R 线性混合 model 事后 lsmeans 问题的不等方差

Question

我将线性混合 model 拟合到农业数据中，通过将weights = varIdent(...)传递给lme来解释组（品种）之间的不相等差异。 lsmeans显示的标准误差与显着差异不一致。

我的代码示例如下。 重现 output 的数据可在此处找到。

library(nlme)
library(multcomp)
library(emmeans)

model <- lme(variable ~ cultivar*year, 
             random = ~1|block, 
             weights = varIdent(form = ~1|cultivar),  
             method = "REML", 
             na.action = na.omit, 
             data = ag.data)

Leastsquare <- lsmeans(model,"cultivar")
cld(Leastsquare, Letters = letters)

 cultivar  lsmean     SE df lower.CL upper.CL .group
 Golden      6.92  3.841  1    -41.9     55.7  a    
 Campfield  10.33  4.330  1    -44.7     65.4  a    
 Tom        17.50  0.167  1     15.4     19.6  a    
 Harrison   25.67 12.649  1   -135.1    186.4  ab   
 Puget      30.58 20.502  1   -229.9    291.1  ab   
 HVC        37.08  5.331  1    -30.7    104.8   b   
 COL        38.08  0.433  1     32.6     43.6   b   
 Brown      62.67 20.207  1   -194.1    319.4  ab   

品种Brown与Golden没有显着差异怎么可能？ 这可以接受吗？ 有没有人看到类似的结果？

Answer 1

我把你的例子变成了一个reprex 。 请在下面找到我的评论。

library(tidyverse)

ag.data <- tibble::tribble(
       ~year,   ~cultivar, ~block,   ~variable,
  "nineteen",       "HVC",     1L, 14.33333333,
  "nineteen",       "HVC",     2L, 23.33333333,
  "nineteen",     "Puget",     1L, 2.333333333,
  "nineteen",     "Puget",     2L, 3.333333333,
  "nineteen", "Campfield",     1L,          NA,
  "nineteen", "Campfield",     2L,           4,
  "nineteen",       "Tom",     1L,          10,
  "nineteen",       "Tom",     2L,          10,
  "nineteen",     "Brown",     1L,          NA,
  "nineteen",     "Brown",     2L, 56.66666667,
  "nineteen",       "COL",     1L,          NA,
  "nineteen",       "COL",     2L, 51.66666667,
  "nineteen",    "Golden",     1L,           5,
  "nineteen",    "Golden",     2L, 1.666666667,
  "nineteen",  "Harrison",     1L, 52.33333333,
  "nineteen",  "Harrison",     2L, 4.333333333,
    "twenty",       "HVC",     1L, 45.66666667,
    "twenty",       "HVC",     2L,          65,
    "twenty",     "Puget",     1L, 17.33333333,
    "twenty",     "Puget",     2L, 99.33333333,
    "twenty", "Campfield",     1L, 11.66666667,
    "twenty", "Campfield",     2L, 21.66666667,
    "twenty",       "Tom",     1L, 25.33333333,
    "twenty",       "Tom",     2L, 24.66666667,
    "twenty",     "Brown",     1L, 45.33333333,
    "twenty",     "Brown",     2L,          92,
    "twenty",       "COL",     1L,          24,
    "twenty",       "COL",     2L,          25,
    "twenty",    "Golden",     1L,           3,
    "twenty",    "Golden",     2L,          18,
    "twenty",  "Harrison",     1L,          31,
    "twenty",  "Harrison",     2L,          15
  )

library(nlme)
library(emmeans)
library(multcomp)
library(multcompView)

model <- lme(
  variable ~ cultivar * year,
  random = ~ 1 | block,
  weights = varIdent(form = ~ 1 | cultivar),
  method = "REML",
  na.action = na.omit,
  data = ag.data
)

anova(model)
#>               numDF denDF   F-value p-value
#> (Intercept)       1    12 16502.874  <.0001
#> cultivar          7    12   193.823  <.0001
#> year              1    12   952.713  <.0001
#> cultivar:year     7    12   296.145  <.0001

ag.data %>%
  filter(!is.na(variable)) %>%
  ggplot(aes(y = variable, x = year)) +
  facet_wrap(vars(cultivar)) +
  geom_point() +
  stat_summary(fun = mean,
               color = "red",
               geom = "line",
               aes(group = 1)) +
  theme_bw()

emm <- emmeans(model, ~ cultivar) %>% 
  cld(Letters = letters) %>% 
  as_tibble() %>% 
  mutate(cultivar = fct_reorder(cultivar, emmean))
#> NOTE: Results may be misleading due to involvement in interactions

ggplot(emm, aes(
  y = emmean,
  ymin = lower.CL,
  ymax = upper.CL,
  x = cultivar,
  label = str_trim(.group)
)) +
  geom_point() +
  geom_errorbar(width = 0.1) +
  geom_text(
    position = position_nudge(x = 0.1),
    hjust = 0,
    color = "red"
  ) +
  theme_bw()

^{由代表 package (v2.0.1) 于 2022 年 1 月 24 日创建}

解决您的问题为什么具有最低和最高 emmeans 的品种没有显着差异：我认为查看第二个 plot 可以清楚地表明，这是由于估计 emmeans 的精度差异很大。 这又部分是由于您在 model 中允许的异质误差差异，以及由于丢失/不平衡的数据。 我会争辩说，您“不习惯看到当中间值存在时，极值彼此之间没有统计学差异”，因为通常使用平衡数据和/或没有异质误差方差时，您不会。 尝试在没有weights =参数的情况下运行代码（即使用标准同质误差方差） - 您将找不到这些结果所遇到的“问题”。

进一步注意，您实际上似乎有栽培品种-年份-见 anova anova()和第一个 plot。 因此，查看栽培品种的平均值可能会产生误导，因为emmeans() function 下方的注释说。 相反，您可以尝试通过emmeans(~ cultivar|year)每年调查 emmean-comparisons。