex + (1 | Subject)
…
Fixed Effects:
    (Intercept)    age:SexMale  age:SexFemale  
        16.7611         0.7555         0.5215 

从这些数据中，我们可以得到关于男性和女性年龄系数差异的统计数据(即age:SexMale - age:SexFemale)。

使用lsmeans意味着：

library(lsmeans)
# Evaluate the contrast at a value of 'age' set to 1,
# so that the resulting value is equal to the regression coefficient
lsm = lsmeans(model, pairwise ~ age : Sex, at = list(age = 1))$contrast

生产：

contrast           estimate         SE    df t.ratio p.value
1,Male - 1,Female 0.2340135 0.06113276 42.64   3.828  0.0004

或者，手动计算：

# Specify the contrasts: age:SexMale - age:SexFemale
# Must have the same order as the fixed effects in the model
K = c("(Intercept)" = 0, "age:SexMale" = 1, "age:SexFemale" = -1)

# Retrieve the adjusted variance-covariance matrix, to calculate the SE
V = pbkrtest::vcovAdj.lmerMod(model, 0)

# Point estimate, SE and df
point_est = sum(K * fixef(model))
SE = sqrt(sum(K * (V %*% K)))
df = pbkrtest::get_Lb_ddf(model, K)

alpha = 0.05 # significance level

# Calculate confidence interval for the difference between the 'age' coefficients for males and females
Delta_age_CI = point_est + SE * qt(c(0.5 * alpha, 1 - 0.5 * alpha), df)

将得到一个点估计值，等于0.2340135、SE 0.06113276、df 42.63844和置信区间[0.1106973, 0.3573297]。