具有重复测量的方差分析和 R 中的 TukeyHSD 事后检验

Question

我想对重复测量方差分析进行 Tukey HSD 事后测试。 输入的公式“TukeyHSD”返回错误。 我无法在论坛中找到答案。 我可以寻求帮助吗？

“treat”是重复测量因子，“vo2”是因变量。

以下是产生此错误的脚本：

my_data <- data.frame(
  stringsAsFactors = FALSE,
  id = c(1L,2L,3L,4L, 5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L),
  treat = c("o","o","o","o","o","j","j","j","j","j","z","z","z","z","z","w","w","w","w","w"),
  vo2 = c("47.48","42.74","45.23","51.65","49.11","51.00","43.82","49.88","54.61","52.20","51.31",
          "47.56","50.69","54.88","55.01","51.89","46.10","50.98","53.62","52.77"))

summary(rm_result <- aov(vo2~factor(treat)+Error(factor(id)), data = my_data))
TukeyHSD(rm_result, "treat", ordered = TRUE)

Answer 1

TukeyHSD()无法处理重复测量方差分析的aovlist结果。 作为替代方案，您可以使用例如lme4::lmer()拟合等效的混合效应模型，并使用multcomp::glht()进行事后测试。

my_data$vo2 <- as.numeric(my_data$vo2)
my_data$treat <- factor(my_data$treat)
m <- lme4::lmer(vo2 ~ treat + (1|id), data = my_data)
summary(multcomp::glht(m, linfct=mcp(treat="Tukey")))

# Simultaneous Tests for General Linear Hypotheses
# 
# Multiple Comparisons of Means: Tukey Contrasts
# 
# 
# Fit: lmer(formula = vo2 ~ treat + (1 | id), data = my_data)
# 
# Linear Hypotheses:
#            Estimate Std. Error z value Pr(>|z|)    
# o - j == 0   -3.060      0.583  -5.248   <0.001 ***
# w - j == 0    0.770      0.583   1.321   0.5497    
# z - j == 0    1.588      0.583   2.724   0.0327 *  
# w - o == 0    3.830      0.583   6.569   <0.001 ***
# z - o == 0    4.648      0.583   7.972   <0.001 ***
# z - w == 0    0.818      0.583   1.403   0.4974    
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# (Adjusted p values reported -- single-step method)

将混合效应模型的方差分析表与您的重复测量方差分析结果进行比较表明，这两种方法在处理treat变量方面是等效的：

anova(m)
# Analysis of Variance Table
#       npar Sum Sq Mean Sq F value
# treat    3 61.775  20.592   24.23

summary(rm_result)
# Error: factor(id)
#           Df Sum Sq Mean Sq F value Pr(>F)
# Residuals  4  175.9   43.98               
# 
# Error: Within
#               Df Sum Sq Mean Sq F value   Pr(>F)    
# factor(treat)  3  61.78   20.59   24.23 2.22e-05 ***
# Residuals     12  10.20    0.85                     
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Answer 2

或者，您也可以按照下面的 reprex 进行操作。 请注意， cld()部分是可选的，它只是尝试通过“紧凑型字母显示”（ 此处有详细信息）来总结结果

# data --------------------------------------------------------------------
my_data <- data.frame(
  stringsAsFactors = FALSE,
  id = c(1L,2L,3L,4L, 5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L),
  treat = c("o","o","o","o","o","j","j","j","j","j","z","z","z","z","z","w","w","w","w","w"),
  vo2 = c("47.48","42.74","45.23","51.65","49.11","51.00","43.82","49.88","54.61","52.20","51.31",
          "47.56","50.69","54.88","55.01","51.89","46.10","50.98","53.62","52.77"))

my_data$vo2 <- as.numeric(my_data$vo2)
my_data$treat <- factor(my_data$treat)


# model -------------------------------------------------------------------
m <- lme4::lmer(vo2 ~ treat + (1|id), data = my_data)


# emmeans -----------------------------------------------------------------
library(emmeans)
emmeans <- emmeans(m, specs = "treat")
pairs(emmeans, adjust = "Tukey")
#>  contrast estimate    SE df t.ratio p.value
#>  j - o       3.060 0.583 12   5.248  0.0010
#>  j - w      -0.770 0.583 12  -1.321  0.5681
#>  j - z      -1.588 0.583 12  -2.724  0.0761
#>  o - w      -3.830 0.583 12  -6.569  0.0001
#>  o - z      -4.648 0.583 12  -7.972  <.0001
#>  w - z      -0.818 0.583 12  -1.403  0.5209
#> 
#> Degrees-of-freedom method: kenward-roger 
#> P value adjustment: tukey method for comparing a family of 4 estimates


# multcomp ----------------------------------------------------------------
library(multcomp)
library(multcompView)
cld(emmeans, Letters = letters)
#>  treat emmean   SE   df lower.CL upper.CL .group
#>  o       47.2 1.53 4.47     43.2     51.3  a    
#>  j       50.3 1.53 4.47     46.2     54.4   b   
#>  w       51.1 1.53 4.47     47.0     55.1   b   
#>  z       51.9 1.53 4.47     47.8     56.0   b   
#> 
#> Degrees-of-freedom method: kenward-roger 
#> Confidence level used: 0.95 
#> P value adjustment: tukey method for comparing a family of 4 estimates 
#> significance level used: alpha = 0.05 
#> NOTE: If two or more means share the same grouping symbol,
#>       then we cannot show them to be different.
#>       But we also did not show them to be the same.

^{创建于 2022-12-20，使用reprex v2.0.2}